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Error: #f88
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.popup {background:[[ColorPalette::TertiaryPale]]; color:[[ColorPalette::TertiaryDark]]; border-left:1px solid [[ColorPalette::TertiaryMid]]; border-top:1px solid [[ColorPalette::TertiaryMid]]; border-right:2px solid [[ColorPalette::TertiaryDark]]; border-bottom:2px solid [[ColorPalette::TertiaryDark]];}
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.title {color:[[ColorPalette::SecondaryDark]];}
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.footer {color:[[ColorPalette::TertiaryLight]];}
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.viewer .listTitle {list-style-type:none; margin-left:-2em;}
.viewer .button {border:1px solid [[ColorPalette::SecondaryMid]];}
.viewer blockquote {border-left:3px solid [[ColorPalette::TertiaryDark]];}

.viewer table, table.twtable {border:2px solid [[ColorPalette::TertiaryDark]];}
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.viewer td, .viewer tr, .twtable td, .twtable tr {border:1px solid [[ColorPalette::TertiaryDark]];}

.viewer pre {border:1px solid [[ColorPalette::SecondaryLight]]; background:[[ColorPalette::SecondaryPale]];}
.viewer code {color:[[ColorPalette::SecondaryDark]];}
.viewer hr {border:0; border-top:dashed 1px [[ColorPalette::TertiaryDark]]; color:[[ColorPalette::TertiaryDark]];}

.highlight, .marked {background:[[ColorPalette::SecondaryLight]];}

.editor input {border:1px solid [[ColorPalette::PrimaryMid]];}
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#backstageArea a {background:[[ColorPalette::Foreground]]; color:[[ColorPalette::Background]]; border:none;}
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body {font-size:.75em; font-family:arial,helvetica; margin:0; padding:0;}

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h1,h2,h3 {padding-bottom:1px; margin-top:1.2em;margin-bottom:0.3em;}
h4,h5,h6 {margin-top:1em;}
h1 {font-size:1.35em;}
h2 {font-size:1.25em;}
h3 {font-size:1.1em;}
h4 {font-size:1em;}
h5 {font-size:.9em;}

hr {height:1px;}

a {text-decoration:none;}

dt {font-weight:bold;}

ol {list-style-type:decimal;}
ol ol {list-style-type:lower-alpha;}
ol ol ol {list-style-type:lower-roman;}
ol ol ol ol {list-style-type:decimal;}
ol ol ol ol ol {list-style-type:lower-alpha;}
ol ol ol ol ol ol {list-style-type:lower-roman;}
ol ol ol ol ol ol ol {list-style-type:decimal;}

.txtOptionInput {width:11em;}

#contentWrapper .chkOptionInput {border:0;}

.externalLink {text-decoration:underline;}

.indent {margin-left:3em;}
.outdent {margin-left:3em; text-indent:-3em;}
code.escaped {white-space:nowrap;}

.tiddlyLinkExisting {font-weight:bold;}
.tiddlyLinkNonExisting {font-style:italic;}

/* the 'a' is required for IE, otherwise it renders the whole tiddler in bold */
a.tiddlyLinkNonExisting.shadow {font-weight:bold;}

#mainMenu .tiddlyLinkExisting,
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	#sidebarTabs .tiddlyLinkNonExisting {font-weight:normal; font-style:normal;}
#sidebarTabs .tiddlyLinkExisting {font-weight:bold; font-style:normal;}

.header {position:relative;}
.header a:hover {background:transparent;}
.headerShadow {position:relative; padding:4.5em 0 1em 1em; left:-1px; top:-1px;}
.headerForeground {position:absolute; padding:4.5em 0 1em 1em; left:0px; top:0px;}

.siteTitle {font-size:3em;}
.siteSubtitle {font-size:1.2em;}

#mainMenu {position:absolute; left:0; width:10em; text-align:right; line-height:1.6em; padding:1.5em 0.5em 0.5em 0.5em; font-size:1.1em;}

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#sidebarOptions {padding-top:0.3em;}
#sidebarOptions a {margin:0 0.2em; padding:0.2em 0.3em; display:block;}
#sidebarOptions input {margin:0.4em 0.5em;}
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#sidebarOptions .sliderPanel input {margin:0 0 0.3em 0;}
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.wizard h1 {font-size:2em; font-weight:bold; background:none; padding:0; margin:0.4em 0 0.2em;}
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.wizard .button {padding:0.1em 0.2em;}

#messageArea {position:fixed; top:2em; right:0; margin:0.5em; padding:0.5em; z-index:2000; _position:absolute;}
.messageToolbar {display:block; text-align:right; padding:0.2em;}
#messageArea a {text-decoration:underline;}

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.popup .popupMessage {padding:0.4em;}
.popup hr {display:block; height:1px; width:auto; padding:0; margin:0.2em 0;}
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.listBreak {font-size:1px; line-height:1px;}
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.tagClear {clear:both;}

.footer {font-size:.9em;}
.footer li {display:inline;}

.annotation {padding:0.5em; margin:0.5em;}

* html .viewer pre {width:99%; padding:0 0 1em 0;}
.viewer {line-height:1.4em; padding-top:0.5em;}
.viewer .button {margin:0 0.25em; padding:0 0.25em;}
.viewer blockquote {line-height:1.5em; padding-left:0.8em;margin-left:2.5em;}
.viewer ul, .viewer ol {margin-left:0.5em; padding-left:1.5em;}

.viewer table, table.twtable {border-collapse:collapse; margin:0.8em 1.0em;}
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table.listView {font-size:0.85em; margin:0.8em 1.0em;}
table.listView th, table.listView td, table.listView tr {padding:0px 3px 0px 3px;}

.viewer pre {padding:0.5em; margin-left:0.5em; font-size:1.2em; line-height:1.4em; overflow:auto;}
.viewer code {font-size:1.2em; line-height:1.4em;}

.editor {font-size:1.1em;}
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.editorFooter {padding:0.25em 0; font-size:.9em;}
.editorFooter .button {padding-top:0px; padding-bottom:0px;}

.fieldsetFix {border:0; padding:0; margin:1px 0px;}

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.zoomer {font-size:1.1em; position:absolute; overflow:hidden;}
.zoomer div {padding:1em;}

* html #backstage {width:99%;}
* html #backstageArea {width:99%;}
#backstageArea {display:none; position:relative; overflow: hidden; z-index:150; padding:0.3em 0.5em;}
#backstageToolbar {position:relative;}
#backstageArea a {font-weight:bold; margin-left:0.5em; padding:0.3em 0.5em;}
#backstageButton {display:none; position:absolute; z-index:175; top:0; right:0;}
#backstageButton a {padding:0.1em 0.4em; margin:0.1em;}
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#backstagePanel {display:none; z-index:100; position:absolute; width:90%; margin-left:3em; padding:1em;}
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.backstagePanelFooter a {padding:0.2em 0.4em;}
#backstageCloak {display:none; z-index:20; position:absolute; width:100%; height:100px;}

.whenBackstage {display:none;}
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/*}}}*/
/***
StyleSheet for use when a translation requires any css style changes.
This StyleSheet can be used directly by languages such as Chinese, Japanese and Korean which need larger font sizes.
***/
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body {font-size:0.8em;}
#sidebarOptions {font-size:1.05em;}
#sidebarOptions a {font-style:normal;}
#sidebarOptions .sliderPanel {font-size:0.95em;}
.subtitle {font-size:0.8em;}
.viewer table.listView {font-size:0.95em;}
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/*{{{*/
@media print {
#mainMenu, #sidebar, #messageArea, .toolbar, #backstageButton, #backstageArea {display: none !important;}
#displayArea {margin: 1em 1em 0em;}
noscript {display:none;} /* Fixes a feature in Firefox 1.5.0.2 where print preview displays the noscript content */
}
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<!--{{{-->
<div class='header' macro='gradient vert [[ColorPalette::PrimaryLight]] [[ColorPalette::PrimaryMid]]'>
<div class='headerShadow'>
<span class='siteTitle' refresh='content' tiddler='SiteTitle'></span>&nbsp;
<span class='siteSubtitle' refresh='content' tiddler='SiteSubtitle'></span>
</div>
<div class='headerForeground'>
<span class='siteTitle' refresh='content' tiddler='SiteTitle'></span>&nbsp;
<span class='siteSubtitle' refresh='content' tiddler='SiteSubtitle'></span>
</div>
</div>
<div id='mainMenu' refresh='content' tiddler='MainMenu'></div>
<div id='sidebar'>
<div id='sidebarOptions' refresh='content' tiddler='SideBarOptions'></div>
<div id='sidebarTabs' refresh='content' force='true' tiddler='SideBarTabs'></div>
</div>
<div id='displayArea'>
<div id='messageArea'></div>
<div id='tiddlerDisplay'></div>
</div>
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<!--{{{-->
<div class='toolbar' macro='toolbar [[ToolbarCommands::ViewToolbar]]'></div>
<div class='title' macro='view title'></div>
<div class='subtitle'><span macro='view modifier link'></span>, <span macro='view modified date'></span> (<span macro='message views.wikified.createdPrompt'></span> <span macro='view created date'></span>)</div>
<div class='tagging' macro='tagging'></div>
<div class='tagged' macro='tags'></div>
<div class='viewer' macro='view text wikified'></div>
<div class='tagClear'></div>
<!--}}}-->
<!--{{{-->
<div class='toolbar' macro='toolbar [[ToolbarCommands::EditToolbar]]'></div>
<div class='title' macro='view title'></div>
<div class='editor' macro='edit title'></div>
<div macro='annotations'></div>
<div class='editor' macro='edit text'></div>
<div class='editor' macro='edit tags'></div><div class='editorFooter'><span macro='message views.editor.tagPrompt'></span><span macro='tagChooser excludeLists'></span></div>
<!--}}}-->
To get started with this blank [[TiddlyWiki]], you'll need to modify the following tiddlers:
* [[SiteTitle]] & [[SiteSubtitle]]: The title and subtitle of the site, as shown above (after saving, they will also appear in the browser title bar)
* [[MainMenu]]: The menu (usually on the left)
* [[DefaultTiddlers]]: Contains the names of the tiddlers that you want to appear when the TiddlyWiki is opened
You'll also need to enter your username for signing your edits: <<option txtUserName>>
These [[InterfaceOptions]] for customising [[TiddlyWiki]] are saved in your browser

Your username for signing your edits. Write it as a [[WikiWord]] (eg [[JoeBloggs]])

<<option txtUserName>>
<<option chkSaveBackups>> [[SaveBackups]]
<<option chkAutoSave>> [[AutoSave]]
<<option chkRegExpSearch>> [[RegExpSearch]]
<<option chkCaseSensitiveSearch>> [[CaseSensitiveSearch]]
<<option chkAnimate>> [[EnableAnimations]]

----
Also see [[AdvancedOptions]]
<<importTiddlers>>
!!!----
!!!
Date of MSC TiddlyWiki creation: 20091214164937
!!![[00|00-XX]]Axx  General and miscellaneous specific topics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/00Axx.html]]}{{moveright{< [[MSC |MSC2010]] | [[00-XX |00-XX]] | [[00Bxx |00Bxx]] >}}}
* ''00A05'' General mathematics
* ''00A06'' Mathematics for nonmathematicians (engineering, social sciences, etc.)
* ''00A07'' Problem books
* ''00A08'' Recreational mathematics [See also [[97A20|97Axx]]]
* ''00A09'' Popularization of mathematics
* ''00A15'' Bibliographies
* ''00A17'' External book reviews
* ''00A20'' Dictionaries and other general reference works
* ''00A22'' Formularies
* ''00A30'' Philosophy of mathematics [See also [[03A05|03Axx]]]
* ''00A35'' Methodology of mathematics, didactics [See also [[97Cxx|97Cxx]], [[97Dxx|97Dxx]]]
* ''00A65'' Mathematics and music
* ''00A66'' Mathematics and visual arts, visualization
* ''00A67'' Mathematics and architecture
* ''00A69'' General applied mathematics {For physics, see [[00A79|00Axx]] and Sections 70 through 86}
* ''00A71'' Theory of mathematical modeling
* ''00A72'' General methods of simulation
* ''00A73'' Dimensional analysis
* ''00A79'' Physics (use more specific entries from Sections 70 through 86 when possible)
* ''00A99'' Miscellaneous topics
!!!00-XX General {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/00-XX.html]]}{{moveright{< [[MSC |MSC2010]] | [[00-XX |00-XX]] | [[00Axx |00Axx]] >}}}
* ''00-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''00-02'' Research exposition (monographs, survey articles)
* ''[[00Axx|00Axx]]''  General and miscellaneous specific topics
* ''[[00Bxx|00Bxx]]''  Conference proceedings and collections of papers
!!![[00|00-XX]]Bxx  Conference proceedings and collections of papers {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/00Bxx.html]]}{{moveright{< [[00Axx |00Axx]] | [[00-XX |00-XX]] | [[01-XX |01-XX]] >}}}
* ''00B05'' Collections of abstracts of lectures
* ''00B10'' Collections of articles of general interest
* ''00B15'' Collections of articles of miscellaneous specific content
* ''00B20'' Proceedings of conferences of general interest
* ''00B25'' Proceedings of conferences of miscellaneous specific interest
* ''00B30'' Festschriften
* ''00B50'' Volumes of selected translations
* ''00B55'' Miscellaneous volumes of translations
* ''00B60'' Collections of reprinted articles [See also [[01A75|01Axx]]]
* ''00B99'' None of the above, but in this section
!!!01-XX History and biography [See also the classification number–03 in the other sections] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/01-XX.html]]}{{moveright{< [[00-XX |00-XX]] | [[MSC |MSC2010]] | [[01Axx |01Axx]] >}}}
* ''01-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''01-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''01-02'' Research exposition (monographs, survey articles)
* ''01-06'' Proceedings, conferences, collections, etc.
* ''01-08'' Computational methods
* ''[[01Axx|01Axx]]''  History of mathematics and mathematicians
!!![[01|01-XX]]Axx  History of mathematics and mathematicians {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/01Axx.html]]}{{moveright{< [[00-XX |00-XX]] | [[01-XX |01-XX]] | [[03-XX |03-XX]] >}}}
* ''01A05'' General histories, source books
* ''01A07'' Ethnomathematics, general
* ''01A10'' Paleolithic, Neolithic
* ''01A12'' Indigenous cultures of the Americas
* ''01A13'' Other indigenous cultures (non-European)
* ''01A15'' Indigenous European cultures (pre-Greek, etc.)
* ''01A16'' Egyptian
* ''01A17'' Babylonian
* ''01A20'' Greek, Roman
* ''01A25'' China
* ''01A27'' Japan
* ''01A29'' Southeast Asia
* ''01A30'' Islam (Medieval)
* ''01A32'' India
* ''01A35'' Medieval
* ''01A40'' 15th and 16th centuries, Renaissance
* ''01A45'' 17th century
* ''01A50'' 18th century
* ''01A55'' 19th century
* ''01A60'' 20th century
* ''01A61'' Twenty-first century
* ''01A65'' Contemporary
* ''01A67'' Future prospectives
* ''01A70'' Biographies, obituaries, personalia, bibliographies
* ''01A72'' Schools of mathematics
* ''01A73'' Universities
* ''01A74'' Other institutions and academies
* ''01A75'' Collected or selected works; reprintings or translations of classics [See also [[00B60|00Bxx]]]
* ''01A80'' Sociology (and profession) of mathematics
* ''01A85'' Historiography
* ''01A90'' Bibliographic studies
* ''01A99'' Miscellaneous topics
!!![[03|03-XX]]Axx  Philosophical aspects of logic and foundations {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/03Axx.html]]}{{moveright{< [[01-XX |01-XX]] | [[03-XX |03-XX]] | [[03Bxx |03Bxx]] >}}}
* ''03A05'' Philosophical and critical {For philosophy of mathematics, see also [[00A30|00Axx]]}
* ''03A10'' Logic in the philosophy of science
* ''03A99'' None of the above, but in this section
!!![[03|03-XX]]Bxx  General logic {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/03Bxx.html]]}{{moveright{< [[03Axx |03Axx]] | [[03-XX |03-XX]] | [[03Cxx |03Cxx]] >}}}
* ''03B05'' Classical propositional logic
* ''03B10'' Classical first-order logic
* ''03B15'' Higher-order logic and type theory
* ''03B20'' Subsystems of classical logic (including intuitionistic logic)
* ''03B22'' Abstract deductive systems
* ''03B25'' Decidability of theories and sets of sentences [See also [[11U05|11Uxx]], [[12L05|12Lxx]], [[20F10|20Fxx]]]
* ''03B30'' Foundations of classical theories (including reverse mathematics) [See also [[03F35|03Fxx]]]
* ''03B35'' Mechanization of proofs and logical operations [See also [[68T15|68Txx]]]
* ''03B40'' Combinatory logic and lambda-calculus [See also [[68N18|68Nxx]]]
* ''03B42'' Logics of knowledge and belief (including belief change)
* ''03B44'' Temporal logic
* ''03B45'' Modal logic (including the logic of norms) {For knowledge and belief, see [[03B42|03Bxx]]; for temporal logic, see [[03B44|03Bxx]]; for provability logic, see also [[03F45|03Fxx]]}
* ''03B47'' Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see [[03F52|03Fxx]]}
* ''03B48'' Probability and inductive logic [See also [[60A05|60Axx]]]
* ''03B50'' Many-valued logic
* ''03B52'' Fuzzy logic; logic of vagueness [See also [[68T27|68Txx]], [[68T37|68Txx]], [[94D05|94Dxx]]]
* ''03B53'' Paraconsistent logics
* ''03B55'' Intermediate logics
* ''03B60'' Other nonclassical logic
* ''03B62'' Combined logics
* ''03B65'' Logic of natural languages [See also [[68T50|68Txx]], [[91F20|91Fxx]]]
* ''03B70'' Logic in computer science [See also [[68-XX|68-XX]]]
* ''03B80'' Other applications of logic
* ''03B99'' None of the above, but in this section
!!![[03|03-XX]]Cxx  Model theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/03Cxx.html]]}{{moveright{< [[03Bxx |03Bxx]] | [[03-XX |03-XX]] | [[03Dxx |03Dxx]] >}}}
* ''03C05'' Equational classes, universal algebra [See also [[08Axx|08Axx]], [[08Bxx|08Bxx]], [[18C05|18Cxx]]]
* ''03C07'' Basic properties of first-order languages and structures
* ''03C10'' Quantifier elimination, model completeness and related topics
* ''03C13'' Finite structures [See also [[68Q15|68Qxx]], [[68Q19|68Qxx]]]
* ''03C15'' Denumerable structures
* ''03C20'' Ultraproducts and related constructions
* ''03C25'' Model-theoretic forcing
* ''03C30'' Other model constructions
* ''03C35'' Categoricity and completeness of theories
* ''03C40'' Interpolation, preservation, definability
* ''03C45'' Classification theory, stability and related concepts [See also [[03C48|03Cxx]]]
* ''03C48'' Abstract elementary classes and related topics [See also [[03C45|03Cxx]]]
* ''03C50'' Models with special properties (saturated, rigid, etc.)
* ''03C52'' Properties of classes of models
* ''03C55'' Set-theoretic model theory
* ''03C57'' Effective and recursion-theoretic model theory [See also [[03D45|03Dxx]]]
* ''03C60'' Model-theoretic algebra [See also [[08C10|08Cxx]], [[12Lxx|12Lxx]], [[13L05|13Lxx]]]
* ''03C62'' Models of arithmetic and set theory [See also [[03Hxx|03Hxx]]]
* ''03C64'' Model theory of ordered structures; o-minimality
* ''03C65'' Models of other mathematical theories
* ''03C68'' Other classical first-order model theory
* ''03C70'' Logic on admissible sets
* ''03C75'' Other infinitary logic
* ''03C80'' Logic with extra quantifiers and operators [See also [[03B42|03Bxx]], [[03B44|03Bxx]], [[03B45|03Bxx]], [[03B48|03Bxx]]]
* ''03C85'' Second- and higher-order model theory
* ''03C90'' Nonclassical models (Boolean-valued, sheaf, etc.)
* ''03C95'' Abstract model theory
* ''03C98'' Applications of model theory [See also [[03C60|03Cxx]]]
* ''03C99'' None of the above, but in this section
!!![[03|03-XX]]Dxx  Computability and recursion theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/03Dxx.html]]}{{moveright{< [[03Cxx |03Cxx]] | [[03-XX |03-XX]] | [[03Exx |03Exx]] >}}}
* ''03D03'' Thue and Post systems, etc.
* ''03D05'' Automata and formal grammars in connection with logical questions [See also [[68Q45|68Qxx]], [[68Q70|68Qxx]], [[68R15|68Rxx]]]
* ''03D10'' Turing machines and related notions [See also [[68Q05|68Qxx]]]
* ''03D15'' Complexity of computation (including implicit computational complexity) [See also [[68Q15|68Qxx]], [[68Q17|68Qxx]]]
* ''03D20'' Recursive functions and relations, subrecursive hierarchies
* ''03D25'' Recursively (computably) enumerable sets and degrees
* ''03D28'' Other Turing degree structures
* ''03D30'' Other degrees and reducibilities
* ''03D32'' Algorithmic randomness and dimension [See also [[68Q30|68Qxx]]]
* ''03D35'' Undecidability and degrees of sets of sentences
* ''03D40'' Word problems, etc. [See also [[06B25|06Bxx]], [[08A50|08Axx]], [[20F10|20Fxx]], [[68R15|68Rxx]]]
* ''03D45'' Theory of numerations, effectively presented structures [See also [[03C57|03Cxx]]; for intuitionistic and similar approaches see [[03F55|03Fxx]]]
* ''03D50'' Recursive equivalence types of sets and structures, isols
* ''03D55'' Hierarchies
* ''03D60'' Computability and recursion theory on ordinals, admissible sets, etc.
* ''03D65'' Higher-type and set recursion theory
* ''03D70'' Inductive definability
* ''03D75'' Abstract and axiomatic computability and recursion theory
* ''03D78'' Computation over the reals {For constructive aspects, see [[03F60|03Fxx]]}
* ''03D80'' Applications of computability and recursion theory
* ''03D99'' None of the above, but in this section
!!![[03|03-XX]]Exx  Set theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/03Exx.html]]}{{moveright{< [[03Dxx |03Dxx]] | [[03-XX |03-XX]] | [[03Fxx |03Fxx]] >}}}
* ''03E02'' Partition relations
* ''03E04'' Ordered sets and their cofinalities; pcf theory
* ''03E05'' Other combinatorial set theory
* ''03E10'' Ordinal and cardinal numbers
* ''03E15'' Descriptive set theory [See also [[28A05|28Axx]], [[54H05|54Hxx]]]
* ''03E17'' Cardinal characteristics of the continuum
* ''03E20'' Other classical set theory (including functions, relations, and set algebra)
* ''03E25'' Axiom of choice and related propositions
* ''03E30'' Axiomatics of classical set theory and its fragments
* ''03E35'' Consistency and independence results
* ''03E40'' Other aspects of forcing and Boolean-valued models
* ''03E45'' Inner models, including constructibility, ordinal definability, and core models
* ''03E47'' Other notions of set-theoretic definability
* ''03E50'' Continuum hypothesis and Martin's axiom [See also [[03E57|03Exx]]]
* ''03E55'' Large cardinals
* ''03E57'' Generic absoluteness and forcing axioms [See also [[03E50|03Exx]]]
* ''03E60'' Determinacy principles
* ''03E65'' Other hypotheses and axioms
* ''03E70'' Nonclassical and second-order set theories
* ''03E72'' Fuzzy set theory
* ''03E75'' Applications of set theory
* ''03E99'' None of the above, but in this section
!!![[03|03-XX]]Fxx  Proof theory and constructive mathematics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/03Fxx.html]]}{{moveright{< [[03Exx |03Exx]] | [[03-XX |03-XX]] | [[03Gxx |03Gxx]] >}}}
* ''03F03'' Proof theory, general
* ''03F05'' Cut-elimination and normal-form theorems
* ''03F07'' Structure of proofs
* ''03F10'' Functionals in proof theory
* ''03F15'' Recursive ordinals and ordinal notations
* ''03F20'' Complexity of proofs
* ''03F25'' Relative consistency and interpretations
* ''03F30'' First-order arithmetic and fragments
* ''03F35'' Second- and higher-order arithmetic and fragments [See also [[03B30|03Bxx]]]
* ''03F40'' Gödel numberings and issues of incompleteness
* ''03F45'' Provability logics and related algebras (e.g., diagonalizable algebras) [See also [[03B45|03Bxx]], [[03G25|03Gxx]], [[06E25|06Exx]]]
* ''03F50'' Metamathematics of constructive systems
* ''03F52'' Linear logic and other substructural logics [See also [[03B47|03Bxx]]]
* ''03F55'' Intuitionistic mathematics
* ''03F60'' Constructive and recursive analysis [See also [[03B30|03Bxx]], [[03D45|03Dxx]], [[03D78|03Dxx]], [[26E40|26Exx]], [[46S30|46Sxx]], [[47S30|47Sxx]]]
* ''03F65'' Other constructive mathematics [See also [[03D45|03Dxx]]]
* ''03F99'' None of the above, but in this section
!!![[03|03-XX]]Gxx  Algebraic logic {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/03Gxx.html]]}{{moveright{< [[03Fxx |03Fxx]] | [[03-XX |03-XX]] | [[03Hxx |03Hxx]] >}}}
* ''03G05'' Boolean algebras [See also [[06Exx|06Exx]]]
* ''03G10'' Lattices and related structures [See also [[06Bxx|06Bxx]]]
* ''03G12'' Quantum logic [See also [[06C15|06Cxx]], [[81P10|81Pxx]]]
* ''03G15'' Cylindric and polyadic algebras; relation algebras
* ''03G20'' Łukasiewicz and Post algebras [See also [[06D25|06Dxx]], [[06D30|06Dxx]]]
* ''03G25'' Other algebras related to logic [See also [[03F45|03Fxx]], [[06D20|06Dxx]], [[06E25|06Exx]], [[06F35|06Fxx]]]
* ''03G27'' Abstract algebraic logic
* ''03G30'' Categorical logic, topoi [See also [[18B25|18Bxx]], [[18C05|18Cxx]], [[18C10|18Cxx]]]
* ''03G99'' None of the above, but in this section
!!!03-XX Mathematical logic and foundations {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/03-XX.html]]}{{moveright{< [[01-XX |01-XX]] | [[MSC |MSC2010]] | [[03Axx |03Axx]] >}}}
* ''03-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''03-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''03-02'' Research exposition (monographs, survey articles)
* ''03-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''03-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''03-06'' Proceedings, conferences, collections, etc.
* ''[[03Axx|03Axx]]''  Philosophical aspects of logic and foundations
* ''[[03Bxx|03Bxx]]''  General logic
* ''[[03Cxx|03Cxx]]''  Model theory
* ''[[03Dxx|03Dxx]]''  Computability and recursion theory
* ''[[03Exx|03Exx]]''  Set theory
* ''[[03Fxx|03Fxx]]''  Proof theory and constructive mathematics
* ''[[03Gxx|03Gxx]]''  Algebraic logic
* ''[[03Hxx|03Hxx]]''  Nonstandard models [See also [[03C62|03Cxx]]]
!!![[03|03-XX]]Hxx  Nonstandard models [See also [[03C62|03Cxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/03Hxx.html]]}{{moveright{< [[03Gxx |03Gxx]] | [[03-XX |03-XX]] | [[05-XX |05-XX]] >}}}
* ''03H05'' Nonstandard models in mathematics [See also [[26E35|26Exx]], [[28E05|28Exx]], [[30G06|30Gxx]], [[46S20|46Sxx]], [[47S20|47Sxx]], [[54J05|54Jxx]]]
* ''03H10'' Other applications of nonstandard models (economics, physics, etc.)
* ''03H15'' Nonstandard models of arithmetic [See also [[11U10|11Uxx]], [[12L15|12Lxx]], [[13L05|13Lxx]]]
* ''03H99'' None of the above, but in this section
!!![[05|05-XX]]Axx  Enumerative combinatorics {For enumeration in graph theory, see [[05C30|05Cxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/05Axx.html]]}{{moveright{< [[03-XX |03-XX]] | [[05-XX |05-XX]] | [[05Bxx |05Bxx]] >}}}
* ''05A05'' Permutations, words, matrices
* ''05A10'' Factorials, binomial coefficients, combinatorial functions [See also [[11B65|11Bxx]], [[33Cxx|33Cxx]]]
* ''05A15'' Exact enumeration problems, generating functions [See also [[33Cxx|33Cxx]], [[33Dxx|33Dxx]]]
* ''05A16'' Asymptotic enumeration
* ''05A17'' Partitions of integers [See also [[11P81|11Pxx]], [[11P82|11Pxx]], [[11P83|11Pxx]]]
* ''05A18'' Partitions of sets
* ''05A19'' Combinatorial identities, bijective combinatorics
* ''05A20'' Combinatorial inequalities
* ''05A30'' $q$-calculus and related topics [See also [[33Dxx|33Dxx]]]
* ''05A40'' Umbral calculus
* ''05A99'' None of the above, but in this section
!!![[05|05-XX]]Bxx  Designs and configurations {For applications of design theory, see [[94C30|94Cxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/05Bxx.html]]}{{moveright{< [[05Axx |05Axx]] | [[05-XX |05-XX]] | [[05Cxx |05Cxx]] >}}}
* ''05B05'' Block designs [See also [[51E05|51Exx]], [[62K10|62Kxx]]]
* ''05B07'' Triple systems
* ''05B10'' Difference sets (number-theoretic, group-theoretic, etc.) [See also [[11B13|11Bxx]]]
* ''05B15'' Orthogonal arrays, Latin squares, Room squares
* ''05B20'' Matrices (incidence, Hadamard, etc.)
* ''05B25'' Finite geometries [See also [[51D20|51Dxx]], [[51Exx|51Exx]]]
* ''05B30'' Other designs, configurations [See also [[51E30|51Exx]]]
* ''05B35'' Matroids, geometric lattices [See also [[52B40|52Bxx]], [[90C27|90Cxx]]]
* ''05B40'' Packing and covering [See also [[11H31|11Hxx]], [[52C15|52Cxx]], [[52C17|52Cxx]]]
* ''05B45'' Tessellation and tiling problems [See also [[52C20|52Cxx]], [[52C22|52Cxx]]]
* ''05B50'' Polyominoes
* ''05B99'' None of the above, but in this section
!!![[05|05-XX]]Cxx  Graph theory {For applications of graphs, see [[68R10|68Rxx]], [[81Q30|81Qxx]], [[81T15|81Txx]], [[82B20|82Bxx]], [[82C20|82Cxx]], [[90C35|90Cxx]], [[92E10|92Exx]], [[94C15|94Cxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/05Cxx.html]]}{{moveright{< [[05Bxx |05Bxx]] | [[05-XX |05-XX]] | [[05Dxx |05Dxx]] >}}}
* ''05C05'' Trees
* ''05C07'' Vertex degrees [See also [[05E30|05Exx]]]
* ''05C10'' Planar graphs; geometric and topological aspects of graph theory [See also [[57M15|57Mxx]], [[57M25|57Mxx]]]
* ''05C12'' Distance in graphs
* ''05C15'' Coloring of graphs and hypergraphs
* ''05C17'' Perfect graphs
* ''05C20'' Directed graphs (digraphs), tournaments
* ''05C21'' Flows in graphs
* ''05C22'' Signed and weighted graphs
* ''05C25'' Graphs and abstract algebra (groups, rings, fields, etc.) [See also [[20F65|20Fxx]]]
* ''05C30'' Enumeration in graph theory
* ''05C31'' Graph polynomials
* ''05C35'' Extremal problems [See also [[90C35|90Cxx]]]
* ''05C38'' Paths and cycles [See also [[90B10|90Bxx]]]
* ''05C40'' Connectivity
* ''05C42'' Density (toughness, etc.)
* ''05C45'' Eulerian and Hamiltonian graphs
* ''05C50'' Graphs and linear algebra (matrices, eigenvalues, etc.)
* ''05C51'' Graph designs and isomomorphic decomposition [See also [[05B30|05Bxx]]]
* ''05C55'' Generalized Ramsey theory [See also [[05D10|05Dxx]]]
* ''05C57'' Games on graphs [See also [[91A43|91Axx]], [[91A46|91Axx]]]
* ''05C60'' Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)
* ''05C62'' Graph representations (geometric and intersection representations, etc.) {For graph drawing, see also [[68R10|68Rxx]]}
* ''05C63'' Infinite graphs
* ''05C65'' Hypergraphs
* ''05C69'' Dominating sets, independent sets, cliques
* ''05C70'' Factorization, matching, partitioning, covering and packing
* ''05C72'' Fractional graph theory, fuzzy graph theory
* ''05C75'' Structural characterization of families of graphs
* ''05C76'' Graph operations (line graphs, products, etc.)
* ''05C78'' Graph labelling (graceful graphs, bandwidth, etc.)
* ''05C80'' Random graphs [See also [[60B20|60Bxx]]]
* ''05C81'' Random walks on graphs
* ''05C82'' Small world graphs, complex networks [See also [[90Bxx|90Bxx]], [[91D30|91Dxx]]]
* ''05C83'' Graph minors
* ''05C85'' Graph algorithms [See also [[68R10|68Rxx]], [[68W05|68Wxx]]]
* ''05C90'' Applications [See also [[68R10|68Rxx]], [[81Q30|81Qxx]], [[81T15|81Txx]], [[82B20|82Bxx]], [[82C20|82Cxx]], [[90C35|90Cxx]], [[92E10|92Exx]], [[94C15|94Cxx]]]
* ''05C99'' None of the above, but in this section
!!![[05|05-XX]]Dxx  Extremal combinatorics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/05Dxx.html]]}{{moveright{< [[05Cxx |05Cxx]] | [[05-XX |05-XX]] | [[05Exx |05Exx]] >}}}
* ''05D05'' Extremal set theory
* ''05D10'' Ramsey theory [See also [[05C55|05Cxx]]]
* ''05D15'' Transversal (matching) theory
* ''05D40'' Probabilistic methods
* ''05D99'' None of the above, but in this section
!!!05-XX Combinatorics {For finite fields, see [[11Txx|11Txx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/05-XX.html]]}{{moveright{< [[03-XX |03-XX]] | [[MSC |MSC2010]] | [[05Axx |05Axx]] >}}}
* ''05-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''05-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''05-02'' Research exposition (monographs, survey articles)
* ''05-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''05-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''05-06'' Proceedings, conferences, collections, etc.
* ''[[05Axx|05Axx]]''  Enumerative combinatorics {For enumeration in graph theory, see [[05C30|05Cxx]]}
* ''[[05Bxx|05Bxx]]''  Designs and configurations {For applications of design theory, see [[94C30|94Cxx]]}
* ''[[05Cxx|05Cxx]]''  Graph theory {For applications of graphs, see [[68R10|68Rxx]], [[81Q30|81Qxx]], [[81T15|81Txx]], [[82B20|82Bxx]], [[82C20|82Cxx]], [[90C35|90Cxx]], [[92E10|92Exx]], [[94C15|94Cxx]]}
* ''[[05Dxx|05Dxx]]''  Extremal combinatorics
* ''[[05Exx|05Exx]]''  Algebraic combinatorics
!!![[05|05-XX]]Exx  Algebraic combinatorics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/05Exx.html]]}{{moveright{< [[05Dxx |05Dxx]] | [[05-XX |05-XX]] | [[06-XX |06-XX]] >}}}
* ''05E05'' Symmetric functions and generalizations
* ''05E10'' Combinatorial aspects of representation theory [See also [[20C30|20Cxx]]]
* ''05E15'' Combinatorial aspects of groups and algebras [See also [[14Nxx|14Nxx]], [[22E45|22Exx]], [[33C80|33Cxx]]]
* ''05E18'' Group actions on combinatorial structures
* ''05E30'' Association schemes, strongly regular graphs
* ''05E40'' Combinatorial aspects of commutative algebra
* ''05E45'' Combinatorial aspects of simplicial complexes
* ''05E99'' None of the above, but in this section
!!![[06|06-XX]]Axx  Ordered sets {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/06Axx.html]]}{{moveright{< [[05-XX |05-XX]] | [[06-XX |06-XX]] | [[06Bxx |06Bxx]] >}}}
* ''06A05'' Total order
* ''06A06'' Partial order, general
* ''06A07'' Combinatorics of partially ordered sets
* ''06A11'' Algebraic aspects of posets
* ''06A12'' Semilattices [See also [[20M10|20Mxx]]; for topological semilattices see [[22A26|22Axx]]]
* ''06A15'' Galois correspondences, closure operators
* ''06A75'' Generalizations of ordered sets
* ''06A99'' None of the above, but in this section
!!![[06|06-XX]]Bxx  Lattices [See also [[03G10|03Gxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/06Bxx.html]]}{{moveright{< [[06Axx |06Axx]] | [[06-XX |06-XX]] | [[06Cxx |06Cxx]] >}}}
* ''06B05'' Structure theory
* ''06B10'' Ideals, congruence relations
* ''06B15'' Representation theory
* ''06B20'' Varieties of lattices
* ''06B23'' Complete lattices, completions
* ''06B25'' Free lattices, projective lattices, word problems [See also [[03D40|03Dxx]], [[08A50|08Axx]], [[20F10|20Fxx]]]
* ''06B30'' Topological lattices, order topologies [See also [[06F30|06Fxx]], [[22A26|22Axx]], [[54F05|54Fxx]], [[54H12|54Hxx]]]
* ''06B35'' Continuous lattices and posets, applications [See also [[06B30|06Bxx]], [[06D10|06Dxx]], [[06F30|06Fxx]], [[18B35|18Bxx]], [[22A26|22Axx]], [[68Q55|68Qxx]]]
* ''06B75'' Generalizations of lattices
* ''06B99'' None of the above, but in this section
!!![[06|06-XX]]Cxx  Modular lattices, complemented lattices {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/06Cxx.html]]}{{moveright{< [[06Bxx |06Bxx]] | [[06-XX |06-XX]] | [[06Dxx |06Dxx]] >}}}
* ''06C05'' Modular lattices, Desarguesian lattices
* ''06C10'' Semimodular lattices, geometric lattices
* ''06C15'' Complemented lattices, orthocomplemented lattices and posets [See also [[03G12|03Gxx]], [[81P10|81Pxx]]]
* ''06C20'' Complemented modular lattices, continuous geometries
* ''06C99'' None of the above, but in this section
!!![[06|06-XX]]Dxx  Distributive lattices {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/06Dxx.html]]}{{moveright{< [[06Cxx |06Cxx]] | [[06-XX |06-XX]] | [[06Exx |06Exx]] >}}}
* ''06D05'' Structure and representation theory
* ''06D10'' Complete distributivity
* ''06D15'' Pseudocomplemented lattices
* ''06D20'' Heyting algebras [See also [[03G25|03Gxx]]]
* ''06D22'' Frames, locales {For topological questions see [[54-XX|54-XX]]}
* ''06D25'' Post algebras [See also [[03G20|03Gxx]]]
* ''06D30'' De Morgan algebras, Łukasiewicz algebras [See also [[03G20|03Gxx]]]
* ''06D35'' ~MV-algebras
* ''06D50'' Lattices and duality
* ''06D72'' Fuzzy lattices (soft algebras) and related topics
* ''06D75'' Other generalizations of distributive lattices
* ''06D99'' None of the above, but in this section
!!![[06|06-XX]]Exx  Boolean algebras (Boolean rings) [See also [[03G05|03Gxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/06Exx.html]]}{{moveright{< [[06Dxx |06Dxx]] | [[06-XX |06-XX]] | [[06Fxx |06Fxx]] >}}}
* ''06E05'' Structure theory
* ''06E10'' Chain conditions, complete algebras
* ''06E15'' Stone spaces (Boolean spaces) and related structures
* ''06E20'' Ring-theoretic properties [See also [[16E50|16Exx]], [[16G30|16Gxx]]]
* ''06E25'' Boolean algebras with additional operations (diagonalizable algebras, etc.) [See also [[03G25|03Gxx]], [[03F45|03Fxx]]]
* ''06E30'' Boolean functions [See also [[94C10|94Cxx]]]
* ''06E75'' Generalizations of Boolean algebras
* ''06E99'' None of the above, but in this section
!!!06-XX Order, lattices, ordered algebraic structures [See also [[18B35|18Bxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/06-XX.html]]}{{moveright{< [[05-XX |05-XX]] | [[MSC |MSC2010]] | [[06Axx |06Axx]] >}}}
* ''06-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''06-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''06-02'' Research exposition (monographs, survey articles)
* ''06-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''06-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''06-06'' Proceedings, conferences, collections, etc.
* ''[[06Axx|06Axx]]''  Ordered sets
* ''[[06Bxx|06Bxx]]''  Lattices [See also [[03G10|03Gxx]]]
* ''[[06Cxx|06Cxx]]''  Modular lattices, complemented lattices
* ''[[06Dxx|06Dxx]]''  Distributive lattices
* ''[[06Exx|06Exx]]''  Boolean algebras (Boolean rings) [See also [[03G05|03Gxx]]]
* ''[[06Fxx|06Fxx]]''  Ordered structures
!!![[06|06-XX]]Fxx  Ordered structures {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/06Fxx.html]]}{{moveright{< [[06Exx |06Exx]] | [[06-XX |06-XX]] | [[08-XX |08-XX]] >}}}
* ''06F05'' Ordered semigroups and monoids [See also [[20Mxx|20Mxx]]]
* ''06F07'' Quantales
* ''06F10'' Noether lattices
* ''06F15'' Ordered groups [See also [[20F60|20Fxx]]]
* ''06F20'' Ordered abelian groups, Riesz groups, ordered linear spaces [See also [[46A40|46Axx]]]
* ''06F25'' Ordered rings, algebras, modules {For ordered fields, see [[12J15|12Jxx]]; see also [[13J25|13Jxx]], [[16W80|16Wxx]]}
* ''06F30'' Topological lattices, order topologies [See also [[06B30|06Bxx]], [[22A26|22Axx]], [[54F05|54Fxx]], [[54H12|54Hxx]]]
* ''06F35'' ~BCK-algebras, ~BCI-algebras [See also [[03G25|03Gxx]]]
* ''06F99'' None of the above, but in this section
!!![[08|08-XX]]Axx  Algebraic structures [See also [[03C05|03Cxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/08Axx.html]]}{{moveright{< [[06-XX |06-XX]] | [[08-XX |08-XX]] | [[08Bxx |08Bxx]] >}}}
* ''08A02'' Relational systems, laws of composition
* ''08A05'' Structure theory
* ''08A30'' Subalgebras, congruence relations
* ''08A35'' Automorphisms, endomorphisms
* ''08A40'' Operations, polynomials, primal algebras
* ''08A45'' Equational compactness
* ''08A50'' Word problems [See also [[03D40|03Dxx]], [[06B25|06Bxx]], [[20F10|20Fxx]], [[68R15|68Rxx]]]
* ''08A55'' Partial algebras
* ''08A60'' Unary algebras
* ''08A62'' Finitary algebras
* ''08A65'' Infinitary algebras
* ''08A68'' Heterogeneous algebras
* ''08A70'' Applications of universal algebra in computer science
* ''08A72'' Fuzzy algebraic structures
* ''08A99'' None of the above, but in this section
!!![[08|08-XX]]Bxx  Varieties [See also [[03C05|03Cxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/08Bxx.html]]}{{moveright{< [[08Axx |08Axx]] | [[08-XX |08-XX]] | [[08Cxx |08Cxx]] >}}}
* ''08B05'' Equational logic, Mal'cev (Mal'tsev) conditions
* ''08B10'' Congruence modularity, congruence distributivity
* ''08B15'' Lattices of varieties
* ''08B20'' Free algebras
* ''08B25'' Products, amalgamated products, and other kinds of limits and colimits [See also [[18A30|18Axx]]]
* ''08B26'' Subdirect products and subdirect irreducibility
* ''08B30'' Injectives, projectives
* ''08B99'' None of the above, but in this section
!!!08-XX General algebraic systems {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/08-XX.html]]}{{moveright{< [[06-XX |06-XX]] | [[MSC |MSC2010]] | [[08Axx |08Axx]] >}}}
* ''08-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''08-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''08-02'' Research exposition (monographs, survey articles)
* ''08-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''08-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''08-06'' Proceedings, conferences, collections, etc.
* ''[[08Axx|08Axx]]''  Algebraic structures [See also [[03C05|03Cxx]]]
* ''[[08Bxx|08Bxx]]''  Varieties [See also [[03C05|03Cxx]]]
* ''[[08Cxx|08Cxx]]''  Other classes of algebras
!!![[08|08-XX]]Cxx  Other classes of algebras {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/08Cxx.html]]}{{moveright{< [[08Bxx |08Bxx]] | [[08-XX |08-XX]] | [[11-XX |11-XX]] >}}}
* ''08C05'' Categories of algebras [See also [[18C05|18Cxx]]]
* ''08C10'' Axiomatic model classes [See also [[03Cxx|03Cxx]], in particular [[03C60|03Cxx]]]
* ''08C15'' Quasivarieties
* ''08C20'' Natural dualities for classes of algebras [See also [[06E15|06Exx]], [[18A40|18Axx]], [[22A30|22Axx]]]
* ''08C99'' None of the above, but in this section
!!![[11|11-XX]]Axx  Elementary number theory {For analogues in number fields, see [[11R04|11Rxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Axx.html]]}{{moveright{< [[08-XX |08-XX]] | [[11-XX |11-XX]] | [[11Bxx |11Bxx]] >}}}
* ''11A05'' Multiplicative structure; Euclidean algorithm; greatest common divisors
* ''11A07'' Congruences; primitive roots; residue systems
* ''11A15'' Power residues, reciprocity
* ''11A25'' Arithmetic functions; related numbers; inversion formulas
* ''11A41'' Primes
* ''11A51'' Factorization; primality
* ''11A55'' Continued fractions {For approximation results, see [[11J70|11Jxx]]} [See also [[11K50|11Kxx]], [[30B70|30Bxx]], [[40A15|40Axx]]]
* ''11A63'' Radix representation; digital problems {For metric results, see [[11K16|11Kxx]]}
* ''11A67'' Other representations
* ''11A99'' None of the above, but in this section
!!![[11|11-XX]]Bxx  Sequences and sets {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Bxx.html]]}{{moveright{< [[11Axx |11Axx]] | [[11-XX |11-XX]] | [[11Cxx |11Cxx]] >}}}
* ''11B05'' Density, gaps, topology
* ''11B13'' Additive bases, including sumsets [See also [[05B10|05Bxx]]]
* ''11B25'' Arithmetic progressions [See also [[11N13|11Nxx]]]
* ''11B30'' Arithmetic combinatorics; higher degree uniformity
* ''11B34'' Representation functions
* ''11B37'' Recurrences {For applications to special functions, see [[33-XX|33-XX]]}
* ''11B39'' Fibonacci and Lucas numbers and polynomials and generalizations
* ''11B50'' Sequences (mod $m$)
* ''11B57'' Farey sequences; the sequences ${1^k, 2^k, \cdots}$
* ''11B65'' Binomial coefficients; factorials; $q$-identities [See also [[05A10|05Axx]], [[05A30|05Axx]]]
* ''11B68'' Bernoulli and Euler numbers and polynomials
* ''11B73'' Bell and Stirling numbers
* ''11B75'' Other combinatorial number theory
* ''11B83'' Special sequences and polynomials
* ''11B85'' Automata sequences
* ''11B99'' None of the above, but in this section
!!![[11|11-XX]]Cxx  Polynomials and matrices {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Cxx.html]]}{{moveright{< [[11Bxx |11Bxx]] | [[11-XX |11-XX]] | [[11Dxx |11Dxx]] >}}}
* ''11C08'' Polynomials [See also [[13F20|13Fxx]]]
* ''11C20'' Matrices, determinants [See also [[15B36|15Bxx]]]
* ''11C99'' None of the above, but in this section
!!![[11|11-XX]]Dxx  Diophantine equations [See also [[11Gxx|11Gxx]], [[14Gxx|14Gxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Dxx.html]]}{{moveright{< [[11Cxx |11Cxx]] | [[11-XX |11-XX]] | [[11Exx |11Exx]] >}}}
* ''11D04'' Linear equations
* ''11D07'' The Frobenius problem
* ''11D09'' Quadratic and bilinear equations
* ''11D25'' Cubic and quartic equations
* ''11D41'' Higher degree equations; Fermat's equation
* ''11D45'' Counting solutions of Diophantine equations
* ''11D57'' Multiplicative and norm form equations
* ''11D59'' ~Thue-Mahler equations
* ''11D61'' Exponential equations
* ''11D68'' Rational numbers as sums of fractions
* ''11D72'' Equations in many variables [See also [[11P55|11Pxx]]]
* ''11D75'' Diophantine inequalities [See also [[11J25|11Jxx]]]
* ''11D79'' Congruences in many variables
* ''11D85'' Representation problems [See also [[11P55|11Pxx]]]
* ''11D88'' $p$-adic and power series fields
* ''11D99'' None of the above, but in this section
!!![[11|11-XX]]Exx  Forms and linear algebraic groups [See also [[19Gxx|19Gxx]]] {For quadratic forms in linear algebra, see [[15A63|15Axx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Exx.html]]}{{moveright{< [[11Dxx |11Dxx]] | [[11-XX |11-XX]] | [[11Fxx |11Fxx]] >}}}
* ''11E04'' Quadratic forms over general fields
* ''11E08'' Quadratic forms over local rings and fields
* ''11E10'' Forms over real fields
* ''11E12'' Quadratic forms over global rings and fields
* ''11E16'' General binary quadratic forms
* ''11E20'' General ternary and quaternary quadratic forms; forms of more than two variables
* ''11E25'' Sums of squares and representations by other particular quadratic forms
* ''11E39'' Bilinear and Hermitian forms
* ''11E41'' Class numbers of quadratic and Hermitian forms
* ''11E45'' Analytic theory (Epstein zeta functions; relations with automorphic forms and functions)
* ''11E57'' Classical groups [See also [[14Lxx|14Lxx]], [[20Gxx|20Gxx]]]
* ''11E70'' $K$-theory of quadratic and Hermitian forms
* ''11E72'' Galois cohomology of linear algebraic groups [See also [[20G10|20Gxx]]]
* ''11E76'' Forms of degree higher than two
* ''11E81'' Algebraic theory of quadratic forms; Witt groups and rings [See also [[19G12|19Gxx]], [[19G24|19Gxx]]]
* ''11E88'' Quadratic spaces; Clifford algebras [See also [[15A63|15Axx]], [[15A66|15Axx]]]
* ''11E95'' $p$-adic theory
* ''11E99'' None of the above, but in this section
!!![[11|11-XX]]Fxx  Discontinuous groups and automorphic forms [See also [[11R39|11Rxx]], [[11S37|11Sxx]], [[14Gxx|14Gxx]], [[14Kxx|14Kxx]], [[22E50|22Exx]], [[22E55|22Exx]], [[30F35|30Fxx]], [[32Nxx|32Nxx]]] {For relations with quadratic forms, see [[11E45|11Exx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Fxx.html]]}{{moveright{< [[11Exx |11Exx]] | [[11-XX |11-XX]] | [[11Gxx |11Gxx]] >}}}
* ''11F03'' Modular and automorphic functions
* ''11F06'' Structure of modular groups and generalizations; arithmetic groups [See also [[20H05|20Hxx]], [[20H10|20Hxx]], [[22E40|22Exx]]]
* ''11F11'' Holomorphic modular forms of integral weight
* ''11F12'' Automorphic forms, one variable
* ''11F20'' Dedekind eta function, Dedekind sums
* ''11F22'' Relationship to Lie algebras and finite simple groups
* ''11F23'' Relations with algebraic geometry and topology
* ''11F25'' ~Hecke-Petersson operators, differential operators (one variable)
* ''11F27'' Theta series; Weil representation; theta correspondences
* ''11F30'' Fourier coefficients of automorphic forms
* ''11F32'' Modular correspondences, etc.
* ''11F33'' Congruences for modular and $p$-adic modular forms [See also [[14G20|14Gxx]], [[22E50|22Exx]]]
* ''11F37'' Forms of half-integer weight; nonholomorphic modular forms
* ''11F41'' Automorphic forms on ${\rm GL}(2)$; Hilbert and ~Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also [[14J20|14Jxx]]]
* ''11F46'' Siegel modular groups; Siegel and ~Hilbert-Siegel modular and automorphic forms
* ''11F50'' Jacobi forms
* ''11F52'' Modular forms associated to Drinfel'd modules
* ''11F55'' Other groups and their modular and automorphic forms (several variables)
* ''11F60'' ~Hecke-Petersson operators, differential operators (several variables)
* ''11F66'' Langlands $L$-functions; one variable Dirichlet series and functional equations
* ''11F67'' Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
* ''11F68'' Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series
* ''11F70'' Representation-theoretic methods; automorphic representations over local and global fields
* ''11F72'' Spectral theory; Selberg trace formula
* ''11F75'' Cohomology of arithmetic groups
* ''11F80'' Galois representations
* ''11F85'' $p$-adic theory, local fields [See also [[14G20|14Gxx]], [[22E50|22Exx]]]
* ''11F99'' None of the above, but in this section
!!![[11|11-XX]]Gxx  Arithmetic algebraic geometry (Diophantine geometry) [See also [[11Dxx|11Dxx]], [[14Gxx|14Gxx]], [[14Kxx|14Kxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Gxx.html]]}{{moveright{< [[11Fxx |11Fxx]] | [[11-XX |11-XX]] | [[11Hxx |11Hxx]] >}}}
* ''11G05'' Elliptic curves over global fields [See also [[14H52|14Hxx]]]
* ''11G07'' Elliptic curves over local fields [See also [[14G20|14Gxx]], [[14H52|14Hxx]]]
* ''11G09'' Drinfel'd modules; higher-dimensional motives, etc. [See also [[14L05|14Lxx]]]
* ''11G10'' Abelian varieties of dimension $> 1$ [See also [[14Kxx|14Kxx]]]
* ''11G15'' Complex multiplication and moduli of abelian varieties [See also [[14K22|14Kxx]]]
* ''11G16'' Elliptic and modular units [See also [[11R27|11Rxx]]]
* ''11G18'' Arithmetic aspects of modular and Shimura varieties [See also [[14G35|14Gxx]]]
* ''11G20'' Curves over finite and local fields [See also [[14H25|14Hxx]]]
* ''11G25'' Varieties over finite and local fields [See also [[14G15|14Gxx]], [[14G20|14Gxx]]]
* ''11G30'' Curves of arbitrary genus or genus $\ne 1$ over global fields [See also [[14H25|14Hxx]]]
* ''11G32'' Dessins d'enfants, Belyĭ theory
* ''11G35'' Varieties over global fields [See also [[14G25|14Gxx]]]
* ''11G40'' $L$-functions of varieties over global fields; ~Birch-Swinnerton-Dyer conjecture [See also [[14G10|14Gxx]]]
* ''11G42'' Arithmetic mirror symmetry [See also [[14J33|14Jxx]]]
* ''11G45'' Geometric class field theory [See also [[11R37|11Rxx]], [[14C35|14Cxx]], [[19F05|19Fxx]]]
* ''11G50'' Heights [See also [[14G40|14Gxx]], [[37P30|37Pxx]]]
* ''11G55'' Polylogarithms and relations with $K$-theory
* ''11G99'' None of the above, but in this section
!!![[11|11-XX]]Hxx  Geometry of numbers {For applications in coding theory, see [[94B75|94Bxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Hxx.html]]}{{moveright{< [[11Gxx |11Gxx]] | [[11-XX |11-XX]] | [[11Jxx |11Jxx]] >}}}
* ''11H06'' Lattices and convex bodies [See also [[11P21|11Pxx]], [[52C05|52Cxx]], [[52C07|52Cxx]]]
* ''11H16'' Nonconvex bodies
* ''11H31'' Lattice packing and covering [See also [[05B40|05Bxx]], [[52C15|52Cxx]], [[52C17|52Cxx]]]
* ''11H46'' Products of linear forms
* ''11H50'' Minima of forms
* ''11H55'' Quadratic forms (reduction theory, extreme forms, etc.)
* ''11H56'' Automorphism groups of lattices
* ''11H60'' Mean value and transfer theorems
* ''11H71'' Relations with coding theory
* ''11H99'' None of the above, but in this section
!!![[11|11-XX]]Jxx  Diophantine approximation, transcendental number theory [See also [[11K60|11Kxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Jxx.html]]}{{moveright{< [[11Hxx |11Hxx]] | [[11-XX |11-XX]] | [[11Kxx |11Kxx]] >}}}
* ''11J04'' Homogeneous approximation to one number
* ''11J06'' Markov and Lagrange spectra and generalizations
* ''11J13'' Simultaneous homogeneous approximation, linear forms
* ''11J17'' Approximation by numbers from a fixed field
* ''11J20'' Inhomogeneous linear forms
* ''11J25'' Diophantine inequalities [See also [[11D75|11Dxx]]]
* ''11J54'' Small fractional parts of polynomials and generalizations
* ''11J61'' Approximation in non-Archimedean valuations
* ''11J68'' Approximation to algebraic numbers
* ''11J70'' Continued fractions and generalizations [See also [[11A55|11Axx]], [[11K50|11Kxx]]]
* ''11J71'' Distribution modulo one [See also [[11K06|11Kxx]]]
* ''11J72'' Irrationality; linear independence over a field
* ''11J81'' Transcendence (general theory)
* ''11J82'' Measures of irrationality and of transcendence
* ''11J83'' Metric theory
* ''11J85'' Algebraic independence; Gel'fond's method
* ''11J86'' Linear forms in logarithms; Baker's method
* ''11J87'' Schmidt Subspace Theorem and applications
* ''11J89'' Transcendence theory of elliptic and abelian functions
* ''11J91'' Transcendence theory of other special functions
* ''11J93'' Transcendence theory of Drinfel'd and $t$-modules
* ''11J95'' Results involving abelian varieties
* ''11J97'' Analogues of methods in Nevanlinna theory (work of Vojta et al.)
* ''11J99'' None of the above, but in this section
!!![[11|11-XX]]Kxx  Probabilistic theory: distribution modulo $1$; metric theory of algorithms {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Kxx.html]]}{{moveright{< [[11Jxx |11Jxx]] | [[11-XX |11-XX]] | [[11Lxx |11Lxx]] >}}}
* ''11K06'' General theory of distribution modulo $1$ [See also [[11J71|11Jxx]]]
* ''11K16'' Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. [See also [[11A63|11Axx]]]
* ''11K31'' Special sequences
* ''11K36'' Well-distributed sequences and other variations
* ''11K38'' Irregularities of distribution, discrepancy [See also [[11Nxx|11Nxx]]]
* ''11K41'' Continuous, $p$-adic and abstract analogues
* ''11K45'' Pseudo-random numbers; Monte Carlo methods
* ''11K50'' Metric theory of continued fractions [See also [[11A55|11Axx]], [[11J70|11Jxx]]]
* ''11K55'' Metric theory of other algorithms and expansions; measure and Hausdorff dimension [See also [[11N99|11Nxx]], [[28Dxx|28Dxx]]]
* ''11K60'' Diophantine approximation [See also [[11Jxx|11Jxx]]]
* ''11K65'' Arithmetic functions [See also [[11Nxx|11Nxx]]]
* ''11K70'' Harmonic analysis and almost periodicity
* ''11K99'' None of the above, but in this section
!!![[11|11-XX]]Lxx  Exponential sums and character sums {For finite fields, see [[11Txx|11Txx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Lxx.html]]}{{moveright{< [[11Kxx |11Kxx]] | [[11-XX |11-XX]] | [[11Mxx |11Mxx]] >}}}
* ''11L03'' Trigonometric and exponential sums, general
* ''11L05'' Gauss and Kloosterman sums; generalizations
* ''11L07'' Estimates on exponential sums
* ''11L10'' Jacobsthal and Brewer sums; other complete character sums
* ''11L15'' Weyl sums
* ''11L20'' Sums over primes
* ''11L26'' Sums over arbitrary intervals
* ''11L40'' Estimates on character sums
* ''11L99'' None of the above, but in this section
!!![[11|11-XX]]Mxx  Zeta and $L$-functions: analytic theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Mxx.html]]}{{moveright{< [[11Lxx |11Lxx]] | [[11-XX |11-XX]] | [[11Nxx |11Nxx]] >}}}
* ''11M06'' $\zeta (s)$ and $L(s, \chi)$
* ''11M20'' Real zeros of $L(s, \chi)$; results on $L(1, \chi)$
* ''11M26'' Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses
* ''11M32'' Multiple Dirichlet series and zeta functions and multizeta values
* ''11M35'' Hurwitz and Lerch zeta functions
* ''11M36'' Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas
* ''11M38'' Zeta and $L$-functions in characteristic $p$
* ''11M41'' Other Dirichlet series and zeta functions {For local and global ground fields, see [[11R42|11Rxx]], [[11R52|11Rxx]], [[11S40|11Sxx]], [[11S45|11Sxx]]; for algebro-geometric methods, see [[14G10|14Gxx]]; see also [[11E45|11Exx]], [[11F66|11Fxx]], [[11F70|11Fxx]], [[11F72|11Fxx]]}
* ''11M45'' Tauberian theorems [See also [[40E05|40Exx]]]
* ''11M50'' Relations with random matrices
* ''11M55'' Relations with noncommutative geometry
* ''11M99'' None of the above, but in this section
!!![[11|11-XX]]Nxx  Multiplicative number theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Nxx.html]]}{{moveright{< [[11Mxx |11Mxx]] | [[11-XX |11-XX]] | [[11Pxx |11Pxx]] >}}}
* ''11N05'' Distribution of primes
* ''11N13'' Primes in progressions [See also [[11B25|11Bxx]]]
* ''11N25'' Distribution of integers with specified multiplicative constraints
* ''11N30'' Turán theory [See also [[30Bxx|30Bxx]]]
* ''11N32'' Primes represented by polynomials; other multiplicative structure of polynomial values
* ''11N35'' Sieves
* ''11N36'' Applications of sieve methods
* ''11N37'' Asymptotic results on arithmetic functions
* ''11N45'' Asymptotic results on counting functions for algebraic and topological structures
* ''11N56'' Rate of growth of arithmetic functions
* ''11N60'' Distribution functions associated with additive and positive multiplicative functions
* ''11N64'' Other results on the distribution of values or the characterization of arithmetic functions
* ''11N69'' Distribution of integers in special residue classes
* ''11N75'' Applications of automorphic functions and forms to multiplicative problems [See also [[11Fxx|11Fxx]]]
* ''11N80'' Generalized primes and integers
* ''11N99'' None of the above, but in this section
!!![[11|11-XX]]Pxx  Additive number theory; partitions {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Pxx.html]]}{{moveright{< [[11Nxx |11Nxx]] | [[11-XX |11-XX]] | [[11Rxx |11Rxx]] >}}}
* ''11P05'' Waring's problem and variants
* ''11P21'' Lattice points in specified regions
* ''11P32'' Goldbach-type theorems; other additive questions involving primes
* ''11P55'' Applications of the ~Hardy-Littlewood method [See also [[11D85|11Dxx]]]
* ''11P70'' Inverse problems of additive number theory, including sumsets
* ''11P81'' Elementary theory of partitions [See also [[05A17|05Axx]]]
* ''11P82'' Analytic theory of partitions
* ''11P83'' Partitions; congruences and congruential restrictions
* ''11P84'' Partition identities; identities of ~Rogers-Ramanujan type
* ''11P99'' None of the above, but in this section
!!![[11|11-XX]]Rxx  Algebraic number theory: global fields {For complex multiplication, see [[11G15|11Gxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Rxx.html]]}{{moveright{< [[11Pxx |11Pxx]] | [[11-XX |11-XX]] | [[11Sxx |11Sxx]] >}}}
* ''11R04'' Algebraic numbers; rings of algebraic integers
* ''11R06'' ~PV-numbers and generalizations; other special algebraic numbers; Mahler measure
* ''11R09'' Polynomials (irreducibility, etc.)
* ''11R11'' Quadratic extensions
* ''11R16'' Cubic and quartic extensions
* ''11R18'' Cyclotomic extensions
* ''11R20'' Other abelian and metabelian extensions
* ''11R21'' Other number fields
* ''11R23'' Iwasawa theory
* ''11R27'' Units and factorization
* ''11R29'' Class numbers, class groups, discriminants
* ''11R32'' Galois theory
* ''11R33'' Integral representations related to algebraic numbers; Galois module structure of rings of integers [See also [[20C10|20Cxx]]]
* ''11R34'' Galois cohomology [See also [[12Gxx|12Gxx]], [[19A31|19Axx]]]
* ''11R37'' Class field theory
* ''11R39'' ~Langlands-Weil conjectures, nonabelian class field theory [See also [[11Fxx|11Fxx]], [[22E55|22Exx]]]
* ''11R42'' Zeta functions and $L$-functions of number fields [See also [[11M41|11Mxx]], [[19F27|19Fxx]]]
* ''11R44'' Distribution of prime ideals [See also [[11N05|11Nxx]]]
* ''11R45'' Density theorems
* ''11R47'' Other analytic theory [See also [[11Nxx|11Nxx]]]
* ''11R52'' Quaternion and other division algebras: arithmetic, zeta functions
* ''11R54'' Other algebras and orders, and their zeta and $L$-functions [See also [[11S45|11Sxx]], [[16Hxx|16Hxx]], [[16Kxx|16Kxx]]]
* ''11R56'' Adèle rings and groups
* ''11R58'' Arithmetic theory of algebraic function fields [See also [[14-XX|14-XX]]]
* ''11R60'' Cyclotomic function fields (class groups, Bernoulli objects, etc.)
* ''11R65'' Class groups and Picard groups of orders
* ''11R70'' $K$-theory of global fields [See also [[19Fxx|19Fxx]]]
* ''11R80'' Totally real fields [See also [[12J15|12Jxx]]]
* ''11R99'' None of the above, but in this section
!!![[11|11-XX]]Sxx  Algebraic number theory: local and $p$-adic fields {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Sxx.html]]}{{moveright{< [[11Rxx |11Rxx]] | [[11-XX |11-XX]] | [[11Txx |11Txx]] >}}}
* ''11S05'' Polynomials
* ''11S15'' Ramification and extension theory
* ''11S20'' Galois theory
* ''11S23'' Integral representations
* ''11S25'' Galois cohomology [See also [[12Gxx|12Gxx]], [[16H05|16Hxx]]]
* ''11S31'' Class field theory; $p$-adic formal groups [See also [[14L05|14Lxx]]]
* ''11S37'' ~Langlands-Weil conjectures, nonabelian class field theory [See also [[11Fxx|11Fxx]], [[22E50|22Exx]]]
* ''11S40'' Zeta functions and $L$-functions [See also [[11M41|11Mxx]], [[19F27|19Fxx]]]
* ''11S45'' Algebras and orders, and their zeta functions [See also [[11R52|11Rxx]], [[11R54|11Rxx]], [[16Hxx|16Hxx]], [[16Kxx|16Kxx]]]
* ''11S70'' $K$-theory of local fields [See also [[19Fxx|19Fxx]]]
* ''11S80'' Other analytic theory (analogues of beta and gamma functions, $p$-adic integration, etc.)
* ''11S82'' ~Non-Archimedean dynamical systems [See mainly [[37Pxx|37Pxx]]]
* ''11S85'' Other nonanalytic theory
* ''11S90'' Prehomogeneous vector spaces
* ''11S99'' None of the above, but in this section
!!![[11|11-XX]]Txx  Finite fields and commutative rings (number-theoretic aspects) {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Txx.html]]}{{moveright{< [[11Sxx |11Sxx]] | [[11-XX |11-XX]] | [[11Uxx |11Uxx]] >}}}
* ''11T06'' Polynomials
* ''11T22'' Cyclotomy
* ''11T23'' Exponential sums
* ''11T24'' Other character sums and Gauss sums
* ''11T30'' Structure theory
* ''11T55'' Arithmetic theory of polynomial rings over finite fields
* ''11T60'' Finite upper half-planes
* ''11T71'' Algebraic coding theory; cryptography
* ''11T99'' None of the above, but in this section
!!![[11|11-XX]]Uxx  Connections with logic {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Uxx.html]]}{{moveright{< [[11Txx |11Txx]] | [[11-XX |11-XX]] | [[11Yxx |11Yxx]] >}}}
* ''11U05'' Decidability [See also [[03B25|03Bxx]]]
* ''11U07'' Ultraproducts [See also [[03C20|03Cxx]]]
* ''11U09'' Model theory [See also [[03Cxx|03Cxx]]]
* ''11U10'' Nonstandard arithmetic [See also [[03H15|03Hxx]]]
* ''11U99'' None of the above, but in this section
!!![[11|11-XX]]Yxx  Computational number theory [See also [[11-04|11-XX]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Yxx.html]]}{{moveright{< [[11Uxx |11Uxx]] | [[11-XX |11-XX]] | [[11Zxx |11Zxx]] >}}}
* ''11Y05'' Factorization
* ''11Y11'' Primality
* ''11Y16'' Algorithms; complexity [See also [[68Q25|68Qxx]]]
* ''11Y35'' Analytic computations
* ''11Y40'' Algebraic number theory computations
* ''11Y50'' Computer solution of Diophantine equations
* ''11Y55'' Calculation of integer sequences
* ''11Y60'' Evaluation of constants
* ''11Y65'' Continued fraction calculations
* ''11Y70'' Values of arithmetic functions; tables
* ''11Y99'' None of the above, but in this section
!!!11-XX Number theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11-XX.html]]}{{moveright{< [[08-XX |08-XX]] | [[MSC |MSC2010]] | [[11Axx |11Axx]] >}}}
* ''11-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''11-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''11-02'' Research exposition (monographs, survey articles)
* ''11-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''11-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''11-06'' Proceedings, conferences, collections, etc.
* ''[[11Axx|11Axx]]''  Elementary number theory {For analogues in number fields, see [[11R04|11Rxx]]}
* ''[[11Bxx|11Bxx]]''  Sequences and sets
* ''[[11Cxx|11Cxx]]''  Polynomials and matrices
* ''[[11Dxx|11Dxx]]''  Diophantine equations [See also [[11Gxx|11Gxx]], [[14Gxx|14Gxx]]]
* ''[[11Exx|11Exx]]''  Forms and linear algebraic groups [See also [[19Gxx|19Gxx]]] {For quadratic forms in linear algebra, see [[15A63|15Axx]]}
* ''[[11Fxx|11Fxx]]''  Discontinuous groups and automorphic forms [See also [[11R39|11Rxx]], [[11S37|11Sxx]], [[14Gxx|14Gxx]], [[14Kxx|14Kxx]], [[22E50|22Exx]], [[22E55|22Exx]], [[30F35|30Fxx]], [[32Nxx|32Nxx]]] {For relations with quadratic forms, see [[11E45|11Exx]]}
* ''[[11Gxx|11Gxx]]''  Arithmetic algebraic geometry (Diophantine geometry) [See also [[11Dxx|11Dxx]], [[14Gxx|14Gxx]], [[14Kxx|14Kxx]]]
* ''[[11Hxx|11Hxx]]''  Geometry of numbers {For applications in coding theory, see [[94B75|94Bxx]]}
* ''[[11Jxx|11Jxx]]''  Diophantine approximation, transcendental number theory [See also [[11K60|11Kxx]]]
* ''[[11Kxx|11Kxx]]''  Probabilistic theory: distribution modulo $1$; metric theory of algorithms
* ''[[11Lxx|11Lxx]]''  Exponential sums and character sums {For finite fields, see [[11Txx|11Txx]]}
* ''[[11Mxx|11Mxx]]''  Zeta and $L$-functions: analytic theory
* ''[[11Nxx|11Nxx]]''  Multiplicative number theory
* ''[[11Pxx|11Pxx]]''  Additive number theory; partitions
* ''[[11Rxx|11Rxx]]''  Algebraic number theory: global fields {For complex multiplication, see [[11G15|11Gxx]]}
* ''[[11Sxx|11Sxx]]''  Algebraic number theory: local and $p$-adic fields
* ''[[11Txx|11Txx]]''  Finite fields and commutative rings (number-theoretic aspects)
* ''[[11Uxx|11Uxx]]''  Connections with logic
* ''[[11Yxx|11Yxx]]''  Computational number theory [See also [[11-04|11-XX]]]
* ''[[11Zxx|11Zxx]]''  Miscellaneous applications of number theory
!!![[11|11-XX]]Zxx  Miscellaneous applications of number theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Zxx.html]]}{{moveright{< [[11Yxx |11Yxx]] | [[11-XX |11-XX]] | [[12-XX |12-XX]] >}}}
* ''11Z05'' Miscellaneous applications of number theory
* ''11Z99'' None of the above, but in this section
!!![[12|12-XX]]Dxx  Real and complex fields {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/12Dxx.html]]}{{moveright{< [[11-XX |11-XX]] | [[12-XX |12-XX]] | [[12Exx |12Exx]] >}}}
* ''12D05'' Polynomials: factorization
* ''12D10'' Polynomials: location of zeros (algebraic theorems) {For the analytic theory, see [[26C10|26Cxx]], [[30C15|30Cxx]]}
* ''12D15'' Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [See also [[11Exx|11Exx]]]
* ''12D99'' None of the above, but in this section
!!![[12|12-XX]]Exx  General field theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/12Exx.html]]}{{moveright{< [[12Dxx |12Dxx]] | [[12-XX |12-XX]] | [[12Fxx |12Fxx]] >}}}
* ''12E05'' Polynomials (irreducibility, etc.)
* ''12E10'' Special polynomials
* ''12E12'' Equations
* ''12E15'' Skew fields, division rings [See also [[11R52|11Rxx]], [[11R54|11Rxx]], [[11S45|11Sxx]], [[16Kxx|16Kxx]]]
* ''12E20'' Finite fields (field-theoretic aspects)
* ''12E25'' Hilbertian fields; Hilbert's irreducibility theorem
* ''12E30'' Field arithmetic
* ''12E99'' None of the above, but in this section
!!![[12|12-XX]]Fxx  Field extensions {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/12Fxx.html]]}{{moveright{< [[12Exx |12Exx]] | [[12-XX |12-XX]] | [[12Gxx |12Gxx]] >}}}
* ''12F05'' Algebraic extensions
* ''12F10'' Separable extensions, Galois theory
* ''12F12'' Inverse Galois theory
* ''12F15'' Inseparable extensions
* ''12F20'' Transcendental extensions
* ''12F99'' None of the above, but in this section
!!![[12|12-XX]]Gxx  Homological methods (field theory) {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/12Gxx.html]]}{{moveright{< [[12Fxx |12Fxx]] | [[12-XX |12-XX]] | [[12Hxx |12Hxx]] >}}}
* ''12G05'' Galois cohomology [See also [[14F22|14Fxx]], [[16Hxx|16Hxx]], [[16K50|16Kxx]]]
* ''12G10'' Cohomological dimension
* ''12G99'' None of the above, but in this section
!!![[12|12-XX]]Hxx  Differential and difference algebra {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/12Hxx.html]]}{{moveright{< [[12Gxx |12Gxx]] | [[12-XX |12-XX]] | [[12Jxx |12Jxx]] >}}}
* ''12H05'' Differential algebra [See also [[13Nxx|13Nxx]]]
* ''12H10'' Difference algebra [See also [[39Axx|39Axx]]]
* ''12H20'' Abstract differential equations [See also [[34Mxx|34Mxx]]]
* ''12H25'' $p$-adic differential equations [See also [[11S80|11Sxx]], [[14G20|14Gxx]]]
* ''12H99'' None of the above, but in this section
!!![[12|12-XX]]Jxx  Topological fields {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/12Jxx.html]]}{{moveright{< [[12Hxx |12Hxx]] | [[12-XX |12-XX]] | [[12Kxx |12Kxx]] >}}}
* ''12J05'' Normed fields
* ''12J10'' Valued fields
* ''12J12'' Formally $p$-adic fields
* ''12J15'' Ordered fields
* ''12J17'' Topological semifields
* ''12J20'' General valuation theory [See also [[13A18|13Axx]]]
* ''12J25'' ~Non-Archimedean valued fields [See also [[30G06|30Gxx]], [[32P05|32Pxx]], [[46S10|46Sxx]], [[47S10|47Sxx]]]
* ''12J27'' ~Krasner-Tate algebras [See mainly [[32P05|32Pxx]]; see also [[46S10|46Sxx]], [[47S10|47Sxx]]]
* ''12J99'' None of the above, but in this section
!!![[12|12-XX]]Kxx  Generalizations of fields {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/12Kxx.html]]}{{moveright{< [[12Jxx |12Jxx]] | [[12-XX |12-XX]] | [[12Lxx |12Lxx]] >}}}
* ''12K05'' Near-fields [See also [[16Y30|16Yxx]]]
* ''12K10'' Semifields [See also [[16Y60|16Yxx]]]
* ''12K99'' None of the above, but in this section
!!![[12|12-XX]]Lxx  Connections with logic {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/12Lxx.html]]}{{moveright{< [[12Kxx |12Kxx]] | [[12-XX |12-XX]] | [[12Yxx |12Yxx]] >}}}
* ''12L05'' Decidability [See also [[03B25|03Bxx]]]
* ''12L10'' Ultraproducts [See also [[03C20|03Cxx]]]
* ''12L12'' Model theory [See also [[03C60|03Cxx]]]
* ''12L15'' Nonstandard arithmetic [See also [[03H15|03Hxx]]]
* ''12L99'' None of the above, but in this section
!!!12-XX Field theory and polynomials {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/12-XX.html]]}{{moveright{< [[11-XX |11-XX]] | [[MSC |MSC2010]] | [[12Dxx |12Dxx]] >}}}
* ''12-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''12-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''12-02'' Research exposition (monographs, survey articles)
* ''12-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''12-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''12-06'' Proceedings, conferences, collections, etc.
* ''[[12Dxx|12Dxx]]''  Real and complex fields
* ''[[12Exx|12Exx]]''  General field theory
* ''[[12Fxx|12Fxx]]''  Field extensions
* ''[[12Gxx|12Gxx]]''  Homological methods (field theory)
* ''[[12Hxx|12Hxx]]''  Differential and difference algebra
* ''[[12Jxx|12Jxx]]''  Topological fields
* ''[[12Kxx|12Kxx]]''  Generalizations of fields
* ''[[12Lxx|12Lxx]]''  Connections with logic
* ''[[12Yxx|12Yxx]]''  Computational aspects of field theory and polynomials
!!![[12|12-XX]]Yxx  Computational aspects of field theory and polynomials {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/12Yxx.html]]}{{moveright{< [[12Lxx |12Lxx]] | [[12-XX |12-XX]] | [[13-XX |13-XX]] >}}}
* ''12Y05'' Computational aspects of field theory and polynomials
* ''12Y99'' None of the above, but in this section
!!![[13|13-XX]]Axx  General commutative ring theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/13Axx.html]]}{{moveright{< [[12-XX |12-XX]] | [[13-XX |13-XX]] | [[13Bxx |13Bxx]] >}}}
* ''13A02'' Graded rings [See also [[16W50|16Wxx]]]
* ''13A05'' Divisibility; factorizations [See also [[13F15|13Fxx]]]
* ''13A15'' Ideals; multiplicative ideal theory
* ''13A18'' Valuations and their generalizations [See also [[12J20|12Jxx]]]
* ''13A30'' Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
* ''13A35'' Characteristic $p$ methods (Frobenius endomorphism) and reduction to characteristic $p$; tight closure [See also [[13B22|13Bxx]]]
* ''13A50'' Actions of groups on commutative rings; invariant theory [See also [[14L24|14Lxx]]]
* ''13A99'' None of the above, but in this section
!!![[13|13-XX]]Bxx  Ring extensions and related topics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/13Bxx.html]]}{{moveright{< [[13Axx |13Axx]] | [[13-XX |13-XX]] | [[13Cxx |13Cxx]] >}}}
* ''13B02'' Extension theory
* ''13B05'' Galois theory
* ''13B10'' Morphisms
* ''13B21'' Integral dependence; going up, going down
* ''13B22'' Integral closure of rings and ideals [See also [[13A35|13Axx]]]; integrally closed rings, related rings (Japanese, etc.)
* ''13B25'' Polynomials over commutative rings [See also [[11C08|11Cxx]], [[11T06|11Txx]], [[13F20|13Fxx]], [[13M10|13Mxx]]]
* ''13B30'' Rings of fractions and localization [See also [[16S85|16Sxx]]]
* ''13B35'' Completion [See also [[13J10|13Jxx]]]
* ''13B40'' Étale and flat extensions; Henselization; Artin approximation [See also [[13J15|13Jxx]], [[14B12|14Bxx]], [[14B25|14Bxx]]]
* ''13B99'' None of the above, but in this section
!!![[13|13-XX]]Cxx  Theory of modules and ideals {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/13Cxx.html]]}{{moveright{< [[13Bxx |13Bxx]] | [[13-XX |13-XX]] | [[13Dxx |13Dxx]] >}}}
* ''13C05'' Structure, classification theorems
* ''13C10'' Projective and free modules and ideals [See also [[19A13|19Axx]]]
* ''13C11'' Injective and flat modules and ideals
* ''13C12'' Torsion modules and ideals
* ''13C13'' Other special types
* ''13C14'' ~Cohen-Macaulay modules [See also [[13H10|13Hxx]]]
* ''13C15'' Dimension theory, depth, related rings (catenary, etc.)
* ''13C20'' Class groups [See also [[11R29|11Rxx]]]
* ''13C40'' Linkage, complete intersections and determinantal ideals [See also [[14M06|14Mxx]], [[14M10|14Mxx]], [[14M12|14Mxx]]]
* ''13C60'' Module categories
* ''13C99'' None of the above, but in this section
!!![[13|13-XX]]Dxx  Homological methods {For noncommutative rings, see [[16Exx|16Exx]]; for general categories, see [[18Gxx|18Gxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/13Dxx.html]]}{{moveright{< [[13Cxx |13Cxx]] | [[13-XX |13-XX]] | [[13Exx |13Exx]] >}}}
* ''13D02'' Syzygies, resolutions, complexes
* ''13D03'' (Co)homology of commutative rings and algebras (e.g., Hochschild, ~André-Quillen, cyclic, dihedral, etc.)
* ''13D05'' Homological dimension
* ''13D07'' Homological functors on modules (Tor, Ext, etc.)
* ''13D09'' Derived categories
* ''13D10'' Deformations and infinitesimal methods [See also [[14B10|14Bxx]], [[14B12|14Bxx]], [[14D15|14Dxx]], [[32Gxx|32Gxx]]]
* ''13D15'' Grothendieck groups, $K$-theory [See also [[14C35|14Cxx]], [[18F30|18Fxx]], [[19Axx|19Axx]], [[19D50|19Dxx]]]
* ''13D22'' Homological conjectures (intersection theorems)
* ''13D30'' Torsion theory [See also [[13C12|13Cxx]], [[18E40|18Exx]]]
* ''13D40'' ~Hilbert-Samuel and ~Hilbert-Kunz functions; Poincaré series
* ''13D45'' Local cohomology [See also [[14B15|14Bxx]]]
* ''13D99'' None of the above, but in this section
!!![[13|13-XX]]Exx  Chain conditions, finiteness conditions {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/13Exx.html]]}{{moveright{< [[13Dxx |13Dxx]] | [[13-XX |13-XX]] | [[13Fxx |13Fxx]] >}}}
* ''13E05'' Noetherian rings and modules
* ''13E10'' Artinian rings and modules, finite-dimensional algebras
* ''13E15'' Rings and modules of finite generation or presentation; number of generators
* ''13E99'' None of the above, but in this section
!!![[13|13-XX]]Fxx  Arithmetic rings and other special rings {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/13Fxx.html]]}{{moveright{< [[13Exx |13Exx]] | [[13-XX |13-XX]] | [[13Gxx |13Gxx]] >}}}
* ''13F05'' Dedekind, Prüfer, Krull and Mori rings and their generalizations
* ''13F07'' Euclidean rings and generalizations
* ''13F10'' Principal ideal rings
* ''13F15'' Rings defined by factorization properties (e.g., atomic, factorial, half-factorial) [See also [[13A05|13Axx]], [[14M05|14Mxx]]]
* ''13F20'' Polynomial rings and ideals; rings of integer-valued polynomials [See also [[11C08|11Cxx]], [[13B25|13Bxx]]]
* ''13F25'' Formal power series rings [See also [[13J05|13Jxx]]]
* ''13F30'' Valuation rings [See also [[13A18|13Axx]]]
* ''13F35'' Witt vectors and related rings
* ''13F40'' Excellent rings
* ''13F45'' Seminormal rings
* ''13F50'' Rings with straightening laws, Hodge algebras
* ''13F55'' ~Stanley-Reisner face rings; simplicial complexes [See also [[55U10|55Uxx]]]
* ''13F60'' Cluster algebras
* ''13F99'' None of the above, but in this section
!!![[13|13-XX]]Gxx  Integral domains {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/13Gxx.html]]}{{moveright{< [[13Fxx |13Fxx]] | [[13-XX |13-XX]] | [[13Hxx |13Hxx]] >}}}
* ''13G05'' Integral domains
* ''13G99'' None of the above, but in this section
!!![[13|13-XX]]Hxx  Local rings and semilocal rings {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/13Hxx.html]]}{{moveright{< [[13Gxx |13Gxx]] | [[13-XX |13-XX]] | [[13Jxx |13Jxx]] >}}}
* ''13H05'' Regular local rings
* ''13H10'' Special types (~Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also [[14M05|14Mxx]]]
* ''13H15'' Multiplicity theory and related topics [See also [[14C17|14Cxx]]]
* ''13H99'' None of the above, but in this section
!!![[13|13-XX]]Jxx  Topological rings and modules [See also [[16W60|16Wxx]], [[16W80|16Wxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/13Jxx.html]]}{{moveright{< [[13Hxx |13Hxx]] | [[13-XX |13-XX]] | [[13Lxx |13Lxx]] >}}}
* ''13J05'' Power series rings [See also [[13F25|13Fxx]]]
* ''13J07'' Analytical algebras and rings [See also [[32B05|32Bxx]]]
* ''13J10'' Complete rings, completion [See also [[13B35|13Bxx]]]
* ''13J15'' Henselian rings [See also [[13B40|13Bxx]]]
* ''13J20'' Global topological rings
* ''13J25'' Ordered rings [See also [[06F25|06Fxx]]]
* ''13J30'' Real algebra [See also [[12D15|12Dxx]], [[14Pxx|14Pxx]]]
* ''13J99'' None of the above, but in this section
!!![[13|13-XX]]Lxx  Applications of logic to commutative algebra [See also [[03Cxx|03Cxx]], [[03Hxx|03Hxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/13Lxx.html]]}{{moveright{< [[13Jxx |13Jxx]] | [[13-XX |13-XX]] | [[13Mxx |13Mxx]] >}}}
* ''13L05'' Applications of logic to commutative algebra [See also [[03Cxx|03Cxx]], [[03Hxx|03Hxx]]]
* ''13L99'' None of the above, but in this section
!!![[13|13-XX]]Mxx  Finite commutative rings {For number-theoretic aspects, see [[11Txx|11Txx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/13Mxx.html]]}{{moveright{< [[13Lxx |13Lxx]] | [[13-XX |13-XX]] | [[13Nxx |13Nxx]] >}}}
* ''13M05'' Structure
* ''13M10'' Polynomials
* ''13M99'' None of the above, but in this section
!!![[13|13-XX]]Nxx  Differential algebra [See also [[12H05|12Hxx]], [[14F10|14Fxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/13Nxx.html]]}{{moveright{< [[13Mxx |13Mxx]] | [[13-XX |13-XX]] | [[13Pxx |13Pxx]] >}}}
* ''13N05'' Modules of differentials
* ''13N10'' Rings of differential operators and their modules [See also [[16S32|16Sxx]], [[32C38|32Cxx]]]
* ''13N15'' Derivations
* ''13N99'' None of the above, but in this section
!!!13-XX Commutative algebra {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/13-XX.html]]}{{moveright{< [[12-XX |12-XX]] | [[MSC |MSC2010]] | [[13Axx |13Axx]] >}}}
* ''13-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''13-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''13-02'' Research exposition (monographs, survey articles)
* ''13-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''13-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''13-06'' Proceedings, conferences, collections, etc.
* ''[[13Axx|13Axx]]''  General commutative ring theory
* ''[[13Bxx|13Bxx]]''  Ring extensions and related topics
* ''[[13Cxx|13Cxx]]''  Theory of modules and ideals
* ''[[13Dxx|13Dxx]]''  Homological methods {For noncommutative rings, see [[16Exx|16Exx]]; for general categories, see [[18Gxx|18Gxx]]}
* ''[[13Exx|13Exx]]''  Chain conditions, finiteness conditions
* ''[[13Fxx|13Fxx]]''  Arithmetic rings and other special rings
* ''[[13Gxx|13Gxx]]''  Integral domains
* ''[[13Hxx|13Hxx]]''  Local rings and semilocal rings
* ''[[13Jxx|13Jxx]]''  Topological rings and modules [See also [[16W60|16Wxx]], [[16W80|16Wxx]]]
* ''[[13Lxx|13Lxx]]''  Applications of logic to commutative algebra [See also [[03Cxx|03Cxx]], [[03Hxx|03Hxx]]]
* ''[[13Mxx|13Mxx]]''  Finite commutative rings {For number-theoretic aspects, see [[11Txx|11Txx]]}
* ''[[13Nxx|13Nxx]]''  Differential algebra [See also [[12H05|12Hxx]], [[14F10|14Fxx]]]
* ''[[13Pxx|13Pxx]]''  Computational aspects and applications [See also [[14Qxx|14Qxx]], [[68W30|68Wxx]]]
!!![[13|13-XX]]Pxx  Computational aspects and applications [See also [[14Qxx|14Qxx]], [[68W30|68Wxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/13Pxx.html]]}{{moveright{< [[13Nxx |13Nxx]] | [[13-XX |13-XX]] | [[14-XX |14-XX]] >}}}
* ''13P05'' Polynomials, factorization [See also [[12Y05|12Yxx]]]
* ''13P10'' Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
* ''13P15'' Solving polynomial systems; resultants
* ''13P20'' Computational homological algebra [See also [[13Dxx|13Dxx]]]
* ''13P25'' Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)
* ''13P99'' None of the above, but in this section
!!![[14|14-XX]]Axx  Foundations {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/14Axx.html]]}{{moveright{< [[13-XX |13-XX]] | [[14-XX |14-XX]] | [[14Bxx |14Bxx]] >}}}
* ''14A05'' Relevant commutative algebra [See also [[13-XX|13-XX]]]
* ''14A10'' Varieties and morphisms
* ''14A15'' Schemes and morphisms
* ''14A20'' Generalizations (algebraic spaces, stacks)
* ''14A22'' Noncommutative algebraic geometry [See also [[16S38|16Sxx]]]
* ''14A25'' Elementary questions
* ''14A99'' None of the above, but in this section
!!![[14|14-XX]]Bxx  Local theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/14Bxx.html]]}{{moveright{< [[14Axx |14Axx]] | [[14-XX |14-XX]] | [[14Cxx |14Cxx]] >}}}
* ''14B05'' Singularities [See also [[14E15|14Exx]], [[14H20|14Hxx]], [[14J17|14Jxx]], [[32Sxx|32Sxx]], [[58Kxx|58Kxx]]]
* ''14B07'' Deformations of singularities [See also [[14D15|14Dxx]], [[32S30|32Sxx]]]
* ''14B10'' Infinitesimal methods [See also [[13D10|13Dxx]]]
* ''14B12'' Local deformation theory, Artin approximation, etc. [See also [[13B40|13Bxx]], [[13D10|13Dxx]]]
* ''14B15'' Local cohomology [See also [[13D45|13Dxx]], [[32C36|32Cxx]]]
* ''14B20'' Formal neighborhoods
* ''14B25'' Local structure of morphisms: étale, flat, etc. [See also [[13B40|13Bxx]]]
* ''14B99'' None of the above, but in this section
!!![[14|14-XX]]Cxx  Cycles and subschemes {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/14Cxx.html]]}{{moveright{< [[14Bxx |14Bxx]] | [[14-XX |14-XX]] | [[14Dxx |14Dxx]] >}}}
* ''14C05'' Parametrization (Chow and Hilbert schemes)
* ''14C15'' (Equivariant) Chow groups and rings; motives
* ''14C17'' Intersection theory, characteristic classes, intersection multiplicities [See also [[13H15|13Hxx]]]
* ''14C20'' Divisors, linear systems, invertible sheaves
* ''14C21'' Pencils, nets, webs [See also [[53A60|53Axx]]]
* ''14C22'' Picard groups
* ''14C25'' Algebraic cycles
* ''14C30'' Transcendental methods, Hodge theory [See also [[14D07|14Dxx]], [[32G20|32Gxx]], [[32J25|32Jxx]], [[32S35|32Sxx]]], Hodge conjecture
* ''14C34'' Torelli problem [See also [[32G20|32Gxx]]]
* ''14C35'' Applications of methods of algebraic $K$-theory [See also [[19Exx|19Exx]]]
* ''14C40'' ~Riemann-Roch theorems [See also [[19E20|19Exx]], [[19L10|19Lxx]]]
* ''14C99'' None of the above, but in this section
!!![[14|14-XX]]Dxx  Families, fibrations {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/14Dxx.html]]}{{moveright{< [[14Cxx |14Cxx]] | [[14-XX |14-XX]] | [[14Exx |14Exx]] >}}}
* ''14D05'' Structure of families (~Picard-Lefschetz, monodromy, etc.)
* ''14D06'' Fibrations, degenerations
* ''14D07'' Variation of Hodge structures [See also [[32G20|32Gxx]]]
* ''14D10'' Arithmetic ground fields (finite, local, global)
* ''14D15'' Formal methods; deformations [See also [[13D10|13Dxx]], [[14B07|14Bxx]], [[32Gxx|32Gxx]]]
* ''14D20'' Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see [[32G13|32Gxx]]}
* ''14D21'' Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) [See also [[32L25|32Lxx]], [[81Txx|81Txx]]]
* ''14D22'' Fine and coarse moduli spaces
* ''14D23'' Stacks and moduli problems
* ''14D24'' Geometric Langlands program: algebro-geometric aspects [See also [[22E57|22Exx]]]
* ''14D99'' None of the above, but in this section
!!![[14|14-XX]]Exx  Birational geometry {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/14Exx.html]]}{{moveright{< [[14Dxx |14Dxx]] | [[14-XX |14-XX]] | [[14Fxx |14Fxx]] >}}}
* ''14E05'' Rational and birational maps
* ''14E07'' Birational automorphisms, Cremona group and generalizations
* ''14E08'' Rationality questions [See also [[14M20|14Mxx]]]
* ''14E15'' Global theory and resolution of singularities [See also [[14B05|14Bxx]], [[32S20|32Sxx]], [[32S45|32Sxx]]]
* ''14E16'' McKay correspondence
* ''14E18'' Arcs and motivic integration
* ''14E20'' Coverings [See also [[14H30|14Hxx]]]
* ''14E22'' Ramification problems [See also [[11S15|11Sxx]]]
* ''14E25'' Embeddings
* ''14E30'' Minimal model program (Mori theory, extremal rays)
* ''14E99'' None of the above, but in this section
!!![[14|14-XX]]Fxx  (Co)homology theory [See also [[13Dxx|13Dxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/14Fxx.html]]}{{moveright{< [[14Exx |14Exx]] | [[14-XX |14-XX]] | [[14Gxx |14Gxx]] >}}}
* ''14F05'' Sheaves, derived categories of sheaves and related constructions [See also [[14H60|14Hxx]], [[14J60|14Jxx]], [[18F20|18Fxx]], [[32Lxx|32Lxx]], [[46M20|46Mxx]]]
* ''14F10'' Differentials and other special sheaves; D-modules; ~Bernstein-Sato ideals and polynomials [See also [[13Nxx|13Nxx]], [[32C38|32Cxx]]]
* ''14F17'' Vanishing theorems [See also [[32L20|32Lxx]]]
* ''14F18'' Multiplier ideals
* ''14F20'' Étale and other Grothendieck topologies and (co)homologies
* ''14F22'' Brauer groups of schemes [See also [[12G05|12Gxx]], [[16K50|16Kxx]]]
* ''14F25'' Classical real and complex (co)homology
* ''14F30'' $p$-adic cohomology, crystalline cohomology
* ''14F35'' Homotopy theory; fundamental groups [See also [[14H30|14Hxx]]]
* ''14F40'' de Rham cohomology [See also [[14C30|14Cxx]], [[32C35|32Cxx]], [[32L10|32Lxx]]]
* ''14F42'' Motivic cohomology; motivic homotopy theory [See also [[19E15|19Exx]]]
* ''14F43'' Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
* ''14F45'' Topological properties
* ''14F99'' None of the above, but in this section
!!![[14|14-XX]]Gxx  Arithmetic problems. Diophantine geometry [See also [[11Dxx|11Dxx]], [[11Gxx|11Gxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/14Gxx.html]]}{{moveright{< [[14Fxx |14Fxx]] | [[14-XX |14-XX]] | [[14Hxx |14Hxx]] >}}}
* ''14G05'' Rational points
* ''14G10'' Zeta-functions and related questions [See also [[11G40|11Gxx]]] (~Birch-Swinnerton-Dyer conjecture)
* ''14G15'' Finite ground fields
* ''14G17'' Positive characteristic ground fields
* ''14G20'' Local ground fields
* ''14G22'' Rigid analytic geometry
* ''14G25'' Global ground fields
* ''14G27'' Other nonalgebraically closed ground fields
* ''14G32'' Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)
* ''14G35'' Modular and Shimura varieties [See also [[11F41|11Fxx]], [[11F46|11Fxx]], [[11G18|11Gxx]]]
* ''14G40'' Arithmetic varieties and schemes; Arakelov theory; heights [See also [[11G50|11Gxx]], [[37P30|37Pxx]]]
* ''14G50'' Applications to coding theory and cryptography [See also [[94A60|94Axx]], [[94B27|94Bxx]], [[94B40|94Bxx]]]
* ''14G99'' None of the above, but in this section
!!![[14|14-XX]]Hxx  Curves {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/14Hxx.html]]}{{moveright{< [[14Gxx |14Gxx]] | [[14-XX |14-XX]] | [[14Jxx |14Jxx]] >}}}
* ''14H05'' Algebraic functions; function fields [See also [[11R58|11Rxx]]]
* ''14H10'' Families, moduli (algebraic)
* ''14H15'' Families, moduli (analytic) [See also [[30F10|30Fxx]], [[32G15|32Gxx]]]
* ''14H20'' Singularities, local rings [See also [[13Hxx|13Hxx]], [[14B05|14Bxx]]]
* ''14H25'' Arithmetic ground fields [See also [[11Dxx|11Dxx]], [[11G05|11Gxx]], [[14Gxx|14Gxx]]]
* ''14H30'' Coverings, fundamental group [See also [[14E20|14Exx]], [[14F35|14Fxx]]]
* ''14H37'' Automorphisms
* ''14H40'' Jacobians, Prym varieties [See also [[32G20|32Gxx]]]
* ''14H42'' Theta functions; Schottky problem [See also [[14K25|14Kxx]], [[32G20|32Gxx]]]
* ''14H45'' Special curves and curves of low genus
* ''14H50'' Plane and space curves
* ''14H51'' Special divisors (gonality, ~Brill-Noether theory)
* ''14H52'' Elliptic curves [See also [[11G05|11Gxx]], [[11G07|11Gxx]], [[14Kxx|14Kxx]]]
* ''14H55'' Riemann surfaces; Weierstrass points; gap sequences [See also [[30Fxx|30Fxx]]]
* ''14H57'' Dessins d'enfants theory {For arithmetic aspects, see [[11G32|11Gxx]]}
* ''14H60'' Vector bundles on curves and their moduli [See also [[14D20|14Dxx]], [[14F05|14Fxx]]]
* ''14H70'' Relationships with integrable systems
* ''14H81'' Relationships with physics
* ''14H99'' None of the above, but in this section
!!![[14|14-XX]]Jxx  Surfaces and higher-dimensional varieties {For analytic theory, see [[32Jxx|32Jxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/14Jxx.html]]}{{moveright{< [[14Hxx |14Hxx]] | [[14-XX |14-XX]] | [[14Kxx |14Kxx]] >}}}
* ''14J10'' Families, moduli, classification: algebraic theory
* ''14J15'' Moduli, classification: analytic theory; relations with modular forms [See also [[32G13|32Gxx]]]
* ''14J17'' Singularities [See also [[14B05|14Bxx]], [[14E15|14Exx]]]
* ''14J20'' Arithmetic ground fields [See also [[11Dxx|11Dxx]], [[11G25|11Gxx]], [[11G35|11Gxx]], [[14Gxx|14Gxx]]]
* ''14J25'' Special surfaces {For Hilbert modular surfaces, see [[14G35|14Gxx]]}
* ''14J26'' Rational and ruled surfaces
* ''14J27'' Elliptic surfaces
* ''14J28'' $K3$ surfaces and Enriques surfaces
* ''14J29'' Surfaces of general type
* ''14J30'' $3$-folds [See also [[32Q25|32Qxx]]]
* ''14J32'' ~Calabi-Yau manifolds
* ''14J33'' Mirror symmetry [See also [[11G42|11Gxx]], [[53D37|53Dxx]]]
* ''14J35'' $4$-folds
* ''14J40'' $n$-folds ($n>4$)
* ''14J45'' Fano varieties
* ''14J50'' Automorphisms of surfaces and higher-dimensional varieties
* ''14J60'' Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also [[14D20|14Dxx]], [[14F05|14Fxx]], [[32Lxx|32Lxx]]]
* ''14J70'' Hypersurfaces
* ''14J80'' Topology of surfaces (Donaldson polynomials, ~Seiberg-Witten invariants)
* ''14J81'' Relationships with physics
* ''14J99'' None of the above, but in this section
!!![[14|14-XX]]Kxx  Abelian varieties and schemes {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/14Kxx.html]]}{{moveright{< [[14Jxx |14Jxx]] | [[14-XX |14-XX]] | [[14Lxx |14Lxx]] >}}}
* ''14K02'' Isogeny
* ''14K05'' Algebraic theory
* ''14K10'' Algebraic moduli, classification [See also [[11G15|11Gxx]]]
* ''14K12'' Subvarieties
* ''14K15'' Arithmetic ground fields [See also [[11Dxx|11Dxx]], [[11Fxx|11Fxx]], [[11G10|11Gxx]], [[14Gxx|14Gxx]]]
* ''14K20'' Analytic theory; abelian integrals and differentials
* ''14K22'' Complex multiplication [See also [[11G15|11Gxx]]]
* ''14K25'' Theta functions [See also [[14H42|14Hxx]]]
* ''14K30'' Picard schemes, higher Jacobians [See also [[14H40|14Hxx]], [[32G20|32Gxx]]]
* ''14K99'' None of the above, but in this section
!!![[14|14-XX]]Lxx  Algebraic groups {For linear algebraic groups, see [[20Gxx|20Gxx]]; for Lie algebras, see [[17B45|17Bxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/14Lxx.html]]}{{moveright{< [[14Kxx |14Kxx]] | [[14-XX |14-XX]] | [[14Mxx |14Mxx]] >}}}
* ''14L05'' Formal groups, $p$-divisible groups [See also [[55N22|55Nxx]]]
* ''14L10'' Group varieties
* ''14L15'' Group schemes
* ''14L17'' Affine algebraic groups, hyperalgebra constructions [See also [[17B45|17Bxx]], [[18D35|18Dxx]]]
* ''14L24'' Geometric invariant theory [See also [[13A50|13Axx]]]
* ''14L30'' Group actions on varieties or schemes (quotients) [See also [[13A50|13Axx]], [[14L24|14Lxx]], [[14M17|14Mxx]]]
* ''14L35'' Classical groups (geometric aspects) [See also [[20Gxx|20Gxx]], [[51N30|51Nxx]]]
* ''14L40'' Other algebraic groups (geometric aspects)
* ''14L99'' None of the above, but in this section
!!![[14|14-XX]]Mxx  Special varieties {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/14Mxx.html]]}{{moveright{< [[14Lxx |14Lxx]] | [[14-XX |14-XX]] | [[14Nxx |14Nxx]] >}}}
* ''14M05'' Varieties defined by ring conditions (factorial, ~Cohen-Macaulay, seminormal) [See also [[13F15|13Fxx]], [[13F45|13Fxx]], [[13H10|13Hxx]]]
* ''14M06'' Linkage [See also [[13C40|13Cxx]]]
* ''14M07'' Low codimension problems
* ''14M10'' Complete intersections [See also [[13C40|13Cxx]]]
* ''14M12'' Determinantal varieties [See also [[13C40|13Cxx]]]
* ''14M15'' Grassmannians, Schubert varieties, flag manifolds [See also [[32M10|32Mxx]], [[51M35|51Mxx]]]
* ''14M17'' Homogeneous spaces and generalizations [See also [[32M10|32Mxx]], [[53C30|53Cxx]], [[57T15|57Txx]]]
* ''14M20'' Rational and unirational varieties [See also [[14E08|14Exx]]]
* ''14M22'' Rationally connected varieties
* ''14M25'' Toric varieties, Newton polyhedra [See also [[52B20|52Bxx]]]
* ''14M27'' Compactifications; symmetric and spherical varieties
* ''14M30'' Supervarieties [See also [[32C11|32Cxx]], [[58A50|58Axx]]]
* ''14M99'' None of the above, but in this section
!!![[14|14-XX]]Nxx  Projective and enumerative geometry [See also [[51-XX|51-XX]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/14Nxx.html]]}{{moveright{< [[14Mxx |14Mxx]] | [[14-XX |14-XX]] | [[14Pxx |14Pxx]] >}}}
* ''14N05'' Projective techniques [See also [[51N35|51Nxx]]]
* ''14N10'' Enumerative problems (combinatorial problems)
* ''14N15'' Classical problems, Schubert calculus
* ''14N20'' Configurations and arrangements of linear subspaces
* ''14N25'' Varieties of low degree
* ''14N30'' Adjunction problems
* ''14N35'' ~Gromov-Witten invariants, quantum cohomology, ~Gopakumar-Vafa invariants, ~Donaldson-Thomas invariants [See also [[53D45|53Dxx]]]
* ''14N99'' None of the above, but in this section
!!![[14|14-XX]]Pxx  Real algebraic and real analytic geometry {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/14Pxx.html]]}{{moveright{< [[14Nxx |14Nxx]] | [[14-XX |14-XX]] | [[14Qxx |14Qxx]] >}}}
* ''14P05'' Real algebraic sets [See also [[12D15|12Dxx]], [[13J30|13Jxx]]]
* ''14P10'' Semialgebraic sets and related spaces
* ''14P15'' Real analytic and semianalytic sets [See also [[32B20|32Bxx]], [[32C05|32Cxx]]]
* ''14P20'' Nash functions and manifolds [See also [[32C07|32Cxx]], [[58A07|58Axx]]]
* ''14P25'' Topology of real algebraic varieties
* ''14P99'' None of the above, but in this section
!!![[14|14-XX]]Qxx  Computational aspects in algebraic geometry [See also [[12Y05|12Yxx]], [[13Pxx|13Pxx]], [[68W30|68Wxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/14Qxx.html]]}{{moveright{< [[14Pxx |14Pxx]] | [[14-XX |14-XX]] | [[14Rxx |14Rxx]] >}}}
* ''14Q05'' Curves
* ''14Q10'' Surfaces, hypersurfaces
* ''14Q15'' Higher-dimensional varieties
* ''14Q20'' Effectivity, complexity
* ''14Q99'' None of the above, but in this section
!!![[14|14-XX]]Rxx  Affine geometry {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/14Rxx.html]]}{{moveright{< [[14Qxx |14Qxx]] | [[14-XX |14-XX]] | [[14Txx |14Txx]] >}}}
* ''14R05'' Classification of affine varieties
* ''14R10'' Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
* ''14R15'' Jacobian problem [See also [[13F20|13Fxx]]]
* ''14R20'' Group actions on affine varieties [See also [[13A50|13Axx]], [[14L30|14Lxx]]]
* ''14R25'' Affine fibrations [See also [[14D06|14Dxx]]]
* ''14R99'' None of the above, but in this section
!!!14-XX Algebraic geometry {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/14-XX.html]]}{{moveright{< [[13-XX |13-XX]] | [[MSC |MSC2010]] | [[14Axx |14Axx]] >}}}
* ''14-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''14-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''14-02'' Research exposition (monographs, survey articles)
* ''14-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''14-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''14-06'' Proceedings, conferences, collections, etc.
* ''[[14Axx|14Axx]]''  Foundations
* ''[[14Bxx|14Bxx]]''  Local theory
* ''[[14Cxx|14Cxx]]''  Cycles and subschemes
* ''[[14Dxx|14Dxx]]''  Families, fibrations
* ''[[14Exx|14Exx]]''  Birational geometry
* ''[[14Fxx|14Fxx]]''  (Co)homology theory [See also [[13Dxx|13Dxx]]]
* ''[[14Gxx|14Gxx]]''  Arithmetic problems. Diophantine geometry [See also [[11Dxx|11Dxx]], [[11Gxx|11Gxx]]]
* ''[[14Hxx|14Hxx]]''  Curves
* ''[[14Jxx|14Jxx]]''  Surfaces and higher-dimensional varieties {For analytic theory, see [[32Jxx|32Jxx]]}
* ''[[14Kxx|14Kxx]]''  Abelian varieties and schemes
* ''[[14Lxx|14Lxx]]''  Algebraic groups {For linear algebraic groups, see [[20Gxx|20Gxx]]; for Lie algebras, see [[17B45|17Bxx]]}
* ''[[14Mxx|14Mxx]]''  Special varieties
* ''[[14Nxx|14Nxx]]''  Projective and enumerative geometry [See also [[51-XX|51-XX]]]
* ''[[14Pxx|14Pxx]]''  Real algebraic and real analytic geometry
* ''[[14Qxx|14Qxx]]''  Computational aspects in algebraic geometry [See also [[12Y05|12Yxx]], [[13Pxx|13Pxx]], [[68W30|68Wxx]]]
* ''[[14Rxx|14Rxx]]''  Affine geometry
* ''[[14Txx|14Txx]]''  Tropical geometry [See also [[12K10|12Kxx]], [[14M25|14Mxx]], [[14N10|14Nxx]], [[52B20|52Bxx]]]
!!![[14|14-XX]]Txx  Tropical geometry [See also [[12K10|12Kxx]], [[14M25|14Mxx]], [[14N10|14Nxx]], [[52B20|52Bxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/14Txx.html]]}{{moveright{< [[14Rxx |14Rxx]] | [[14-XX |14-XX]] | [[15-XX |15-XX]] >}}}
* ''14T05'' Tropical geometry [See also [[12K10|12Kxx]], [[14M25|14Mxx]], [[14N10|14Nxx]], [[52B20|52Bxx]]]
* ''14T99'' None of the above, but in this section
!!![[15|15-XX]]Axx  Basic linear algebra {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/15Axx.html]]}{{moveright{< [[14-XX |14-XX]] | [[15-XX |15-XX]] | [[15Bxx |15Bxx]] >}}}
* ''15A03'' Vector spaces, linear dependence, rank
* ''15A04'' Linear transformations, semilinear transformations
* ''15A06'' Linear equations
* ''15A09'' Matrix inversion, generalized inverses
* ''15A12'' Conditioning of matrices [See also [[65F35|65Fxx]]]
* ''15A15'' Determinants, permanents, other special matrix functions [See also [[19B10|19Bxx]], [[19B14|19Bxx]]]
* ''15A16'' Matrix exponential and similar functions of matrices
* ''15A18'' Eigenvalues, singular values, and eigenvectors
* ''15A21'' Canonical forms, reductions, classification
* ''15A22'' Matrix pencils [See also [[47A56|47Axx]]]
* ''15A23'' Factorization of matrices
* ''15A24'' Matrix equations and identities
* ''15A27'' Commutativity
* ''15A29'' Inverse problems
* ''15A30'' Algebraic systems of matrices [See also [[16S50|16Sxx]], [[20Gxx|20Gxx]], [[20Hxx|20Hxx]]]
* ''15A39'' Linear inequalities
* ''15A42'' Inequalities involving eigenvalues and eigenvectors
* ''15A45'' Miscellaneous inequalities involving matrices
* ''15A54'' Matrices over function rings in one or more variables
* ''15A60'' Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also [[65F35|65Fxx]], [[65J05|65Jxx]]]
* ''15A63'' Quadratic and bilinear forms, inner products [See mainly [[11Exx|11Exx]]]
* ''15A66'' Clifford algebras, spinors
* ''15A69'' Multilinear algebra, tensor products
* ''15A72'' Vector and tensor algebra, theory of invariants [See also [[13A50|13Axx]], [[14L24|14Lxx]]]
* ''15A75'' Exterior algebra, Grassmann algebras
* ''15A78'' Other algebras built from modules
* ''15A80'' Max-plus and related algebras
* ''15A83'' Matrix completion problems
* ''15A86'' Linear preserver problems
* ''15A99'' Miscellaneous topics
!!!15-XX Linear and multilinear algebra; matrix theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/15-XX.html]]}{{moveright{< [[14-XX |14-XX]] | [[MSC |MSC2010]] | [[15Axx |15Axx]] >}}}
* ''15-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''15-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''15-02'' Research exposition (monographs, survey articles)
* ''15-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''15-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''15-06'' Proceedings, conferences, collections, etc.
* ''[[15Axx|15Axx]]''  Basic linear algebra
* ''[[15Bxx|15Bxx]]''  Special matrices
!!![[15|15-XX]]Bxx  Special matrices {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/15Bxx.html]]}{{moveright{< [[15Axx |15Axx]] | [[15-XX |15-XX]] | [[16-XX |16-XX]] >}}}
* ''15B05'' Toeplitz, Cauchy, and related matrices
* ''15B10'' Orthogonal matrices
* ''15B15'' Fuzzy matrices
* ''15B33'' Matrices over special rings (quaternions, finite fields, etc.)
* ''15B34'' Boolean and Hadamard matrices
* ''15B35'' Sign pattern matrices
* ''15B36'' Matrices of integers [See also [[11C20|11Cxx]]]
* ''15B48'' Positive matrices and their generalizations; cones of matrices
* ''15B51'' Stochastic matrices
* ''15B52'' Random matrices
* ''15B57'' Hermitian, skew-Hermitian, and related matrices
* ''15B99'' None of the above, but in this section
!!![[16|16-XX]]Bxx  General and miscellaneous {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/16Bxx.html]]}{{moveright{< [[15-XX |15-XX]] | [[16-XX |16-XX]] | [[16Dxx |16Dxx]] >}}}
* ''16B50'' Category-theoretic methods and results (except as in [[16D90|16Dxx]]) [See also [[18-XX|18-XX]]]
* ''16B70'' Applications of logic [See also [[03Cxx|03Cxx]]]
* ''16B99'' None of the above, but in this section
!!![[16|16-XX]]Dxx  Modules, bimodules and ideals {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/16Dxx.html]]}{{moveright{< [[16Bxx |16Bxx]] | [[16-XX |16-XX]] | [[16Exx |16Exx]] >}}}
* ''16D10'' General module theory
* ''16D20'' Bimodules
* ''16D25'' Ideals
* ''16D30'' Infinite-dimensional simple rings (except as in [[16Kxx|16Kxx]])
* ''16D40'' Free, projective, and flat modules and ideals [See also [[19A13|19Axx]]]
* ''16D50'' Injective modules, self-injective rings [See also [[16L60|16Lxx]]]
* ''16D60'' Simple and semisimple modules, primitive rings and ideals
* ''16D70'' Structure and classification (except as in [[16Gxx|16Gxx]]), direct sum decomposition, cancellation
* ''16D80'' Other classes of modules and ideals [See also [[16G50|16Gxx]]]
* ''16D90'' Module categories [See also [[16Gxx|16Gxx]], [[16S90|16Sxx]]]; module theory in a category-theoretic context; Morita equivalence and duality
* ''16D99'' None of the above, but in this section
!!![[16|16-XX]]Exx  Homological methods {For commutative rings, see [[13Dxx|13Dxx]]; for general categories, see [[18Gxx|18Gxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/16Exx.html]]}{{moveright{< [[16Dxx |16Dxx]] | [[16-XX |16-XX]] | [[16Gxx |16Gxx]] >}}}
* ''16E05'' Syzygies, resolutions, complexes
* ''16E10'' Homological dimension
* ''16E20'' Grothendieck groups, $K$-theory, etc. [See also [[18F30|18Fxx]], [[19Axx|19Axx]], [[19D50|19Dxx]]]
* ''16E30'' Homological functors on modules (Tor, Ext, etc.)
* ''16E35'' Derived categories
* ''16E40'' (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
* ''16E45'' Differential graded algebras and applications
* ''16E50'' von Neumann regular rings and generalizations
* ''16E60'' Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.
* ''16E65'' Homological conditions on rings (generalizations of regular, Gorenstein, ~Cohen-Macaulay rings, etc.)
* ''16E99'' None of the above, but in this section
!!![[16|16-XX]]Gxx  Representation theory of rings and algebras {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/16Gxx.html]]}{{moveright{< [[16Exx |16Exx]] | [[16-XX |16-XX]] | [[16Hxx |16Hxx]] >}}}
* ''16G10'' Representations of Artinian rings
* ''16G20'' Representations of quivers and partially ordered sets
* ''16G30'' Representations of orders, lattices, algebras over commutative rings [See also [[16Hxx|16Hxx]]]
* ''16G50'' ~Cohen-Macaulay modules
* ''16G60'' Representation type (finite, tame, wild, etc.)
* ''16G70'' ~Auslander-Reiten sequences (almost split sequences) and ~Auslander-Reiten quivers
* ''16G99'' None of the above, but in this section
!!![[16|16-XX]]Hxx  Algebras and orders {For arithmetic aspects, see [[11R52|11Rxx]], [[11R54|11Rxx]], [[11S45|11Sxx]]; for representation theory, see [[16G30|16Gxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/16Hxx.html]]}{{moveright{< [[16Gxx |16Gxx]] | [[16-XX |16-XX]] | [[16Kxx |16Kxx]] >}}}
* ''16H05'' Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)
* ''16H10'' Orders in separable algebras
* ''16H15'' Commutative orders
* ''16H20'' Lattices over orders
* ''16H99'' None of the above, but in this section
!!![[16|16-XX]]Kxx  Division rings and semisimple Artin rings [See also [[12E15|12Exx]], [[15A30|15Axx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/16Kxx.html]]}{{moveright{< [[16Hxx |16Hxx]] | [[16-XX |16-XX]] | [[16Lxx |16Lxx]] >}}}
* ''16K20'' Finite-dimensional {For crossed products, see [[16S35|16Sxx]]}
* ''16K40'' Infinite-dimensional and general
* ''16K50'' Brauer groups [See also [[12G05|12Gxx]], [[14F22|14Fxx]]]
* ''16K99'' None of the above, but in this section
!!![[16|16-XX]]Lxx  Local rings and generalizations {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/16Lxx.html]]}{{moveright{< [[16Kxx |16Kxx]] | [[16-XX |16-XX]] | [[16Nxx |16Nxx]] >}}}
* ''16L30'' Noncommutative local and semilocal rings, perfect rings
* ''16L60'' ~Quasi-Frobenius rings [See also [[16D50|16Dxx]]]
* ''16L99'' None of the above, but in this section
!!![[16|16-XX]]Nxx  Radicals and radical properties of rings {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/16Nxx.html]]}{{moveright{< [[16Lxx |16Lxx]] | [[16-XX |16-XX]] | [[16Pxx |16Pxx]] >}}}
* ''16N20'' Jacobson radical, quasimultiplication
* ''16N40'' Nil and nilpotent radicals, sets, ideals, rings
* ''16N60'' Prime and semiprime rings [See also [[16D60|16Dxx]], [[16U10|16Uxx]]]
* ''16N80'' General radicals and rings {For radicals in module categories, see [[16S90|16Sxx]]}
* ''16N99'' None of the above, but in this section
!!![[16|16-XX]]Pxx  Chain conditions, growth conditions, and other forms of finiteness {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/16Pxx.html]]}{{moveright{< [[16Nxx |16Nxx]] | [[16-XX |16-XX]] | [[16Rxx |16Rxx]] >}}}
* ''16P10'' Finite rings and finite-dimensional algebras {For semisimple, see [[16K20|16Kxx]]; for commutative, see [[11Txx|11Txx]], [[13Mxx|13Mxx]]}
* ''16P20'' Artinian rings and modules
* ''16P40'' Noetherian rings and modules
* ''16P50'' Localization and Noetherian rings [See also [[16U20|16Uxx]]]
* ''16P60'' Chain conditions on annihilators and summands: Goldie-type conditions [See also [[16U20|16Uxx]]], Krull dimension
* ''16P70'' Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence
* ''16P90'' Growth rate, Gelfand-Kirillov dimension
* ''16P99'' None of the above, but in this section
!!![[16|16-XX]]Rxx  Rings with polynomial identity {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/16Rxx.html]]}{{moveright{< [[16Pxx |16Pxx]] | [[16-XX |16-XX]] | [[16Sxx |16Sxx]] >}}}
* ''16R10'' $T$-ideals, identities, varieties of rings and algebras
* ''16R20'' Semiprime p.i. rings, rings embeddable in matrices over commutative rings
* ''16R30'' Trace rings and invariant theory
* ''16R40'' Identities other than those of matrices over commutative rings
* ''16R50'' Other kinds of identities (generalized polynomial, rational, involution)
* ''16R60'' Functional identities
* ''16R99'' None of the above, but in this section
!!![[16|16-XX]]Sxx  Rings and algebras arising under various constructions {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/16Sxx.html]]}{{moveright{< [[16Rxx |16Rxx]] | [[16-XX |16-XX]] | [[16Txx |16Txx]] >}}}
* ''16S10'' Rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)
* ''16S15'' Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)
* ''16S20'' Centralizing and normalizing extensions
* ''16S30'' Universal enveloping algebras of Lie algebras [See mainly [[17B35|17Bxx]]]
* ''16S32'' Rings of differential operators [See also [[13N10|13Nxx]], [[32C38|32Cxx]]]
* ''16S34'' Group rings [See also [[20C05|20Cxx]], [[20C07|20Cxx]]], Laurent polynomial rings
* ''16S35'' Twisted and skew group rings, crossed products
* ''16S36'' Ordinary and skew polynomial rings and semigroup rings [See also [[20M25|20Mxx]]]
* ''16S37'' Quadratic and Koszul algebras
* ''16S38'' Rings arising from non-commutative algebraic geometry [See also [[14A22|14Axx]]]
* ''16S40'' Smash products of general Hopf actions [See also [[16T05|16Txx]]]
* ''16S50'' Endomorphism rings; matrix rings [See also [[15-XX|15-XX]]]
* ''16S60'' Rings of functions, subdirect products, sheaves of rings
* ''16S70'' Extensions of rings by ideals
* ''16S80'' Deformations of rings [See also [[13D10|13Dxx]], [[14D15|14Dxx]]]
* ''16S85'' Rings of fractions and localizations [See also [[13B30|13Bxx]]]
* ''16S90'' Torsion theories; radicals on module categories [See also [[13D30|13Dxx]], [[18E40|18Exx]]] {For radicals of rings, see [[16Nxx|16Nxx]]}
* ''16S99'' None of the above, but in this section
!!![[16|16-XX]]Txx  Hopf algebras, quantum groups and related topics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/16Txx.html]]}{{moveright{< [[16Sxx |16Sxx]] | [[16-XX |16-XX]] | [[16Uxx |16Uxx]] >}}}
* ''16T05'' Hopf algebras and their applications [See also [[16S40|16Sxx]], [[57T05|57Txx]]]
* ''16T10'' Bialgebras
* ''16T15'' Coalgebras and comodules; corings
* ''16T20'' Ring-theoretic aspects of quantum groups [See also [[17B37|17Bxx]], [[20G42|20Gxx]], [[81R50|81Rxx]]]
* ''16T25'' Yang-Baxter equations
* ''16T30'' Connections with combinatorics
* ''16T99'' None of the above, but in this section
!!![[16|16-XX]]Uxx  Conditions on elements {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/16Uxx.html]]}{{moveright{< [[16Txx |16Txx]] | [[16-XX |16-XX]] | [[16Wxx |16Wxx]] >}}}
* ''16U10'' Integral domains
* ''16U20'' Ore rings, multiplicative sets, Ore localization
* ''16U30'' Divisibility, noncommutative ~UFDs
* ''16U60'' Units, groups of units
* ''16U70'' Center, normalizer (invariant elements)
* ''16U80'' Generalizations of commutativity
* ''16U99'' None of the above, but in this section
!!![[16|16-XX]]Wxx  Rings and algebras with additional structure {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/16Wxx.html]]}{{moveright{< [[16Uxx |16Uxx]] | [[16-XX |16-XX]] | [[16Yxx |16Yxx]] >}}}
* ''16W10'' Rings with involution; Lie, Jordan and other nonassociative structures [See also [[17B60|17Bxx]], [[17C50|17Cxx]], [[46Kxx|46Kxx]]]
* ''16W20'' Automorphisms and endomorphisms
* ''16W22'' Actions of groups and semigroups; invariant theory
* ''16W25'' Derivations, actions of Lie algebras
* ''16W50'' Graded rings and modules
* ''16W55'' “Super” (or “skew”) structure [See also [[17A70|17Axx]], [[17Bxx|17Bxx]], [[17C70|17Cxx]]] {For exterior algebras, see [[15A75|15Axx]]; for Clifford algebras, see [[11E88|11Exx]], [[15A66|15Axx]]}
* ''16W60'' Valuations, completions, formal power series and related constructions [See also [[13Jxx|13Jxx]]]
* ''16W70'' Filtered rings; filtrational and graded techniques
* ''16W80'' Topological and ordered rings and modules [See also [[06F25|06Fxx]], [[13Jxx|13Jxx]]]
* ''16W99'' None of the above, but in this section
!!![[16|16-XX]]Yxx  Generalizations {For nonassociative rings, see [[17-XX|17-XX]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/16Yxx.html]]}{{moveright{< [[16Wxx |16Wxx]] | [[16-XX |16-XX]] | [[16Zxx |16Zxx]] >}}}
* ''16Y30'' Near-rings [See also [[12K05|12Kxx]]]
* ''16Y60'' Semirings [See also [[12K10|12Kxx]]]
* ''16Y99'' None of the above, but in this section
!!!16-XX Associative rings and algebras {For the commutative case, see [[13-XX|13-XX]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/16-XX.html]]}{{moveright{< [[15-XX |15-XX]] | [[MSC |MSC2010]] | [[16Bxx |16Bxx]] >}}}
* ''16-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''16-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''16-02'' Research exposition (monographs, survey articles)
* ''16-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''16-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''16-06'' Proceedings, conferences, collections, etc.
* ''[[16Bxx|16Bxx]]''  General and miscellaneous
* ''[[16Dxx|16Dxx]]''  Modules, bimodules and ideals
* ''[[16Exx|16Exx]]''  Homological methods {For commutative rings, see [[13Dxx|13Dxx]]; for general categories, see [[18Gxx|18Gxx]]}
* ''[[16Gxx|16Gxx]]''  Representation theory of rings and algebras
* ''[[16Hxx|16Hxx]]''  Algebras and orders {For arithmetic aspects, see [[11R52|11Rxx]], [[11R54|11Rxx]], [[11S45|11Sxx]]; for representation theory, see [[16G30|16Gxx]]}
* ''[[16Kxx|16Kxx]]''  Division rings and semisimple Artin rings [See also [[12E15|12Exx]], [[15A30|15Axx]]]
* ''[[16Lxx|16Lxx]]''  Local rings and generalizations
* ''[[16Nxx|16Nxx]]''  Radicals and radical properties of rings
* ''[[16Pxx|16Pxx]]''  Chain conditions, growth conditions, and other forms of finiteness
* ''[[16Rxx|16Rxx]]''  Rings with polynomial identity
* ''[[16Sxx|16Sxx]]''  Rings and algebras arising under various constructions
* ''[[16Txx|16Txx]]''  Hopf algebras, quantum groups and related topics
* ''[[16Uxx|16Uxx]]''  Conditions on elements
* ''[[16Wxx|16Wxx]]''  Rings and algebras with additional structure
* ''[[16Yxx|16Yxx]]''  Generalizations {For nonassociative rings, see [[17-XX|17-XX]]}
* ''[[16Zxx|16Zxx]]''  Computational aspects of associative rings
!!![[16|16-XX]]Zxx  Computational aspects of associative rings {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/16Zxx.html]]}{{moveright{< [[16Yxx |16Yxx]] | [[16-XX |16-XX]] | [[17-XX |17-XX]] >}}}
* ''16Z05'' Computational aspects of associative rings [See also [[68W30|68Wxx]]]
* ''16Z99'' None of the above, but in this section
!!![[17|17-XX]]Axx  General nonassociative rings {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/17Axx.html]]}{{moveright{< [[16-XX |16-XX]] | [[17-XX |17-XX]] | [[17Bxx |17Bxx]] >}}}
* ''17A01'' General theory
* ''17A05'' Power-associative rings
* ''17A15'' Noncommutative Jordan algebras
* ''17A20'' Flexible algebras
* ''17A30'' Algebras satisfying other identities
* ''17A32'' Leibniz algebras
* ''17A35'' Division algebras
* ''17A36'' Automorphisms, derivations, other operators
* ''17A40'' Ternary compositions
* ''17A42'' Other $n$-ary compositions $(n \ge 3)$
* ''17A45'' Quadratic algebras (but not quadratic Jordan algebras)
* ''17A50'' Free algebras
* ''17A60'' Structure theory
* ''17A65'' Radical theory
* ''17A70'' Superalgebras
* ''17A75'' Composition algebras
* ''17A80'' Valued algebras
* ''17A99'' None of the above, but in this section
!!![[17|17-XX]]Bxx  Lie algebras and Lie superalgebras {For Lie groups, see [[22Exx|22Exx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/17Bxx.html]]}{{moveright{< [[17Axx |17Axx]] | [[17-XX |17-XX]] | [[17Cxx |17Cxx]] >}}}
* ''17B01'' Identities, free Lie (super)algebras
* ''17B05'' Structure theory
* ''17B08'' Coadjoint orbits; nilpotent varieties
* ''17B10'' Representations, algebraic theory (weights)
* ''17B15'' Representations, analytic theory
* ''17B20'' Simple, semisimple, reductive (super)algebras
* ''17B22'' Root systems
* ''17B25'' Exceptional (super)algebras
* ''17B30'' Solvable, nilpotent (super)algebras
* ''17B35'' Universal enveloping (super)algebras [See also [[16S30|16Sxx]]]
* ''17B37'' Quantum groups (quantized enveloping algebras) and related deformations [See also [[16T20|16Txx]], [[20G42|20Gxx]], [[81R50|81Rxx]], [[82B23|82Bxx]]]
* ''17B40'' Automorphisms, derivations, other operators
* ''17B45'' Lie algebras of linear algebraic groups [See also [[14Lxx|14Lxx]] and [[20Gxx|20Gxx]]]
* ''17B50'' Modular Lie (super)algebras
* ''17B55'' Homological methods in Lie (super)algebras
* ''17B56'' Cohomology of Lie (super)algebras
* ''17B60'' Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also [[16W10|16Wxx]], [[17C40|17Cxx]], [[17C50|17Cxx]]]
* ''17B62'' Lie bialgebras; Lie coalgebras
* ''17B63'' Poisson algebras
* ''17B65'' Infinite-dimensional Lie (super)algebras [See also [[22E65|22Exx]]]
* ''17B66'' Lie algebras of vector fields and related (super) algebras
* ''17B67'' ~Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
* ''17B68'' Virasoro and related algebras
* ''17B69'' Vertex operators; vertex operator algebras and related structures
* ''17B70'' Graded Lie (super)algebras
* ''17B75'' Color Lie (super)algebras
* ''17B80'' Applications to integrable systems
* ''17B81'' Applications to physics
* ''17B99'' None of the above, but in this section
!!![[17|17-XX]]Cxx  Jordan algebras (algebras, triples and pairs) {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/17Cxx.html]]}{{moveright{< [[17Bxx |17Bxx]] | [[17-XX |17-XX]] | [[17Dxx |17Dxx]] >}}}
* ''17C05'' Identities and free Jordan structures
* ''17C10'' Structure theory
* ''17C17'' Radicals
* ''17C20'' Simple, semisimple algebras
* ''17C27'' Idempotents, Peirce decompositions
* ''17C30'' Associated groups, automorphisms
* ''17C36'' Associated manifolds
* ''17C37'' Associated geometries
* ''17C40'' Exceptional Jordan structures
* ''17C50'' Jordan structures associated with other structures [See also [[16W10|16Wxx]]]
* ''17C55'' Finite-dimensional structures
* ''17C60'' Division algebras
* ''17C65'' Jordan structures on Banach spaces and algebras [See also [[46H70|46Hxx]], [[46L70|46Lxx]]]
* ''17C70'' Super structures
* ''17C90'' Applications to physics
* ''17C99'' None of the above, but in this section
!!!17-XX Nonassociative rings and algebras {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/17-XX.html]]}{{moveright{< [[16-XX |16-XX]] | [[MSC |MSC2010]] | [[17Axx |17Axx]] >}}}
* ''17-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''17-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''17-02'' Research exposition (monographs, survey articles)
* ''17-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''17-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''17-06'' Proceedings, conferences, collections, etc.
* ''17-08'' Computational methods
* ''[[17Axx|17Axx]]''  General nonassociative rings
* ''[[17Bxx|17Bxx]]''  Lie algebras and Lie superalgebras {For Lie groups, see [[22Exx|22Exx]]}
* ''[[17Cxx|17Cxx]]''  Jordan algebras (algebras, triples and pairs)
* ''[[17Dxx|17Dxx]]''  Other nonassociative rings and algebras
!!![[17|17-XX]]Dxx  Other nonassociative rings and algebras {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/17Dxx.html]]}{{moveright{< [[17Cxx |17Cxx]] | [[17-XX |17-XX]] | [[18-XX |18-XX]] >}}}
* ''17D05'' Alternative rings
* ''17D10'' Mal'cev (Mal'tsev) rings and algebras
* ''17D15'' Right alternative rings
* ''17D20'' $(\gamma, \delta)$-rings, including $(1,-1)$-rings
* ''17D25'' Lie-admissible algebras
* ''17D92'' Genetic algebras
* ''17D99'' None of the above, but in this section
!!![[18|18-XX]]Axx  General theory of categories and functors {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/18Axx.html]]}{{moveright{< [[17-XX |17-XX]] | [[18-XX |18-XX]] | [[18Bxx |18Bxx]] >}}}
* ''18A05'' Definitions, generalizations
* ''18A10'' Graphs, diagram schemes, precategories [See especially [[20L05|20Lxx]]]
* ''18A15'' Foundations, relations to logic and deductive systems [See also [[03-XX|03-XX]]]
* ''18A20'' Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
* ''18A22'' Special properties of functors (faithful, full, etc.)
* ''18A23'' Natural morphisms, dinatural morphisms
* ''18A25'' Functor categories, comma categories
* ''18A30'' Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
* ''18A32'' Factorization of morphisms, substructures, quotient structures, congruences, amalgams
* ''18A35'' Categories admitting limits (complete categories), functors preserving limits, completions
* ''18A40'' Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
* ''18A99'' None of the above, but in this section
!!![[18|18-XX]]Bxx  Special categories {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/18Bxx.html]]}{{moveright{< [[18Axx |18Axx]] | [[18-XX |18-XX]] | [[18Cxx |18Cxx]] >}}}
* ''18B05'' Category of sets, characterizations [See also [[03-XX|03-XX]]]
* ''18B10'' Category of relations, additive relations
* ''18B15'' Embedding theorems, universal categories [See also [[18E20|18Exx]]]
* ''18B20'' Categories of machines, automata, operative categories [See also [[03D05|03Dxx]], [[68Qxx|68Qxx]]]
* ''18B25'' Topoi [See also [[03G30|03Gxx]]]
* ''18B30'' Categories of topological spaces and continuous mappings [See also [[54-XX|54-XX]]]
* ''18B35'' Preorders, orders and lattices (viewed as categories) [See also [[06-XX|06-XX]]]
* ''18B40'' Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also [[20Axx|20Axx]], [[20L05|20Lxx]], [[20Mxx|20Mxx]]]
* ''18B99'' None of the above, but in this section
!!![[18|18-XX]]Cxx  Categories and theories {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/18Cxx.html]]}{{moveright{< [[18Bxx |18Bxx]] | [[18-XX |18-XX]] | [[18Dxx |18Dxx]] >}}}
* ''18C05'' Equational categories [See also [[03C05|03Cxx]], [[08C05|08Cxx]]]
* ''18C10'' Theories (e.g. algebraic theories), structure, and semantics [See also [[03G30|03Gxx]]]
* ''18C15'' Triples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples [See also [[18Gxx|18Gxx]]]
* ''18C20'' Algebras and Kleisli categories associated with monads
* ''18C30'' Sketches and generalizations
* ''18C35'' Accessible and locally presentable categories
* ''18C50'' Categorical semantics of formal languages [See also [[68Q55|68Qxx]], [[68Q65|68Qxx]]]
* ''18C99'' None of the above, but in this section
!!![[18|18-XX]]Dxx  Categories with structure {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/18Dxx.html]]}{{moveright{< [[18Cxx |18Cxx]] | [[18-XX |18-XX]] | [[18Exx |18Exx]] >}}}
* ''18D05'' Double categories, $2$-categories, bicategories and generalizations
* ''18D10'' Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also [[19D23|19Dxx]]]
* ''18D15'' Closed categories (closed monoidal and Cartesian closed categories, etc.)
* ''18D20'' Enriched categories (over closed or monoidal categories)
* ''18D25'' Strong functors, strong adjunctions
* ''18D30'' Fibered categories
* ''18D35'' Structured objects in a category (group objects, etc.)
* ''18D50'' Operads [See also [[55P48|55Pxx]]]
* ''18D99'' None of the above, but in this section
!!![[18|18-XX]]Exx  Abelian categories {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/18Exx.html]]}{{moveright{< [[18Dxx |18Dxx]] | [[18-XX |18-XX]] | [[18Fxx |18Fxx]] >}}}
* ''18E05'' Preadditive, additive categories
* ''18E10'' Exact categories, abelian categories
* ''18E15'' Grothendieck categories
* ''18E20'' Embedding theorems [See also [[18B15|18Bxx]]]
* ''18E25'' Derived functors and satellites
* ''18E30'' Derived categories, triangulated categories
* ''18E35'' Localization of categories
* ''18E40'' Torsion theories, radicals [See also [[13D30|13Dxx]], [[16S90|16Sxx]]]
* ''18E99'' None of the above, but in this section
!!![[18|18-XX]]Fxx  Categories and geometry {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/18Fxx.html]]}{{moveright{< [[18Exx |18Exx]] | [[18-XX |18-XX]] | [[18Gxx |18Gxx]] >}}}
* ''18F05'' Local categories and functors
* ''18F10'' Grothendieck topologies [See also [[14F20|14Fxx]]]
* ''18F15'' Abstract manifolds and fiber bundles [See also [[55Rxx|55Rxx]], [[57Pxx|57Pxx]]]
* ''18F20'' Presheaves and sheaves [See also [[14F05|14Fxx]], [[32C35|32Cxx]], [[32L10|32Lxx]], [[54B40|54Bxx]], [[55N30|55Nxx]]]
* ''18F25'' Algebraic $K$-theory and $L$-theory [See also [[11Exx|11Exx]], [[11R70|11Rxx]], [[11S70|11Sxx]], [[12-XX|12-XX]], [[13D15|13Dxx]], [[14Cxx|14Cxx]], [[16E20|16Exx]], [[19-XX|19-XX]], [[46L80|46Lxx]], [[57R65|57Rxx]], [[57R67|57Rxx]]]
* ''18F30'' Grothendieck groups [See also [[13D15|13Dxx]], [[16E20|16Exx]], [[19Axx|19Axx]]]
* ''18F99'' None of the above, but in this section
!!!18-XX Category theory; homological algebra {For commutative rings see [[13Dxx|13Dxx]], for associative rings [[16Exx|16Exx]], for groups [[20Jxx|20Jxx]], for topological groups and related structures [[57Txx|57Txx]]; see also [[55Nxx|55Nxx]] and [[55Uxx|55Uxx]] for algebraic topology} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/18-XX.html]]}{{moveright{< [[17-XX |17-XX]] | [[MSC |MSC2010]] | [[18Axx |18Axx]] >}}}
* ''18-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''18-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''18-02'' Research exposition (monographs, survey articles)
* ''18-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''18-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''18-06'' Proceedings, conferences, collections, etc.
* ''[[18Axx|18Axx]]''  General theory of categories and functors
* ''[[18Bxx|18Bxx]]''  Special categories
* ''[[18Cxx|18Cxx]]''  Categories and theories
* ''[[18Dxx|18Dxx]]''  Categories with structure
* ''[[18Exx|18Exx]]''  Abelian categories
* ''[[18Fxx|18Fxx]]''  Categories and geometry
* ''[[18Gxx|18Gxx]]''  Homological algebra [See also [[13Dxx|13Dxx]], [[16Exx|16Exx]], [[20Jxx|20Jxx]], [[55Nxx|55Nxx]], [[55Uxx|55Uxx]], [[57Txx|57Txx]]]
!!![[18|18-XX]]Gxx  Homological algebra [See also [[13Dxx|13Dxx]], [[16Exx|16Exx]], [[20Jxx|20Jxx]], [[55Nxx|55Nxx]], [[55Uxx|55Uxx]], [[57Txx|57Txx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/18Gxx.html]]}{{moveright{< [[18Fxx |18Fxx]] | [[18-XX |18-XX]] | [[19-XX |19-XX]] >}}}
* ''18G05'' Projectives and injectives [See also [[13C10|13Cxx]], [[13C11|13Cxx]], [[16D40|16Dxx]], [[16D50|16Dxx]]]
* ''18G10'' Resolutions; derived functors [See also [[13D02|13Dxx]], [[16E05|16Exx]], [[18E25|18Exx]]]
* ''18G15'' Ext and Tor, generalizations, Künneth formula [See also [[55U25|55Uxx]]]
* ''18G20'' Homological dimension [See also [[13D05|13Dxx]], [[16E10|16Exx]]]
* ''18G25'' Relative homological algebra, projective classes
* ''18G30'' Simplicial sets, simplicial objects (in a category) [See also [[55U10|55Uxx]]]
* ''18G35'' Chain complexes [See also [[18E30|18Exx]], [[55U15|55Uxx]]]
* ''18G40'' Spectral sequences, hypercohomology [See also [[55Txx|55Txx]]]
* ''18G50'' Nonabelian homological algebra
* ''18G55'' Homotopical algebra
* ''18G60'' Other (co)homology theories [See also [[19D55|19Dxx]], [[46L80|46Lxx]], [[58J20|58Jxx]], [[58J22|58Jxx]]]
* ''18G99'' None of the above, but in this section
!!![[19|19-XX]]Axx  Grothendieck groups and $K_0$ [See also [[13D15|13Dxx]], [[18F30|18Fxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/19Axx.html]]}{{moveright{< [[18-XX |18-XX]] | [[19-XX |19-XX]] | [[19Bxx |19Bxx]] >}}}
* ''19A13'' Stability for projective modules [See also [[13C10|13Cxx]]]
* ''19A15'' Efficient generation
* ''19A22'' Frobenius induction, Burnside and representation rings
* ''19A31'' $K_0$ of group rings and orders
* ''19A49'' $K_0$ of other rings
* ''19A99'' None of the above, but in this section
!!![[19|19-XX]]Bxx  Whitehead groups and $K_1$ {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/19Bxx.html]]}{{moveright{< [[19Axx |19Axx]] | [[19-XX |19-XX]] | [[19Cxx |19Cxx]] >}}}
* ''19B10'' Stable range conditions
* ''19B14'' Stability for linear groups
* ''19B28'' $K_1$ of group rings and orders [See also [[57Q10|57Qxx]]]
* ''19B37'' Congruence subgroup problems [See also [[20H05|20Hxx]]]
* ''19B99'' None of the above, but in this section
!!![[19|19-XX]]Cxx  Steinberg groups and $K_2$ {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/19Cxx.html]]}{{moveright{< [[19Bxx |19Bxx]] | [[19-XX |19-XX]] | [[19Dxx |19Dxx]] >}}}
* ''19C09'' Central extensions and Schur multipliers
* ''19C20'' Symbols, presentations and stability of $K_2$
* ''19C30'' $K_2$ and the Brauer group
* ''19C40'' Excision for $K_2$
* ''19C99'' None of the above, but in this section
!!![[19|19-XX]]Dxx  Higher algebraic $K$-theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/19Dxx.html]]}{{moveright{< [[19Cxx |19Cxx]] | [[19-XX |19-XX]] | [[19Exx |19Exx]] >}}}
* ''19D06'' $Q$- and plus-constructions
* ''19D10'' Algebraic $K$-theory of spaces
* ''19D23'' Symmetric monoidal categories [See also [[18D10|18Dxx]]]
* ''19D25'' ~Karoubi-Villamayor-Gersten $K$-theory
* ''19D35'' Negative $K$-theory, NK and Nil
* ''19D45'' Higher symbols, Milnor $K$-theory
* ''19D50'' Computations of higher $K$-theory of rings [See also [[13D15|13Dxx]], [[16E20|16Exx]]]
* ''19D55'' $K$-theory and homology; cyclic homology and cohomology [See also [[18G60|18Gxx]]]
* ''19D99'' None of the above, but in this section
!!![[19|19-XX]]Exx  $K$-theory in geometry {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/19Exx.html]]}{{moveright{< [[19Dxx |19Dxx]] | [[19-XX |19-XX]] | [[19Fxx |19Fxx]] >}}}
* ''19E08'' $K$-theory of schemes [See also [[14C35|14Cxx]]]
* ''19E15'' Algebraic cycles and motivic cohomology [See also [[14C25|14Cxx]], [[14C35|14Cxx]], [[14F42|14Fxx]]]
* ''19E20'' Relations with cohomology theories [See also [[14Fxx|14Fxx]]]
* ''19E99'' None of the above, but in this section
!!![[19|19-XX]]Fxx  $K$-theory in number theory [See also [[11R70|11Rxx]], [[11S70|11Sxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/19Fxx.html]]}{{moveright{< [[19Exx |19Exx]] | [[19-XX |19-XX]] | [[19Gxx |19Gxx]] >}}}
* ''19F05'' Generalized class field theory [See also [[11G45|11Gxx]]]
* ''19F15'' Symbols and arithmetic [See also [[11R37|11Rxx]]]
* ''19F27'' Étale cohomology, higher regulators, zeta and $L$-functions [See also [[11G40|11Gxx]], [[11R42|11Rxx]], [[11S40|11Sxx]], [[14F20|14Fxx]], [[14G10|14Gxx]]]
* ''19F99'' None of the above, but in this section
!!![[19|19-XX]]Gxx  $K$-theory of forms [See also [[11Exx|11Exx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/19Gxx.html]]}{{moveright{< [[19Fxx |19Fxx]] | [[19-XX |19-XX]] | [[19Jxx |19Jxx]] >}}}
* ''19G05'' Stability for quadratic modules
* ''19G12'' Witt groups of rings [See also [[11E81|11Exx]]]
* ''19G24'' $L$-theory of group rings [See also [[11E81|11Exx]]]
* ''19G38'' Hermitian $K$-theory, relations with $K$-theory of rings
* ''19G99'' None of the above, but in this section
!!![[19|19-XX]]Jxx  Obstructions from topology {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/19Jxx.html]]}{{moveright{< [[19Gxx |19Gxx]] | [[19-XX |19-XX]] | [[19Kxx |19Kxx]] >}}}
* ''19J05'' Finiteness and other obstructions in $K_0$
* ''19J10'' Whitehead (and related) torsion
* ''19J25'' Surgery obstructions [See also [[57R67|57Rxx]]]
* ''19J35'' Obstructions to group actions
* ''19J99'' None of the above, but in this section
!!![[19|19-XX]]Kxx  $K$-theory and operator algebras [See mainly [[46L80|46Lxx]], and also [[46M20|46Mxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/19Kxx.html]]}{{moveright{< [[19Jxx |19Jxx]] | [[19-XX |19-XX]] | [[19Lxx |19Lxx]] >}}}
* ''19K14'' $K_0$ as an ordered group, traces
* ''19K33'' EXT and $K$-homology [See also [[55N22|55Nxx]]]
* ''19K35'' Kasparov theory ($KK$-theory) [See also [[58J22|58Jxx]]]
* ''19K56'' Index theory [See also [[58J20|58Jxx]], [[58J22|58Jxx]]]
* ''19K99'' None of the above, but in this section
!!![[19|19-XX]]Lxx  Topological $K$-theory [See also [[55N15|55Nxx]], [[55R50|55Rxx]], [[55S25|55Sxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/19Lxx.html]]}{{moveright{< [[19Kxx |19Kxx]] | [[19-XX |19-XX]] | [[19Mxx |19Mxx]] >}}}
* ''19L10'' ~Riemann-Roch theorems, Chern characters
* ''19L20'' $J$-homomorphism, Adams operations [See also [[55Q50|55Qxx]]]
* ''19L41'' Connective $K$-theory, cobordism [See also [[55N22|55Nxx]]]
* ''19L47'' Equivariant $K$-theory [See also [[55N91|55Nxx]], [[55P91|55Pxx]], [[55Q91|55Qxx]], [[55R91|55Rxx]], [[55S91|55Sxx]]]
* ''19L50'' Twisted $K$-theory; differential $K$-theory
* ''19L64'' Computations, geometric applications
* ''19L99'' None of the above, but in this section
!!!19-XX $K$-theory [See also [[16E20|16Exx]], [[18F25|18Fxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/19-XX.html]]}{{moveright{< [[18-XX |18-XX]] | [[MSC |MSC2010]] | [[19Axx |19Axx]] >}}}
* ''19-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''19-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''19-02'' Research exposition (monographs, survey articles)
* ''19-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''19-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''19-06'' Proceedings, conferences, collections, etc.
* ''[[19Axx|19Axx]]''  Grothendieck groups and $K_0$ [See also [[13D15|13Dxx]], [[18F30|18Fxx]]]
* ''[[19Bxx|19Bxx]]''  Whitehead groups and $K_1$
* ''[[19Cxx|19Cxx]]''  Steinberg groups and $K_2$
* ''[[19Dxx|19Dxx]]''  Higher algebraic $K$-theory
* ''[[19Exx|19Exx]]''  $K$-theory in geometry
* ''[[19Fxx|19Fxx]]''  $K$-theory in number theory [See also [[11R70|11Rxx]], [[11S70|11Sxx]]]
* ''[[19Gxx|19Gxx]]''  $K$-theory of forms [See also [[11Exx|11Exx]]]
* ''[[19Jxx|19Jxx]]''  Obstructions from topology
* ''[[19Kxx|19Kxx]]''  $K$-theory and operator algebras [See mainly [[46L80|46Lxx]], and also [[46M20|46Mxx]]]
* ''[[19Lxx|19Lxx]]''  Topological $K$-theory [See also [[55N15|55Nxx]], [[55R50|55Rxx]], [[55S25|55Sxx]]]
* ''[[19Mxx|19Mxx]]''  Miscellaneous applications of $K$-theory
!!![[19|19-XX]]Mxx  Miscellaneous applications of $K$-theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/19Mxx.html]]}{{moveright{< [[19Lxx |19Lxx]] | [[19-XX |19-XX]] | [[20-XX |20-XX]] >}}}
* ''19M05'' Miscellaneous applications of $K$-theory
* ''19M99'' None of the above, but in this section
!!![[20|20-XX]]Axx  Foundations {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/20Axx.html]]}{{moveright{< [[19-XX |19-XX]] | [[20-XX |20-XX]] | [[20Bxx |20Bxx]] >}}}
* ''20A05'' Axiomatics and elementary properties
* ''20A10'' Metamathematical considerations {For word problems, see [[20F10|20Fxx]]}
* ''20A15'' Applications of logic to group theory
* ''20A99'' None of the above, but in this section
!!![[20|20-XX]]Bxx  Permutation groups {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/20Bxx.html]]}{{moveright{< [[20Axx |20Axx]] | [[20-XX |20-XX]] | [[20Cxx |20Cxx]] >}}}
* ''20B05'' General theory for finite groups
* ''20B07'' General theory for infinite groups
* ''20B10'' Characterization theorems
* ''20B15'' Primitive groups
* ''20B20'' Multiply transitive finite groups
* ''20B22'' Multiply transitive infinite groups
* ''20B25'' Finite automorphism groups of algebraic, geometric, or combinatorial structures [See also [[05Bxx|05Bxx]], [[12F10|12Fxx]], [[20G40|20Gxx]], [[20H30|20Hxx]], [[51-XX|51-XX]]]
* ''20B27'' Infinite automorphism groups [See also [[12F10|12Fxx]]]
* ''20B30'' Symmetric groups
* ''20B35'' Subgroups of symmetric groups
* ''20B40'' Computational methods
* ''20B99'' None of the above, but in this section
!!![[20|20-XX]]Cxx  Representation theory of groups [See also [[19A22|19Axx]] (for representation rings and Burnside rings)] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/20Cxx.html]]}{{moveright{< [[20Bxx |20Bxx]] | [[20-XX |20-XX]] | [[20Dxx |20Dxx]] >}}}
* ''20C05'' Group rings of finite groups and their modules [See also [[16S34|16Sxx]]]
* ''20C07'' Group rings of infinite groups and their modules [See also [[16S34|16Sxx]]]
* ''20C08'' Hecke algebras and their representations
* ''20C10'' Integral representations of finite groups
* ''20C11'' $p$-adic representations of finite groups
* ''20C12'' Integral representations of infinite groups
* ''20C15'' Ordinary representations and characters
* ''20C20'' Modular representations and characters
* ''20C25'' Projective representations and multipliers
* ''20C30'' Representations of finite symmetric groups
* ''20C32'' Representations of infinite symmetric groups
* ''20C33'' Representations of finite groups of Lie type
* ''20C34'' Representations of sporadic groups
* ''20C35'' Applications of group representations to physics
* ''20C40'' Computational methods
* ''20C99'' None of the above, but in this section
!!![[20|20-XX]]Dxx  Abstract finite groups {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/20Dxx.html]]}{{moveright{< [[20Cxx |20Cxx]] | [[20-XX |20-XX]] | [[20Exx |20Exx]] >}}}
* ''20D05'' Finite simple groups and their classification
* ''20D06'' Simple groups: alternating groups and groups of Lie type [See also [[20Gxx|20Gxx]]]
* ''20D08'' Simple groups: sporadic groups
* ''20D10'' Solvable groups, theory of formations, Schunck classes, Fitting classes, $\pi$-length, ranks [See also [[20F17|20Fxx]]]
* ''20D15'' Nilpotent groups, $p$-groups
* ''20D20'' Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure
* ''20D25'' Special subgroups (Frattini, Fitting, etc.)
* ''20D30'' Series and lattices of subgroups
* ''20D35'' Subnormal subgroups
* ''20D40'' Products of subgroups
* ''20D45'' Automorphisms
* ''20D60'' Arithmetic and combinatorial problems
* ''20D99'' None of the above, but in this section
!!![[20|20-XX]]Exx  Structure and classification of infinite or finite groups {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/20Exx.html]]}{{moveright{< [[20Dxx |20Dxx]] | [[20-XX |20-XX]] | [[20Fxx |20Fxx]] >}}}
* ''20E05'' Free nonabelian groups
* ''20E06'' Free products, free products with amalgamation, ~Higman-Neumann-Neumann extensions, and generalizations
* ''20E07'' Subgroup theorems; subgroup growth
* ''20E08'' Groups acting on trees [See also [[20F65|20Fxx]]]
* ''20E10'' Quasivarieties and varieties of groups
* ''20E15'' Chains and lattices of subgroups, subnormal subgroups [See also [[20F22|20Fxx]]]
* ''20E18'' Limits, profinite groups
* ''20E22'' Extensions, wreath products, and other compositions [See also [[20J05|20Jxx]]]
* ''20E25'' Local properties
* ''20E26'' Residual properties and generalizations; residually finite groups
* ''20E28'' Maximal subgroups
* ''20E32'' Simple groups [See also [[20D05|20Dxx]]]
* ''20E34'' General structure theorems
* ''20E36'' Automorphisms of infinite groups [For automorphisms of finite groups, see [[20D45|20Dxx]]]
* ''20E42'' Groups with a $BN$-pair; buildings [See also [[51E24|51Exx]]]
* ''20E45'' Conjugacy classes
* ''20E99'' None of the above, but in this section
!!![[20|20-XX]]Fxx  Special aspects of infinite or finite groups {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/20Fxx.html]]}{{moveright{< [[20Exx |20Exx]] | [[20-XX |20-XX]] | [[20Gxx |20Gxx]] >}}}
* ''20F05'' Generators, relations, and presentations
* ''20F06'' Cancellation theory; application of van Kampen diagrams [See also [[57M05|57Mxx]]]
* ''20F10'' Word problems, other decision problems, connections with logic and automata [See also [[03B25|03Bxx]], [[03D05|03Dxx]], [[03D40|03Dxx]], [[06B25|06Bxx]], [[08A50|08Axx]], [[20M05|20Mxx]], [[68Q70|68Qxx]]]
* ''20F11'' Groups of finite Morley rank [See also [[03C45|03Cxx]], [[03C60|03Cxx]]]
* ''20F12'' Commutator calculus
* ''20F14'' Derived series, central series, and generalizations
* ''20F16'' Solvable groups, supersolvable groups [See also [[20D10|20Dxx]]]
* ''20F17'' Formations of groups, Fitting classes [See also [[20D10|20Dxx]]]
* ''20F18'' Nilpotent groups [See also [[20D15|20Dxx]]]
* ''20F19'' Generalizations of solvable and nilpotent groups
* ''20F22'' Other classes of groups defined by subgroup chains
* ''20F24'' ~FC-groups and their generalizations
* ''20F28'' Automorphism groups of groups [See also [[20E36|20Exx]]]
* ''20F29'' Representations of groups as automorphism groups of algebraic systems
* ''20F34'' Fundamental groups and their automorphisms [See also [[57M05|57Mxx]], [[57Sxx|57Sxx]]]
* ''20F36'' Braid groups; Artin groups
* ''20F38'' Other groups related to topology or analysis
* ''20F40'' Associated Lie structures
* ''20F45'' Engel conditions
* ''20F50'' Periodic groups; locally finite groups
* ''20F55'' Reflection and Coxeter groups [See also [[22E40|22Exx]], [[51F15|51Fxx]]]
* ''20F60'' Ordered groups [See mainly [[06F15|06Fxx]]]
* ''20F65'' Geometric group theory [See also [[05C25|05Cxx]], [[20E08|20Exx]], [[57Mxx|57Mxx]]]
* ''20F67'' Hyperbolic groups and nonpositively curved groups
* ''20F69'' Asymptotic properties of groups
* ''20F70'' Algebraic geometry over groups; equations over groups
* ''20F99'' None of the above, but in this section
!!![[20|20-XX]]Gxx  Linear algebraic groups and related topics {For arithmetic theory, see [[11E57|11Exx]], [[11H56|11Hxx]]; for geometric theory, see [[14Lxx|14Lxx]], [[22Exx|22Exx]]; for other methods in representation theory, see [[15A30|15Axx]], [[22E45|22Exx]], [[22E46|22Exx]], [[22E47|22Exx]], [[22E50|22Exx]], [[22E55|22Exx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/20Gxx.html]]}{{moveright{< [[20Fxx |20Fxx]] | [[20-XX |20-XX]] | [[20Hxx |20Hxx]] >}}}
* ''20G05'' Representation theory
* ''20G07'' Structure theory
* ''20G10'' Cohomology theory
* ''20G15'' Linear algebraic groups over arbitrary fields
* ''20G20'' Linear algebraic groups over the reals, the complexes, the quaternions
* ''20G25'' Linear algebraic groups over local fields and their integers
* ''20G30'' Linear algebraic groups over global fields and their integers
* ''20G35'' Linear algebraic groups over adèles and other rings and schemes
* ''20G40'' Linear algebraic groups over finite fields
* ''20G41'' Exceptional groups
* ''20G42'' Quantum groups (quantized function algebras) and their representations [See also [[16T20|16Txx]], [[17B37|17Bxx]], [[81R50|81Rxx]]]
* ''20G43'' Schur and $q$-Schur algebras
* ''20G44'' ~Kac-Moody groups
* ''20G45'' Applications to physics
* ''20G99'' None of the above, but in this section
!!![[20|20-XX]]Hxx  Other groups of matrices [See also [[15A30|15Axx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/20Hxx.html]]}{{moveright{< [[20Gxx |20Gxx]] | [[20-XX |20-XX]] | [[20Jxx |20Jxx]] >}}}
* ''20H05'' Unimodular groups, congruence subgroups [See also [[11F06|11Fxx]], [[19B37|19Bxx]], [[22E40|22Exx]], [[51F20|51Fxx]]]
* ''20H10'' Fuchsian groups and their generalizations [See also [[11F06|11Fxx]], [[22E40|22Exx]], [[30F35|30Fxx]], [[32Nxx|32Nxx]]]
* ''20H15'' Other geometric groups, including crystallographic groups [See also [[51-XX|51-XX]], especially [[51F15|51Fxx]], and [[82D25|82Dxx]]]
* ''20H20'' Other matrix groups over fields
* ''20H25'' Other matrix groups over rings
* ''20H30'' Other matrix groups over finite fields
* ''20H99'' None of the above, but in this section
!!![[20|20-XX]]Jxx  Connections with homological algebra and category theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/20Jxx.html]]}{{moveright{< [[20Hxx |20Hxx]] | [[20-XX |20-XX]] | [[20Kxx |20Kxx]] >}}}
* ''20J05'' Homological methods in group theory
* ''20J06'' Cohomology of groups
* ''20J15'' Category of groups
* ''20J99'' None of the above, but in this section
!!![[20|20-XX]]Kxx  Abelian groups {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/20Kxx.html]]}{{moveright{< [[20Jxx |20Jxx]] | [[20-XX |20-XX]] | [[20Lxx |20Lxx]] >}}}
* ''20K01'' Finite abelian groups [For sumsets, see [[11B13|11Bxx]] and [[11P70|11Pxx]]]
* ''20K10'' Torsion groups, primary groups and generalized primary groups
* ''20K15'' Torsion-free groups, finite rank
* ''20K20'' Torsion-free groups, infinite rank
* ''20K21'' Mixed groups
* ''20K25'' Direct sums, direct products, etc.
* ''20K27'' Subgroups
* ''20K30'' Automorphisms, homomorphisms, endomorphisms, etc.
* ''20K35'' Extensions
* ''20K40'' Homological and categorical methods
* ''20K45'' Topological methods [See also [[22A05|22Axx]], [[22B05|22Bxx]]]
* ''20K99'' None of the above, but in this section
!!![[20|20-XX]]Lxx  Groupoids (i.e. small categories in which all morphisms are isomorphisms) {For sets with a single binary operation, see [[20N02|20Nxx]]; for topological groupoids, see [[22A22|22Axx]], [[58H05|58Hxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/20Lxx.html]]}{{moveright{< [[20Kxx |20Kxx]] | [[20-XX |20-XX]] | [[20Mxx |20Mxx]] >}}}
* ''20L05'' Groupoids (i.e. small categories in which all morphisms are isomorphisms) {For sets with a single binary operation, see [[20N02|20Nxx]]; for topological groupoids, see [[22A22|22Axx]], [[58H05|58Hxx]]}
* ''20L99'' None of the above, but in this section
!!![[20|20-XX]]Mxx  Semigroups {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/20Mxx.html]]}{{moveright{< [[20Lxx |20Lxx]] | [[20-XX |20-XX]] | [[20Nxx |20Nxx]] >}}}
* ''20M05'' Free semigroups, generators and relations, word problems [See also [[03D40|03Dxx]], [[08A50|08Axx]], [[20F10|20Fxx]]]
* ''20M07'' Varieties and pseudovarieties of semigroups
* ''20M10'' General structure theory
* ''20M11'' Radical theory
* ''20M12'' Ideal theory
* ''20M13'' Arithmetic theory of monoids
* ''20M14'' Commutative semigroups
* ''20M15'' Mappings of semigroups
* ''20M17'' Regular semigroups
* ''20M18'' Inverse semigroups
* ''20M19'' Orthodox semigroups
* ''20M20'' Semigroups of transformations, etc. [See also [[47D03|47Dxx]], [[47H20|47Hxx]], [[54H15|54Hxx]]]
* ''20M25'' Semigroup rings, multiplicative semigroups of rings [See also [[16S36|16Sxx]], [[16Y60|16Yxx]]]
* ''20M30'' Representation of semigroups; actions of semigroups on sets
* ''20M32'' Algebraic monoids
* ''20M35'' Semigroups in automata theory, linguistics, etc. [See also [[03D05|03Dxx]], [[68Q70|68Qxx]], [[68T50|68Txx]]]
* ''20M50'' Connections of semigroups with homological algebra and category theory
* ''20M99'' None of the above, but in this section
!!![[20|20-XX]]Nxx  Other generalizations of groups {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/20Nxx.html]]}{{moveright{< [[20Mxx |20Mxx]] | [[20-XX |20-XX]] | [[20Pxx |20Pxx]] >}}}
* ''20N02'' Sets with a single binary operation (groupoids)
* ''20N05'' Loops, quasigroups [See also [[05Bxx|05Bxx]]]
* ''20N10'' Ternary systems (heaps, semiheaps, heapoids, etc.)
* ''20N15'' $n$-ary systems $(n\ge 3)$
* ''20N20'' Hypergroups
* ''20N25'' Fuzzy groups [See also [[03E72|03Exx]]]
* ''20N99'' None of the above, but in this section
!!!20-XX Group theory and generalizations {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/20-XX.html]]}{{moveright{< [[19-XX |19-XX]] | [[MSC |MSC2010]] | [[20Axx |20Axx]] >}}}
* ''20-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''20-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''20-02'' Research exposition (monographs, survey articles)
* ''20-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''20-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''20-06'' Proceedings, conferences, collections, etc.
* ''[[20Axx|20Axx]]''  Foundations
* ''[[20Bxx|20Bxx]]''  Permutation groups
* ''[[20Cxx|20Cxx]]''  Representation theory of groups [See also [[19A22|19Axx]] (for representation rings and Burnside rings)]
* ''[[20Dxx|20Dxx]]''  Abstract finite groups
* ''[[20Exx|20Exx]]''  Structure and classification of infinite or finite groups
* ''[[20Fxx|20Fxx]]''  Special aspects of infinite or finite groups
* ''[[20Gxx|20Gxx]]''  Linear algebraic groups and related topics {For arithmetic theory, see [[11E57|11Exx]], [[11H56|11Hxx]]; for geometric theory, see [[14Lxx|14Lxx]], [[22Exx|22Exx]]; for other methods in representation theory, see [[15A30|15Axx]], [[22E45|22Exx]], [[22E46|22Exx]], [[22E47|22Exx]], [[22E50|22Exx]], [[22E55|22Exx]]}
* ''[[20Hxx|20Hxx]]''  Other groups of matrices [See also [[15A30|15Axx]]]
* ''[[20Jxx|20Jxx]]''  Connections with homological algebra and category theory
* ''[[20Kxx|20Kxx]]''  Abelian groups
* ''[[20Lxx|20Lxx]]''  Groupoids (i.e. small categories in which all morphisms are isomorphisms) {For sets with a single binary operation, see [[20N02|20Nxx]]; for topological groupoids, see [[22A22|22Axx]], [[58H05|58Hxx]]}
* ''[[20Mxx|20Mxx]]''  Semigroups
* ''[[20Nxx|20Nxx]]''  Other generalizations of groups
* ''[[20Pxx|20Pxx]]''  Probabilistic methods in group theory [See also [[60Bxx|60Bxx]]]
!!![[20|20-XX]]Pxx  Probabilistic methods in group theory [See also [[60Bxx|60Bxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/20Pxx.html]]}{{moveright{< [[20Nxx |20Nxx]] | [[20-XX |20-XX]] | [[22-XX |22-XX]] >}}}
* ''20P05'' Probabilistic methods in group theory [See also [[60Bxx|60Bxx]]]
* ''20P99'' None of the above, but in this section
!!![[22|22-XX]]Axx  Topological and differentiable algebraic systems {For topological rings and fields, see [[12Jxx|12Jxx]], [[13Jxx|13Jxx]], [[16W80|16Wxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/22Axx.html]]}{{moveright{< [[20-XX |20-XX]] | [[22-XX |22-XX]] | [[22Bxx |22Bxx]] >}}}
* ''22A05'' Structure of general topological groups
* ''22A10'' Analysis on general topological groups
* ''22A15'' Structure of topological semigroups
* ''22A20'' Analysis on topological semigroups
* ''22A22'' Topological groupoids (including differentiable and Lie groupoids) [See also [[58H05|58Hxx]]]
* ''22A25'' Representations of general topological groups and semigroups
* ''22A26'' Topological semilattices, lattices and applications [See also [[06B30|06Bxx]], [[06B35|06Bxx]], [[06F30|06Fxx]]]
* ''22A30'' Other topological algebraic systems and their representations
* ''22A99'' None of the above, but in this section
!!![[22|22-XX]]Bxx  Locally compact abelian groups (LCA groups) {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/22Bxx.html]]}{{moveright{< [[22Axx |22Axx]] | [[22-XX |22-XX]] | [[22Cxx |22Cxx]] >}}}
* ''22B05'' General properties and structure of LCA groups
* ''22B10'' Structure of group algebras of LCA groups
* ''22B99'' None of the above, but in this section
!!![[22|22-XX]]Cxx  Compact groups {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/22Cxx.html]]}{{moveright{< [[22Bxx |22Bxx]] | [[22-XX |22-XX]] | [[22Dxx |22Dxx]] >}}}
* ''22C05'' Compact groups
* ''22C99'' None of the above, but in this section
!!![[22|22-XX]]Dxx  Locally compact groups and their algebras {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/22Dxx.html]]}{{moveright{< [[22Cxx |22Cxx]] | [[22-XX |22-XX]] | [[22Exx |22Exx]] >}}}
* ''22D05'' General properties and structure of locally compact groups
* ''22D10'' Unitary representations of locally compact groups
* ''22D12'' Other representations of locally compact groups
* ''22D15'' Group algebras of locally compact groups
* ''22D20'' Representations of group algebras
* ''22D25'' $C^*$-algebras and $W^*$-algebras in relation to group representations [See also [[46Lxx|46Lxx]]]
* ''22D30'' Induced representations
* ''22D35'' Duality theorems
* ''22D40'' Ergodic theory on groups [See also [[28Dxx|28Dxx]]]
* ''22D45'' Automorphism groups of locally compact groups
* ''22D99'' None of the above, but in this section
!!![[22|22-XX]]Exx  Lie groups {For the topology of Lie groups and homogeneous spaces, see [[57Sxx|57Sxx]], [[57Txx|57Txx]]; for analysis thereon, see [[43A80|43Axx]], [[43A85|43Axx]], [[43A90|43Axx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/22Exx.html]]}{{moveright{< [[22Dxx |22Dxx]] | [[22-XX |22-XX]] | [[22Fxx |22Fxx]] >}}}
* ''22E05'' Local Lie groups [See also [[34-XX|34-XX]], [[35-XX|35-XX]], [[58H05|58Hxx]]]
* ''22E10'' General properties and structure of complex Lie groups [See also [[32M05|32Mxx]]]
* ''22E15'' General properties and structure of real Lie groups
* ''22E20'' General properties and structure of other Lie groups
* ''22E25'' Nilpotent and solvable Lie groups
* ''22E27'' Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
* ''22E30'' Analysis on real and complex Lie groups [See also [[33C80|33Cxx]], [[43-XX|43-XX]]]
* ''22E35'' Analysis on $p$-adic Lie groups
* ''22E40'' Discrete subgroups of Lie groups [See also [[20Hxx|20Hxx]], [[32Nxx|32Nxx]]]
* ''22E41'' Continuous cohomology [See also [[57R32|57Rxx]], [[57Txx|57Txx]], [[58H10|58Hxx]]]
* ''22E43'' Structure and representation of the Lorentz group
* ''22E45'' Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see [[20G05|20Gxx]]}
* ''22E46'' Semisimple Lie groups and their representations
* ''22E47'' Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) [See also [[17B10|17Bxx]]]
* ''22E50'' Representations of Lie and linear algebraic groups over local fields [See also [[20G05|20Gxx]]]
* ''22E55'' Representations of Lie and linear algebraic groups over global fields and adèle rings [See also [[20G05|20Gxx]]]
* ''22E57'' Geometric Langlands program: representation-theoretic aspects [See also [[14D24|14Dxx]]]
* ''22E60'' Lie algebras of Lie groups {For the algebraic theory of Lie algebras, see [[17Bxx|17Bxx]]}
* ''22E65'' Infinite-dimensional Lie groups and their Lie algebras: general properties [See also [[17B65|17Bxx]], [[58B25|58Bxx]], [[58H05|58Hxx]]]
* ''22E66'' Analysis on and representations of infinite-dimensional Lie groups
* ''22E67'' Loop groups and related constructions, group-theoretic treatment [See also [[58D05|58Dxx]]]
* ''22E70'' Applications of Lie groups to physics; explicit representations [See also [[81R05|81Rxx]], [[81R10|81Rxx]]]
* ''22E99'' None of the above, but in this section
!!!22-XX Topological groups, Lie groups {For transformation groups, see [[54H15|54Hxx]], [[57Sxx|57Sxx]], [[58-XX|58-XX]]. For abstract harmonic analysis, see [[43-XX|43-XX]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/22-XX.html]]}{{moveright{< [[20-XX |20-XX]] | [[MSC |MSC2010]] | [[22Axx |22Axx]] >}}}
* ''22-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''22-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''22-02'' Research exposition (monographs, survey articles)
* ''22-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''22-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''22-06'' Proceedings, conferences, collections, etc.
* ''[[22Axx|22Axx]]''  Topological and differentiable algebraic systems {For topological rings and fields, see [[12Jxx|12Jxx]], [[13Jxx|13Jxx]], [[16W80|16Wxx]]}
* ''[[22Bxx|22Bxx]]''  Locally compact abelian groups (LCA groups)
* ''[[22Cxx|22Cxx]]''  Compact groups
* ''[[22Dxx|22Dxx]]''  Locally compact groups and their algebras
* ''[[22Exx|22Exx]]''  Lie groups {For the topology of Lie groups and homogeneous spaces, see [[57Sxx|57Sxx]], [[57Txx|57Txx]]; for analysis thereon, see [[43A80|43Axx]], [[43A85|43Axx]], [[43A90|43Axx]]}
* ''[[22Fxx|22Fxx]]''  Noncompact transformation groups
!!![[22|22-XX]]Fxx  Noncompact transformation groups {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/22Fxx.html]]}{{moveright{< [[22Exx |22Exx]] | [[22-XX |22-XX]] | [[26-XX |26-XX]] >}}}
* ''22F05'' General theory of group and pseudogroup actions {For topological properties of spaces with an action, see [[57S20|57Sxx]]}
* ''22F10'' Measurable group actions [See also [[22D40|22Dxx]], [[28Dxx|28Dxx]], [[37Axx|37Axx]]]
* ''22F30'' Homogeneous spaces {For general actions on manifolds or preserving geometrical structures, see [[57M60|57Mxx]], [[57Sxx|57Sxx]]; for discrete subgroups of Lie groups, see especially [[22E40|22Exx]]}
* ''22F50'' Groups as automorphisms of other structures
* ''22F99'' None of the above, but in this section
!!![[26|26-XX]]Axx  Functions of one variable {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/26Axx.html]]}{{moveright{< [[22-XX |22-XX]] | [[26-XX |26-XX]] | [[26Bxx |26Bxx]] >}}}
* ''26A03'' Foundations: limits and generalizations, elementary topology of the line
* ''26A06'' One-variable calculus
* ''26A09'' Elementary functions
* ''26A12'' Rate of growth of functions, orders of infinity, slowly varying functions [See also [[26A48|26Axx]]]
* ''26A15'' Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see [[42A16|42Axx]]; for those determined by approximation properties, see [[41A25|41Axx]], [[41A27|41Axx]]}
* ''26A16'' Lipschitz (Hölder) classes
* ''26A18'' Iteration [See also [[37Bxx|37Bxx]], [[37Cxx|37Cxx]], [[37Exx|37Exx]], [[39B12|39Bxx]], [[47H10|47Hxx]], [[54H25|54Hxx]]]
* ''26A21'' Classification of real functions; Baire classification of sets and functions [See also [[03E15|03Exx]], [[28A05|28Axx]], [[54C50|54Cxx]], [[54H05|54Hxx]]]
* ''26A24'' Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also [[28A15|28Axx]]]
* ''26A27'' Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
* ''26A30'' Singular functions, Cantor functions, functions with other special properties
* ''26A33'' Fractional derivatives and integrals
* ''26A36'' Antidifferentiation
* ''26A39'' Denjoy and Perron integrals, other special integrals
* ''26A42'' Integrals of Riemann, Stieltjes and Lebesgue type [See also [[28-XX|28-XX]]]
* ''26A45'' Functions of bounded variation, generalizations
* ''26A46'' Absolutely continuous functions
* ''26A48'' Monotonic functions, generalizations
* ''26A51'' Convexity, generalizations
* ''26A99'' None of the above, but in this section
!!![[26|26-XX]]Bxx  Functions of several variables {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/26Bxx.html]]}{{moveright{< [[26Axx |26Axx]] | [[26-XX |26-XX]] | [[26Cxx |26Cxx]] >}}}
* ''26B05'' Continuity and differentiation questions
* ''26B10'' Implicit function theorems, Jacobians, transformations with several variables
* ''26B12'' Calculus of vector functions
* ''26B15'' Integration: length, area, volume [See also [[28A75|28Axx]], [[51M25|51Mxx]]]
* ''26B20'' Integral formulas (Stokes, Gauss, Green, etc.)
* ''26B25'' Convexity, generalizations
* ''26B30'' Absolutely continuous functions, functions of bounded variation
* ''26B35'' Special properties of functions of several variables, Hölder conditions, etc.
* ''26B40'' Representation and superposition of functions
* ''26B99'' None of the above, but in this section
!!![[26|26-XX]]Cxx  Polynomials, rational functions {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/26Cxx.html]]}{{moveright{< [[26Bxx |26Bxx]] | [[26-XX |26-XX]] | [[26Dxx |26Dxx]] >}}}
* ''26C05'' Polynomials: analytic properties, etc. [See also [[12Dxx|12Dxx]], [[12Exx|12Exx]]]
* ''26C10'' Polynomials: location of zeros [See also [[12D10|12Dxx]], [[30C15|30Cxx]], [[65H05|65Hxx]]]
* ''26C15'' Rational functions [See also [[14Pxx|14Pxx]]]
* ''26C99'' None of the above, but in this section
!!![[26|26-XX]]Dxx  Inequalities {For maximal function inequalities, see [[42B25|42Bxx]]; for functional inequalities, see [[39B72|39Bxx]]; for probabilistic inequalities, see [[60E15|60Exx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/26Dxx.html]]}{{moveright{< [[26Cxx |26Cxx]] | [[26-XX |26-XX]] | [[26Exx |26Exx]] >}}}
* ''26D05'' Inequalities for trigonometric functions and polynomials
* ''26D07'' Inequalities involving other types of functions
* ''26D10'' Inequalities involving derivatives and differential and integral operators
* ''26D15'' Inequalities for sums, series and integrals
* ''26D20'' Other analytical inequalities
* ''26D99'' None of the above, but in this section
!!!26-XX Real functions [See also [[54C30|54Cxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/26-XX.html]]}{{moveright{< [[22-XX |22-XX]] | [[MSC |MSC2010]] | [[26Axx |26Axx]] >}}}
* ''26-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''26-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''26-02'' Research exposition (monographs, survey articles)
* ''26-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''26-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''26-06'' Proceedings, conferences, collections, etc.
* ''[[26Axx|26Axx]]''  Functions of one variable
* ''[[26Bxx|26Bxx]]''  Functions of several variables
* ''[[26Cxx|26Cxx]]''  Polynomials, rational functions
* ''[[26Dxx|26Dxx]]''  Inequalities {For maximal function inequalities, see [[42B25|42Bxx]]; for functional inequalities, see [[39B72|39Bxx]]; for probabilistic inequalities, see [[60E15|60Exx]]}
* ''[[26Exx|26Exx]]''  Miscellaneous topics [See also [[58Cxx|58Cxx]]]
!!![[26|26-XX]]Exx  Miscellaneous topics [See also [[58Cxx|58Cxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/26Exx.html]]}{{moveright{< [[26Dxx |26Dxx]] | [[26-XX |26-XX]] | [[28-XX |28-XX]] >}}}
* ''26E05'' Real-analytic functions [See also [[32B05|32Bxx]], [[32C05|32Cxx]]]
* ''26E10'' $C^\infty$-functions, quasi-analytic functions [See also [[58C25|58Cxx]]]
* ''26E15'' Calculus of functions on infinite-dimensional spaces [See also [[46G05|46Gxx]], [[58Cxx|58Cxx]]]
* ''26E20'' Calculus of functions taking values in infinite-dimensional spaces [See also [[46E40|46Exx]], [[46G10|46Gxx]], [[58Cxx|58Cxx]]]
* ''26E25'' Set-valued functions [See also [[28B20|28Bxx]], [[49J53|49Jxx]], [[54C60|54Cxx]]] {For nonsmooth analysis, see [[49J52|49Jxx]], [[58Cxx|58Cxx]], [[90Cxx|90Cxx]]}
* ''26E30'' ~Non-Archimedean analysis [See also [[12J25|12Jxx]]]
* ''26E35'' Nonstandard analysis [See also [[03H05|03Hxx]], [[28E05|28Exx]], [[54J05|54Jxx]]]
* ''26E40'' Constructive real analysis [See also [[03F60|03Fxx]]]
* ''26E50'' Fuzzy real analysis [See also [[03E72|03Exx]], [[28E10|28Exx]]]
* ''26E60'' Means [See also [[47A64|47Axx]]]
* ''26E70'' Real analysis on time scales or measure chains {For dynamic equations on time scales or measure chains see [[34N05|34Nxx]]}
* ''26E99'' None of the above, but in this section
!!![[28|28-XX]]Axx  Classical measure theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/28Axx.html]]}{{moveright{< [[26-XX |26-XX]] | [[28-XX |28-XX]] | [[28Bxx |28Bxx]] >}}}
* ''28A05'' Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also [[03E15|03Exx]], [[26A21|26Axx]], [[54H05|54Hxx]]]
* ''28A10'' Real- or complex-valued set functions
* ''28A12'' Contents, measures, outer measures, capacities
* ''28A15'' Abstract differentiation theory, differentiation of set functions [See also [[26A24|26Axx]]]
* ''28A20'' Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
* ''28A25'' Integration with respect to measures and other set functions
* ''28A33'' Spaces of measures, convergence of measures [See also [[46E27|46Exx]], [[60Bxx|60Bxx]]]
* ''28A35'' Measures and integrals in product spaces
* ''28A50'' Integration and disintegration of measures
* ''28A51'' Lifting theory [See also [[46G15|46Gxx]]]
* ''28A60'' Measures on Boolean rings, measure algebras [See also [[54H10|54Hxx]]]
* ''28A75'' Length, area, volume, other geometric measure theory [See also [[26B15|26Bxx]], [[49Q15|49Qxx]]]
* ''28A78'' Hausdorff and packing measures
* ''28A80'' Fractals [See also [[37Fxx|37Fxx]]]
* ''28A99'' None of the above, but in this section
!!![[28|28-XX]]Bxx  Set functions, measures and integrals with values in abstract spaces {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/28Bxx.html]]}{{moveright{< [[28Axx |28Axx]] | [[28-XX |28-XX]] | [[28Cxx |28Cxx]] >}}}
* ''28B05'' Vector-valued set functions, measures and integrals [See also [[46G10|46Gxx]]]
* ''28B10'' Group- or semigroup-valued set functions, measures and integrals
* ''28B15'' Set functions, measures and integrals with values in ordered spaces
* ''28B20'' Set-valued set functions and measures; integration of set-valued functions; measurable selections [See also [[26E25|26Exx]], [[54C60|54Cxx]], [[54C65|54Cxx]], [[91B14|91Bxx]]]
* ''28B99'' None of the above, but in this section
!!![[28|28-XX]]Cxx  Set functions and measures on spaces with additional structure [See also [[46G12|46Gxx]], [[58C35|58Cxx]], [[58D20|58Dxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/28Cxx.html]]}{{moveright{< [[28Bxx |28Bxx]] | [[28-XX |28-XX]] | [[28Dxx |28Dxx]] >}}}
* ''28C05'' Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
* ''28C10'' Set functions and measures on topological groups or semigroups, Haar measures, invariant measures [See also [[22Axx|22Axx]], [[43A05|43Axx]]]
* ''28C15'' Set functions and measures on topological spaces (regularity of measures, etc.)
* ''28C20'' Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also [[46G12|46Gxx]], [[58C35|58Cxx]], [[58D20|58Dxx]], [[60B11|60Bxx]]]
* ''28C99'' None of the above, but in this section
!!![[28|28-XX]]Dxx  Measure-theoretic ergodic theory [See also [[11K50|11Kxx]], [[11K55|11Kxx]], [[22D40|22Dxx]], [[37Axx|37Axx]], [[47A35|47Axx]], [[54H20|54Hxx]], [[60Fxx|60Fxx]], [[60G10|60Gxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/28Dxx.html]]}{{moveright{< [[28Cxx |28Cxx]] | [[28-XX |28-XX]] | [[28Exx |28Exx]] >}}}
* ''28D05'' Measure-preserving transformations
* ''28D10'' One-parameter continuous families of measure-preserving transformations
* ''28D15'' General groups of measure-preserving transformations
* ''28D20'' Entropy and other invariants
* ''28D99'' None of the above, but in this section
!!!28-XX Measure and integration {For analysis on manifolds, see [[58-XX|58-XX]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/28-XX.html]]}{{moveright{< [[26-XX |26-XX]] | [[MSC |MSC2010]] | [[28Axx |28Axx]] >}}}
* ''28-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''28-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''28-02'' Research exposition (monographs, survey articles)
* ''28-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''28-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''28-06'' Proceedings, conferences, collections, etc.
* ''[[28Axx|28Axx]]''  Classical measure theory
* ''[[28Bxx|28Bxx]]''  Set functions, measures and integrals with values in abstract spaces
* ''[[28Cxx|28Cxx]]''  Set functions and measures on spaces with additional structure [See also [[46G12|46Gxx]], [[58C35|58Cxx]], [[58D20|58Dxx]]]
* ''[[28Dxx|28Dxx]]''  Measure-theoretic ergodic theory [See also [[11K50|11Kxx]], [[11K55|11Kxx]], [[22D40|22Dxx]], [[37Axx|37Axx]], [[47A35|47Axx]], [[54H20|54Hxx]], [[60Fxx|60Fxx]], [[60G10|60Gxx]]]
* ''[[28Exx|28Exx]]''  Miscellaneous topics in measure theory
!!![[28|28-XX]]Exx  Miscellaneous topics in measure theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/28Exx.html]]}{{moveright{< [[28Dxx |28Dxx]] | [[28-XX |28-XX]] | [[30-XX |30-XX]] >}}}
* ''28E05'' Nonstandard measure theory [See also [[03H05|03Hxx]], [[26E35|26Exx]]]
* ''28E10'' Fuzzy measure theory [See also [[03E72|03Exx]], [[26E50|26Exx]], [[94D05|94Dxx]]]
* ''28E15'' Other connections with logic and set theory
* ''28E99'' None of the above, but in this section
!!![[30|30-XX]]Axx  General properties {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/30Axx.html]]}{{moveright{< [[28-XX |28-XX]] | [[30-XX |30-XX]] | [[30Bxx |30Bxx]] >}}}
* ''30A05'' Monogenic properties of complex functions (including polygenic and areolar monogenic functions)
* ''30A10'' Inequalities in the complex domain
* ''30A99'' None of the above, but in this section
!!![[30|30-XX]]Bxx  Series expansions {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/30Bxx.html]]}{{moveright{< [[30Axx |30Axx]] | [[30-XX |30-XX]] | [[30Cxx |30Cxx]] >}}}
* ''30B10'' Power series (including lacunary series)
* ''30B20'' Random power series
* ''30B30'' Boundary behavior of power series, over-convergence
* ''30B40'' Analytic continuation
* ''30B50'' Dirichlet series and other series expansions, exponential series [See also [[11M41|11Mxx]], [[42-XX|42-XX]]]
* ''30B60'' Completeness problems, closure of a system of functions
* ''30B70'' Continued fractions [See also [[11A55|11Axx]], [[40A15|40Axx]]]
* ''30B99'' None of the above, but in this section
!!![[30|30-XX]]Cxx  Geometric function theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/30Cxx.html]]}{{moveright{< [[30Bxx |30Bxx]] | [[30-XX |30-XX]] | [[30Dxx |30Dxx]] >}}}
* ''30C10'' Polynomials
* ''30C15'' Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral) {For algebraic theory, see [[12D10|12Dxx]]; for real methods, see [[26C10|26Cxx]]}
* ''30C20'' Conformal mappings of special domains
* ''30C25'' Covering theorems in conformal mapping theory
* ''30C30'' Numerical methods in conformal mapping theory [See also [[65E05|65Exx]]]
* ''30C35'' General theory of conformal mappings
* ''30C40'' Kernel functions and applications
* ''30C45'' Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
* ''30C50'' Coefficient problems for univalent and multivalent functions
* ''30C55'' General theory of univalent and multivalent functions
* ''30C62'' Quasiconformal mappings in the plane
* ''30C65'' Quasiconformal mappings in ${\bf R}^n$, other generalizations
* ''30C70'' Extremal problems for conformal and quasiconformal mappings, variational methods
* ''30C75'' Extremal problems for conformal and quasiconformal mappings, other methods
* ''30C80'' Maximum principle; Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination
* ''30C85'' Capacity and harmonic measure in the complex plane [See also [[31A15|31Axx]]]
* ''30C99'' None of the above, but in this section
!!![[30|30-XX]]Dxx  Entire and meromorphic functions, and related topics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/30Dxx.html]]}{{moveright{< [[30Cxx |30Cxx]] | [[30-XX |30-XX]] | [[30Exx |30Exx]] >}}}
* ''30D05'' Functional equations in the complex domain, iteration and composition of analytic functions [See also [[34Mxx|34Mxx]], [[37Fxx|37Fxx]], [[39-XX|39-XX]]]
* ''30D10'' Representations of entire functions by series and integrals
* ''30D15'' Special classes of entire functions and growth estimates
* ''30D20'' Entire functions, general theory
* ''30D30'' Meromorphic functions, general theory
* ''30D35'' Distribution of values, Nevanlinna theory
* ''30D40'' Cluster sets, prime ends, boundary behavior
* ''30D45'' Bloch functions, normal functions, normal families
* ''30D60'' Quasi-analytic and other classes of functions
* ''30D99'' None of the above, but in this section
!!![[30|30-XX]]Exx  Miscellaneous topics of analysis in the complex domain {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/30Exx.html]]}{{moveright{< [[30Dxx |30Dxx]] | [[30-XX |30-XX]] | [[30Fxx |30Fxx]] >}}}
* ''30E05'' Moment problems, interpolation problems
* ''30E10'' Approximation in the complex domain
* ''30E15'' Asymptotic representations in the complex domain
* ''30E20'' Integration, integrals of Cauchy type, integral representations of analytic functions [See also [[45Exx|45Exx]]]
* ''30E25'' Boundary value problems [See also [[45Exx|45Exx]]]
* ''30E99'' None of the above, but in this section
!!![[30|30-XX]]Fxx  Riemann surfaces {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/30Fxx.html]]}{{moveright{< [[30Exx |30Exx]] | [[30-XX |30-XX]] | [[30Gxx |30Gxx]] >}}}
* ''30F10'' Compact Riemann surfaces and uniformization [See also [[14H15|14Hxx]], [[32G15|32Gxx]]]
* ''30F15'' Harmonic functions on Riemann surfaces
* ''30F20'' Classification theory of Riemann surfaces
* ''30F25'' Ideal boundary theory
* ''30F30'' Differentials on Riemann surfaces
* ''30F35'' Fuchsian groups and automorphic functions [See also [[11Fxx|11Fxx]], [[20H10|20Hxx]], [[22E40|22Exx]], [[32Gxx|32Gxx]], [[32Nxx|32Nxx]]]
* ''30F40'' Kleinian groups [See also [[20H10|20Hxx]]]
* ''30F45'' Conformal metrics (hyperbolic, Poincaré, distance functions)
* ''30F50'' Klein surfaces
* ''30F60'' Teichmüller theory [See also [[32G15|32Gxx]]]
* ''30F99'' None of the above, but in this section
!!![[30|30-XX]]Gxx  Generalized function theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/30Gxx.html]]}{{moveright{< [[30Fxx |30Fxx]] | [[30-XX |30-XX]] | [[30Hxx |30Hxx]] >}}}
* ''30G06'' ~Non-Archimedean function theory [See also [[12J25|12Jxx]]]; nonstandard function theory [See also [[03H05|03Hxx]]]
* ''30G12'' Finely holomorphic functions and topological function theory
* ''30G20'' Generalizations of Bers or Vekua type (pseudoanalytic, $p$-analytic, etc.)
* ''30G25'' Discrete analytic functions
* ''30G30'' Other generalizations of analytic functions (including abstract-valued functions)
* ''30G35'' Functions of hypercomplex variables and generalized variables
* ''30G99'' None of the above, but in this section
!!![[30|30-XX]]Hxx  Spaces and algebras of analytic functions {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/30Hxx.html]]}{{moveright{< [[30Gxx |30Gxx]] | [[30-XX |30-XX]] | [[30Jxx |30Jxx]] >}}}
* ''30H05'' Bounded analytic functions
* ''30H10'' Hardy spaces
* ''30H15'' Nevanlinna class and Smirnov class
* ''30H20'' Bergman spaces, Fock spaces
* ''30H25'' Besov spaces and $Q_p$-spaces
* ''30H30'' Bloch spaces
* ''30H35'' BMO-spaces
* ''30H50'' Algebras of analytic functions
* ''30H80'' Corona theorems
* ''30H99'' None of the above, but in this section
!!![[30|30-XX]]Jxx  Function theory on the disc {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/30Jxx.html]]}{{moveright{< [[30Hxx |30Hxx]] | [[30-XX |30-XX]] | [[30Kxx |30Kxx]] >}}}
* ''30J05'' Inner functions
* ''30J10'' Blaschke products
* ''30J15'' Singular inner functions
* ''30J99'' None of the above, but in this section
!!![[30|30-XX]]Kxx  Universal holomorphic functions {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/30Kxx.html]]}{{moveright{< [[30Jxx |30Jxx]] | [[30-XX |30-XX]] | [[30Lxx |30Lxx]] >}}}
* ''30K05'' Universal Taylor series
* ''30K10'' Universal Dirichlet series
* ''30K15'' Bounded universal functions
* ''30K20'' Compositional universality
* ''30K99'' None of the above, but in this section
!!!30-XX Functions of a complex variable {For analysis on manifolds, see [[58-XX|58-XX]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/30-XX.html]]}{{moveright{< [[28-XX |28-XX]] | [[MSC |MSC2010]] | [[30Axx |30Axx]] >}}}
* ''30-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''30-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''30-02'' Research exposition (monographs, survey articles)
* ''30-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''30-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''30-06'' Proceedings, conferences, collections, etc.
* ''[[30Axx|30Axx]]''  General properties
* ''[[30Bxx|30Bxx]]''  Series expansions
* ''[[30Cxx|30Cxx]]''  Geometric function theory
* ''[[30Dxx|30Dxx]]''  Entire and meromorphic functions, and related topics
* ''[[30Exx|30Exx]]''  Miscellaneous topics of analysis in the complex domain
* ''[[30Fxx|30Fxx]]''  Riemann surfaces
* ''[[30Gxx|30Gxx]]''  Generalized function theory
* ''[[30Hxx|30Hxx]]''  Spaces and algebras of analytic functions
* ''[[30Jxx|30Jxx]]''  Function theory on the disc
* ''[[30Kxx|30Kxx]]''  Universal holomorphic functions
* ''[[30Lxx|30Lxx]]''  Analysis on metric spaces
!!![[30|30-XX]]Lxx  Analysis on metric spaces {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/30Lxx.html]]}{{moveright{< [[30Kxx |30Kxx]] | [[30-XX |30-XX]] | [[31-XX |31-XX]] >}}}
* ''30L05'' Geometric embeddings of metric spaces
* ''30L10'' Quasiconformal mappings in metric spaces
* ''30L99'' None of the above, but in this section
!!![[31|31-XX]]Axx  Two-dimensional theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/31Axx.html]]}{{moveright{< [[30-XX |30-XX]] | [[31-XX |31-XX]] | [[31Bxx |31Bxx]] >}}}
* ''31A05'' Harmonic, subharmonic, superharmonic functions
* ''31A10'' Integral representations, integral operators, integral equations methods
* ''31A15'' Potentials and capacity, harmonic measure, extremal length [See also [[30C85|30Cxx]]]
* ''31A20'' Boundary behavior (theorems of Fatou type, etc.)
* ''31A25'' Boundary value and inverse problems
* ''31A30'' Biharmonic, polyharmonic functions and equations, Poisson's equation
* ''31A35'' Connections with differential equations
* ''31A99'' None of the above, but in this section
!!![[31|31-XX]]Bxx  Higher-dimensional theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/31Bxx.html]]}{{moveright{< [[31Axx |31Axx]] | [[31-XX |31-XX]] | [[31Cxx |31Cxx]] >}}}
* ''31B05'' Harmonic, subharmonic, superharmonic functions
* ''31B10'' Integral representations, integral operators, integral equations methods
* ''31B15'' Potentials and capacities, extremal length
* ''31B20'' Boundary value and inverse problems
* ''31B25'' Boundary behavior
* ''31B30'' Biharmonic and polyharmonic equations and functions
* ''31B35'' Connections with differential equations
* ''31B99'' None of the above, but in this section
!!![[31|31-XX]]Cxx  Other generalizations {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/31Cxx.html]]}{{moveright{< [[31Bxx |31Bxx]] | [[31-XX |31-XX]] | [[31Dxx |31Dxx]] >}}}
* ''31C05'' Harmonic, subharmonic, superharmonic functions
* ''31C10'' Pluriharmonic and plurisubharmonic functions [See also [[32U05|32Uxx]]]
* ''31C12'' Potential theory on Riemannian manifolds [See also [[53C20|53Cxx]]; for Hodge theory, see [[58A14|58Axx]]]
* ''31C15'' Potentials and capacities
* ''31C20'' Discrete potential theory and numerical methods
* ''31C25'' Dirichlet spaces
* ''31C35'' Martin boundary theory [See also [[60J50|60Jxx]]]
* ''31C40'' Fine potential theory
* ''31C45'' Other generalizations (nonlinear potential theory, etc.)
* ''31C99'' None of the above, but in this section
!!![[31|31-XX]]Dxx  Axiomatic potential theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/31Dxx.html]]}{{moveright{< [[31Cxx |31Cxx]] | [[31-XX |31-XX]] | [[31Exx |31Exx]] >}}}
* ''31D05'' Axiomatic potential theory
* ''31D99'' None of the above, but in this section
!!!31-XX Potential theory {For probabilistic potential theory, see [[60J45|60Jxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/31-XX.html]]}{{moveright{< [[30-XX |30-XX]] | [[MSC |MSC2010]] | [[31Axx |31Axx]] >}}}
* ''31-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''31-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''31-02'' Research exposition (monographs, survey articles)
* ''31-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''31-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''31-06'' Proceedings, conferences, collections, etc.
* ''[[31Axx|31Axx]]''  Two-dimensional theory
* ''[[31Bxx|31Bxx]]''  Higher-dimensional theory
* ''[[31Cxx|31Cxx]]''  Other generalizations
* ''[[31Dxx|31Dxx]]''  Axiomatic potential theory
* ''[[31Exx|31Exx]]''  Potential theory on metric spaces
!!![[31|31-XX]]Exx  Potential theory on metric spaces {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/31Exx.html]]}{{moveright{< [[31Dxx |31Dxx]] | [[31-XX |31-XX]] | [[32-XX |32-XX]] >}}}
* ''31E05'' Potential theory on metric spaces
* ''31E99'' None of the above, but in this section
!!![[32|32-XX]]Axx  Holomorphic functions of several complex variables {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/32Axx.html]]}{{moveright{< [[31-XX |31-XX]] | [[32-XX |32-XX]] | [[32Bxx |32Bxx]] >}}}
* ''32A05'' Power series, series of functions
* ''32A07'' Special domains (Reinhardt, Hartogs, circular, tube)
* ''32A10'' Holomorphic functions
* ''32A12'' Multifunctions
* ''32A15'' Entire functions
* ''32A17'' Special families of functions
* ''32A18'' Bloch functions, normal functions
* ''32A19'' Normal families of functions, mappings
* ''32A20'' Meromorphic functions
* ''32A22'' Nevanlinna theory (local); growth estimates; other inequalities {For geometric theory, see [[32H25|32Hxx]], [[32H30|32Hxx]]}
* ''32A25'' Integral representations; canonical kernels (Szegő, Bergman, etc.)
* ''32A26'' Integral representations, constructed kernels (e.g. Cauchy, Fantappiè-type kernels)
* ''32A27'' Local theory of residues [See also [[32C30|32Cxx]]]
* ''32A30'' Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30) {For functions of several hypercomplex variables, see [[30G35|30Gxx]]}
* ''32A35'' $H^p$-spaces, Nevanlinna spaces [See also [[32M15|32Mxx]], [[42B30|42Bxx]], [[43A85|43Axx]], [[46J15|46Jxx]]]
* ''32A36'' Bergman spaces
* ''32A37'' Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also [[46Exx|46Exx]]]
* ''32A38'' Algebras of holomorphic functions [See also [[30H05|30Hxx]], [[46J10|46Jxx]], [[46J15|46Jxx]]]
* ''32A40'' Boundary behavior of holomorphic functions
* ''32A45'' Hyperfunctions [See also [[46F15|46Fxx]]]
* ''32A50'' Harmonic analysis of several complex variables [See mainly [[43-XX|43-XX]]]
* ''32A55'' Singular integrals
* ''32A60'' Zero sets of holomorphic functions
* ''32A65'' Banach algebra techniques [See mainly [[46Jxx|46Jxx]]]
* ''32A70'' Functional analysis techniques [See mainly [[46Exx|46Exx]]]
* ''32A99'' None of the above, but in this section
!!![[32|32-XX]]Bxx  Local analytic geometry [See also [[13-XX|13-XX]] and [[14-XX|14-XX]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/32Bxx.html]]}{{moveright{< [[32Axx |32Axx]] | [[32-XX |32-XX]] | [[32Cxx |32Cxx]] >}}}
* ''32B05'' Analytic algebras and generalizations, preparation theorems
* ''32B10'' Germs of analytic sets, local parametrization
* ''32B15'' Analytic subsets of affine space
* ''32B20'' Semi-analytic sets and subanalytic sets [See also [[14P15|14Pxx]]]
* ''32B25'' Triangulation and related questions
* ''32B99'' None of the above, but in this section
!!![[32|32-XX]]Cxx  Analytic spaces {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/32Cxx.html]]}{{moveright{< [[32Bxx |32Bxx]] | [[32-XX |32-XX]] | [[32Dxx |32Dxx]] >}}}
* ''32C05'' Real-analytic manifolds, real-analytic spaces [See also [[14Pxx|14Pxx]], [[58A07|58Axx]]]
* ''32C07'' Real-analytic sets, complex Nash functions [See also [[14P15|14Pxx]], [[14P20|14Pxx]]]
* ''32C09'' Embedding of real analytic manifolds
* ''32C11'' Complex supergeometry [See also [[14A22|14Axx]], [[14M30|14Mxx]], [[58A50|58Axx]]]
* ''32C15'' Complex spaces
* ''32C18'' Topology of analytic spaces
* ''32C20'' Normal analytic spaces
* ''32C22'' Embedding of analytic spaces
* ''32C25'' Analytic subsets and submanifolds
* ''32C30'' Integration on analytic sets and spaces, currents {For local theory, see [[32A25|32Axx]] or [[32A27|32Axx]]}
* ''32C35'' Analytic sheaves and cohomology groups [See also [[14Fxx|14Fxx]], [[18F20|18Fxx]], [[55N30|55Nxx]]]
* ''32C36'' Local cohomology of analytic spaces
* ''32C37'' Duality theorems
* ''32C38'' Sheaves of differential operators and their modules, $D$-modules [See also [[14F10|14Fxx]], [[16S32|16Sxx]], [[35A27|35Axx]], [[58J15|58Jxx]]]
* ''32C55'' The Levi problem in complex spaces; generalizations
* ''32C81'' Applications to physics
* ''32C99'' None of the above, but in this section
!!![[32|32-XX]]Dxx  Analytic continuation {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/32Dxx.html]]}{{moveright{< [[32Cxx |32Cxx]] | [[32-XX |32-XX]] | [[32Exx |32Exx]] >}}}
* ''32D05'' Domains of holomorphy
* ''32D10'' Envelopes of holomorphy
* ''32D15'' Continuation of analytic objects
* ''32D20'' Removable singularities
* ''32D26'' Riemann domains
* ''32D99'' None of the above, but in this section
!!![[32|32-XX]]Exx  Holomorphic convexity {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/32Exx.html]]}{{moveright{< [[32Dxx |32Dxx]] | [[32-XX |32-XX]] | [[32Fxx |32Fxx]] >}}}
* ''32E05'' Holomorphically convex complex spaces, reduction theory
* ''32E10'' Stein spaces, Stein manifolds
* ''32E20'' Polynomial convexity
* ''32E30'' Holomorphic and polynomial approximation, Runge pairs, interpolation
* ''32E35'' Global boundary behavior of holomorphic functions
* ''32E40'' The Levi problem
* ''32E99'' None of the above, but in this section
!!![[32|32-XX]]Fxx  Geometric convexity {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/32Fxx.html]]}{{moveright{< [[32Exx |32Exx]] | [[32-XX |32-XX]] | [[32Gxx |32Gxx]] >}}}
* ''32F10'' $q$-convexity, $q$-concavity
* ''32F17'' Other notions of convexity
* ''32F18'' Finite-type conditions
* ''32F27'' Topological consequences of geometric convexity
* ''32F32'' Analytical consequences of geometric convexity (vanishing theorems, etc.)
* ''32F45'' Invariant metrics and pseudodistances
* ''32F99'' None of the above, but in this section
!!![[32|32-XX]]Gxx  Deformations of analytic structures {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/32Gxx.html]]}{{moveright{< [[32Fxx |32Fxx]] | [[32-XX |32-XX]] | [[32Hxx |32Hxx]] >}}}
* ''32G05'' Deformations of complex structures [See also [[13D10|13Dxx]], [[16S80|16Sxx]], [[58H10|58Hxx]], [[58H15|58Hxx]]]
* ''32G07'' Deformations of special (e.g. CR) structures
* ''32G08'' Deformations of fiber bundles
* ''32G10'' Deformations of submanifolds and subspaces
* ''32G13'' Analytic moduli problems {For algebraic moduli problems, see [[14D20|14Dxx]], [[14D22|14Dxx]], [[14H10|14Hxx]], [[14J10|14Jxx]]} [See also [[14H15|14Hxx]], [[14J15|14Jxx]]]
* ''32G15'' Moduli of Riemann surfaces, Teichmüller theory [See also [[14H15|14Hxx]], [[30Fxx|30Fxx]]]
* ''32G20'' Period matrices, variation of Hodge structure; degenerations [See also [[14D05|14Dxx]], [[14D07|14Dxx]], [[14K30|14Kxx]]]
* ''32G34'' Moduli and deformations for ordinary differential equations (e.g. ~Knizhnik-Zamolodchikov equation) [See also [[34Mxx|34Mxx]]]
* ''32G81'' Applications to physics
* ''32G99'' None of the above, but in this section
!!![[32|32-XX]]Hxx  Holomorphic mappings and correspondences {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/32Hxx.html]]}{{moveright{< [[32Gxx |32Gxx]] | [[32-XX |32-XX]] | [[32Jxx |32Jxx]] >}}}
* ''32H02'' Holomorphic mappings, (holomorphic) embeddings and related questions
* ''32H04'' Meromorphic mappings
* ''32H12'' Boundary uniqueness of mappings
* ''32H25'' Picard-type theorems and generalizations {For function-theoretic properties, see [[32A22|32Axx]]}
* ''32H30'' Value distribution theory in higher dimensions {For function-theoretic properties, see [[32A22|32Axx]]}
* ''32H35'' Proper mappings, finiteness theorems
* ''32H40'' Boundary regularity of mappings
* ''32H50'' Iteration problems
* ''32H99'' None of the above, but in this section
!!![[32|32-XX]]Jxx  Compact analytic spaces {For Riemann surfaces, see [[14Hxx|14Hxx]], [[30Fxx|30Fxx]]; for algebraic theory, see [[14Jxx|14Jxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/32Jxx.html]]}{{moveright{< [[32Hxx |32Hxx]] | [[32-XX |32-XX]] | [[32Kxx |32Kxx]] >}}}
* ''32J05'' Compactification of analytic spaces
* ''32J10'' Algebraic dependence theorems
* ''32J15'' Compact surfaces
* ''32J17'' Compact $3$-folds
* ''32J18'' Compact $n$-folds
* ''32J25'' Transcendental methods of algebraic geometry [See also [[14C30|14Cxx]]]
* ''32J27'' Compact Kähler manifolds: generalizations, classification
* ''32J81'' Applications to physics
* ''32J99'' None of the above, but in this section
!!![[32|32-XX]]Kxx  Generalizations of analytic spaces (should also be assigned at least one other classification number from Section 32 describing the type of problem) {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/32Kxx.html]]}{{moveright{< [[32Jxx |32Jxx]] | [[32-XX |32-XX]] | [[32Lxx |32Lxx]] >}}}
* ''32K05'' Banach analytic spaces [See also [[58Bxx|58Bxx]]]
* ''32K07'' Formal and graded complex spaces [See also [[58C50|58Cxx]]]
* ''32K15'' Differentiable functions on analytic spaces, differentiable spaces [See also [[58C25|58Cxx]]]
* ''32K99'' None of the above, but in this section
!!![[32|32-XX]]Lxx  Holomorphic fiber spaces [See also [[55Rxx|55Rxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/32Lxx.html]]}{{moveright{< [[32Kxx |32Kxx]] | [[32-XX |32-XX]] | [[32Mxx |32Mxx]] >}}}
* ''32L05'' Holomorphic bundles and generalizations
* ''32L10'' Sheaves and cohomology of sections of holomorphic vector bundles, general results [See also [[14F05|14Fxx]], [[18F20|18Fxx]], [[55N30|55Nxx]]]
* ''32L15'' Bundle convexity [See also [[32F10|32Fxx]]]
* ''32L20'' Vanishing theorems
* ''32L25'' Twistor theory, double fibrations [See also [[53C28|53Cxx]]]
* ''32L81'' Applications to physics
* ''32L99'' None of the above, but in this section
!!![[32|32-XX]]Mxx  Complex spaces with a group of automorphisms {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/32Mxx.html]]}{{moveright{< [[32Lxx |32Lxx]] | [[32-XX |32-XX]] | [[32Nxx |32Nxx]] >}}}
* ''32M05'' Complex Lie groups, automorphism groups acting on complex spaces [See also [[22E10|22Exx]]]
* ''32M10'' Homogeneous complex manifolds [See also [[14M17|14Mxx]], [[57T15|57Txx]]]
* ''32M12'' Almost homogeneous manifolds and spaces [See also [[14M17|14Mxx]]]
* ''32M15'' Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also [[22E10|22Exx]], [[22E40|22Exx]], [[53C35|53Cxx]], [[57T15|57Txx]]]
* ''32M17'' Automorphism groups of ${\bf C}^n$ and affine manifolds
* ''32M25'' Complex vector fields
* ''32M99'' None of the above, but in this section
!!![[32|32-XX]]Nxx  Automorphic functions [See also [[11Fxx|11Fxx]], [[20H10|20Hxx]], [[22E40|22Exx]], [[30F35|30Fxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/32Nxx.html]]}{{moveright{< [[32Mxx |32Mxx]] | [[32-XX |32-XX]] | [[32Pxx |32Pxx]] >}}}
* ''32N05'' General theory of automorphic functions of several complex variables
* ''32N10'' Automorphic forms
* ''32N15'' Automorphic functions in symmetric domains
* ''32N99'' None of the above, but in this section
!!![[32|32-XX]]Pxx  ~Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem) {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/32Pxx.html]]}{{moveright{< [[32Nxx |32Nxx]] | [[32-XX |32-XX]] | [[32Qxx |32Qxx]] >}}}
* ''32P05'' ~Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem)
* ''32P99'' None of the above, but in this section
!!![[32|32-XX]]Qxx  Complex manifolds {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/32Qxx.html]]}{{moveright{< [[32Pxx |32Pxx]] | [[32-XX |32-XX]] | [[32Sxx |32Sxx]] >}}}
* ''32Q05'' Negative curvature manifolds
* ''32Q10'' Positive curvature manifolds
* ''32Q15'' Kähler manifolds
* ''32Q20'' ~Kähler-Einstein manifolds [See also [[53Cxx|53Cxx]]]
* ''32Q25'' ~Calabi-Yau theory [See also [[14J30|14Jxx]]]
* ''32Q26'' Notions of stability
* ''32Q28'' Stein manifolds
* ''32Q30'' Uniformization
* ''32Q35'' Complex manifolds as subdomains of Euclidean space
* ''32Q40'' Embedding theorems
* ''32Q45'' Hyperbolic and Kobayashi hyperbolic manifolds
* ''32Q55'' Topological aspects of complex manifolds
* ''32Q57'' Classification theorems
* ''32Q60'' Almost complex manifolds
* ''32Q65'' Pseudoholomorphic curves
* ''32Q99'' None of the above, but in this section
!!![[32|32-XX]]Sxx  Singularities [See also [[58Kxx|58Kxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/32Sxx.html]]}{{moveright{< [[32Qxx |32Qxx]] | [[32-XX |32-XX]] | [[32Txx |32Txx]] >}}}
* ''32S05'' Local singularities [See also [[14J17|14Jxx]]]
* ''32S10'' Invariants of analytic local rings
* ''32S15'' Equisingularity (topological and analytic) [See also [[14E15|14Exx]]]
* ''32S20'' Global theory of singularities; cohomological properties [See also [[14E15|14Exx]]]
* ''32S22'' Relations with arrangements of hyperplanes [See also [[52C35|52Cxx]]]
* ''32S25'' Surface and hypersurface singularities [See also [[14J17|14Jxx]]]
* ''32S30'' Deformations of singularities; vanishing cycles [See also [[14B07|14Bxx]]]
* ''32S35'' Mixed Hodge theory of singular varieties [See also [[14C30|14Cxx]], [[14D07|14Dxx]]]
* ''32S40'' Monodromy; relations with differential equations and $D$-modules
* ''32S45'' Modifications; resolution of singularities [See also [[14E15|14Exx]]]
* ''32S50'' Topological aspects: Lefschetz theorems, topological classification, invariants
* ''32S55'' Milnor fibration; relations with knot theory [See also [[57M25|57Mxx]], [[57Q45|57Qxx]]]
* ''32S60'' Stratifications; constructible sheaves; intersection cohomology [See also [[58Kxx|58Kxx]]]
* ''32S65'' Singularities of holomorphic vector fields and foliations
* ''32S70'' Other operations on singularities
* ''32S99'' None of the above, but in this section
!!![[32|32-XX]]Txx  Pseudoconvex domains {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/32Txx.html]]}{{moveright{< [[32Sxx |32Sxx]] | [[32-XX |32-XX]] | [[32Uxx |32Uxx]] >}}}
* ''32T05'' Domains of holomorphy
* ''32T15'' Strongly pseudoconvex domains
* ''32T20'' Worm domains
* ''32T25'' Finite type domains
* ''32T27'' Geometric and analytic invariants on weakly pseudoconvex boundaries
* ''32T35'' Exhaustion functions
* ''32T40'' Peak functions
* ''32T99'' None of the above, but in this section
!!![[32|32-XX]]Uxx  Pluripotential theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/32Uxx.html]]}{{moveright{< [[32Txx |32Txx]] | [[32-XX |32-XX]] | [[32Vxx |32Vxx]] >}}}
* ''32U05'' Plurisubharmonic functions and generalizations [See also [[31C10|31Cxx]]]
* ''32U10'' Plurisubharmonic exhaustion functions
* ''32U15'' General pluripotential theory
* ''32U20'' Capacity theory and generalizations
* ''32U25'' Lelong numbers
* ''32U30'' Removable sets
* ''32U35'' Pluricomplex Green functions
* ''32U40'' Currents
* ''32U99'' None of the above, but in this section
!!![[32|32-XX]]Vxx  CR manifolds {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/32Vxx.html]]}{{moveright{< [[32Uxx |32Uxx]] | [[32-XX |32-XX]] | [[32Wxx |32Wxx]] >}}}
* ''32V05'' CR structures, CR operators, and generalizations
* ''32V10'' CR functions
* ''32V15'' CR manifolds as boundaries of domains
* ''32V20'' Analysis on CR manifolds
* ''32V25'' Extension of functions and other analytic objects from CR manifolds
* ''32V30'' Embeddings of CR manifolds
* ''32V35'' Finite type conditions on CR manifolds
* ''32V40'' Real submanifolds in complex manifolds
* ''32V99'' None of the above, but in this section
!!!32-XX Several complex variables and analytic spaces {For infinite-dimensional holomorphy, see [[46G20|46Gxx]], [[58B12|58Bxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/32-XX.html]]}{{moveright{< [[31-XX |31-XX]] | [[MSC |MSC2010]] | [[32Axx |32Axx]] >}}}
* ''32-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''32-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''32-02'' Research exposition (monographs, survey articles)
* ''32-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''32-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''32-06'' Proceedings, conferences, collections, etc.
* ''[[32Axx|32Axx]]''  Holomorphic functions of several complex variables
* ''[[32Bxx|32Bxx]]''  Local analytic geometry [See also [[13-XX|13-XX]] and [[14-XX|14-XX]]]
* ''[[32Cxx|32Cxx]]''  Analytic spaces
* ''[[32Dxx|32Dxx]]''  Analytic continuation
* ''[[32Exx|32Exx]]''  Holomorphic convexity
* ''[[32Fxx|32Fxx]]''  Geometric convexity
* ''[[32Gxx|32Gxx]]''  Deformations of analytic structures
* ''[[32Hxx|32Hxx]]''  Holomorphic mappings and correspondences
* ''[[32Jxx|32Jxx]]''  Compact analytic spaces {For Riemann surfaces, see [[14Hxx|14Hxx]], [[30Fxx|30Fxx]]; for algebraic theory, see [[14Jxx|14Jxx]]}
* ''[[32Kxx|32Kxx]]''  Generalizations of analytic spaces (should also be assigned at least one other classification number from Section 32 describing the type of problem)
* ''[[32Lxx|32Lxx]]''  Holomorphic fiber spaces [See also [[55Rxx|55Rxx]]]
* ''[[32Mxx|32Mxx]]''  Complex spaces with a group of automorphisms
* ''[[32Nxx|32Nxx]]''  Automorphic functions [See also [[11Fxx|11Fxx]], [[20H10|20Hxx]], [[22E40|22Exx]], [[30F35|30Fxx]]]
* ''[[32Pxx|32Pxx]]''  ~Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem)
* ''[[32Qxx|32Qxx]]''  Complex manifolds
* ''[[32Sxx|32Sxx]]''  Singularities [See also [[58Kxx|58Kxx]]]
* ''[[32Txx|32Txx]]''  Pseudoconvex domains
* ''[[32Uxx|32Uxx]]''  Pluripotential theory
* ''[[32Vxx|32Vxx]]''  CR manifolds
* ''[[32Wxx|32Wxx]]''  Differential operators in several variables
!!![[32|32-XX]]Wxx  Differential operators in several variables {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/32Wxx.html]]}{{moveright{< [[32Vxx |32Vxx]] | [[32-XX |32-XX]] | [[33-XX |33-XX]] >}}}
* ''32W05'' $\overline\partial$ and $\overline\partial$-Neumann operators
* ''32W10'' $\overline\partial_b$ and $\overline\partial_b$-Neumann operators
* ''32W20'' Complex ~Monge-Ampère operators
* ''32W25'' Pseudodifferential operators in several complex variables
* ''32W30'' Heat kernels in several complex variables
* ''32W50'' Other partial differential equations of complex analysis
* ''32W99'' None of the above, but in this section
!!![[33|33-XX]]Bxx  Elementary classical functions {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/33Bxx.html]]}{{moveright{< [[32-XX |32-XX]] | [[33-XX |33-XX]] | [[33Cxx |33Cxx]] >}}}
* ''33B10'' Exponential and trigonometric functions
* ''33B15'' Gamma, beta and polygamma functions
* ''33B20'' Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)
* ''33B30'' Higher logarithm functions
* ''33B99'' None of the above, but in this section
!!![[33|33-XX]]Cxx  Hypergeometric functions {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/33Cxx.html]]}{{moveright{< [[33Bxx |33Bxx]] | [[33-XX |33-XX]] | [[33Dxx |33Dxx]] >}}}
* ''33C05'' Classical hypergeometric functions, ${}_2F_1$
* ''33C10'' Bessel and Airy functions, cylinder functions, ${}_0F_1$
* ''33C15'' Confluent hypergeometric functions, Whittaker functions, ${}_1F_1$
* ''33C20'' Generalized hypergeometric series, ${}_pF_q$
* ''33C45'' Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also [[42C05|42Cxx]] for general orthogonal polynomials and functions]
* ''33C47'' Other special orthogonal polynomials and functions
* ''33C50'' Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable
* ''33C52'' Orthogonal polynomials and functions associated with root systems
* ''33C55'' Spherical harmonics
* ''33C60'' Hypergeometric integrals and functions defined by them ($E$, $G$, $H$ and $I$ functions)
* ''33C65'' Appell, Horn and Lauricella functions
* ''33C67'' Hypergeometric functions associated with root systems
* ''33C70'' Other hypergeometric functions and integrals in several variables
* ''33C75'' Elliptic integrals as hypergeometric functions
* ''33C80'' Connections with groups and algebras, and related topics
* ''33C90'' Applications
* ''33C99'' None of the above, but in this section
!!![[33|33-XX]]Dxx  Basic hypergeometric functions {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/33Dxx.html]]}{{moveright{< [[33Cxx |33Cxx]] | [[33-XX |33-XX]] | [[33Exx |33Exx]] >}}}
* ''33D05'' $q$-gamma functions, $q$-beta functions and integrals
* ''33D15'' Basic hypergeometric functions in one variable, ${}_r\phi_s$
* ''33D45'' Basic orthogonal polynomials and functions (~Askey-Wilson polynomials, etc.)
* ''33D50'' Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable
* ''33D52'' Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)
* ''33D60'' Basic hypergeometric integrals and functions defined by them
* ''33D65'' Bibasic functions and multiple bases
* ''33D67'' Basic hypergeometric functions associated with root systems
* ''33D70'' Other basic hypergeometric functions and integrals in several variables
* ''33D80'' Connections with quantum groups, Chevalley groups, $p$-adic groups, Hecke algebras, and related topics
* ''33D90'' Applications
* ''33D99'' None of the above, but in this section
!!![[33|33-XX]]Exx  Other special functions {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/33Exx.html]]}{{moveright{< [[33Dxx |33Dxx]] | [[33-XX |33-XX]] | [[33Fxx |33Fxx]] >}}}
* ''33E05'' Elliptic functions and integrals
* ''33E10'' Lamé, Mathieu, and spheroidal wave functions
* ''33E12'' ~Mittag-Leffler functions and generalizations
* ''33E15'' Other wave functions
* ''33E17'' Painlevé-type functions
* ''33E20'' Other functions defined by series and integrals
* ''33E30'' Other functions coming from differential, difference and integral equations
* ''33E50'' Special functions in characteristic $p$ (gamma functions, etc.)
* ''33E99'' None of the above, but in this section
!!!33-XX Special functions ([[33-XX|33-XX]] deals with the properties of functions as functions) {For orthogonal functions, see [[42Cxx|42Cxx]]; for aspects of combinatorics see [[05Axx|05Axx]]; for number-theoretic aspects see [[11-XX|11-XX]]; for representation theory see [[22Exx|22Exx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/33-XX.html]]}{{moveright{< [[32-XX |32-XX]] | [[MSC |MSC2010]] | [[33Bxx |33Bxx]] >}}}
* ''33-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''33-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''33-02'' Research exposition (monographs, survey articles)
* ''33-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''33-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''33-06'' Proceedings, conferences, collections, etc.
* ''[[33Bxx|33Bxx]]''  Elementary classical functions
* ''[[33Cxx|33Cxx]]''  Hypergeometric functions
* ''[[33Dxx|33Dxx]]''  Basic hypergeometric functions
* ''[[33Exx|33Exx]]''  Other special functions
* ''[[33Fxx|33Fxx]]''  Computational aspects
!!![[33|33-XX]]Fxx  Computational aspects {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/33Fxx.html]]}{{moveright{< [[33Exx |33Exx]] | [[33-XX |33-XX]] | [[34-XX |34-XX]] >}}}
* ''33F05'' Numerical approximation and evaluation [See also [[65D20|65Dxx]]]
* ''33F10'' Symbolic computation (Gosper and Zeilberger algorithms, etc.) [See also [[68W30|68Wxx]]]
* ''33F99'' None of the above, but in this section
!!![[34|34-XX]]Axx  General theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/34Axx.html]]}{{moveright{< [[33-XX |33-XX]] | [[34-XX |34-XX]] | [[34Bxx |34Bxx]] >}}}
* ''34A05'' Explicit solutions and reductions
* ''34A07'' Fuzzy differential equations
* ''34A08'' Fractional differential equations
* ''34A09'' Implicit equations, differential-algebraic equations [See also [[65L80|65Lxx]]]
* ''34A12'' Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions
* ''34A25'' Analytical theory: series, transformations, transforms, operational calculus, etc. [See also [[44-XX|44-XX]]]
* ''34A26'' Geometric methods in differential equations
* ''34A30'' Linear equations and systems, general
* ''34A33'' Lattice differential equations
* ''34A34'' Nonlinear equations and systems, general
* ''34A35'' Differential equations of infinite order
* ''34A36'' Discontinuous equations
* ''34A37'' Differential equations with impulses
* ''34A38'' Hybrid systems
* ''34A40'' Differential inequalities [See also [[26D20|26Dxx]]]
* ''34A45'' Theoretical approximation of solutions {For numerical analysis, see [[65Lxx|65Lxx]]}
* ''34A55'' Inverse problems
* ''34A60'' Differential inclusions [See also [[49J21|49Jxx]], [[49K21|49Kxx]]]
* ''34A99'' None of the above, but in this section
!!![[34|34-XX]]Bxx  Boundary value problems {For ordinary differential operators, see [[34Lxx|34Lxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/34Bxx.html]]}{{moveright{< [[34Axx |34Axx]] | [[34-XX |34-XX]] | [[34Cxx |34Cxx]] >}}}
* ''34B05'' Linear boundary value problems
* ''34B07'' Linear boundary value problems with nonlinear dependence on the spectral parameter
* ''34B08'' Parameter dependent boundary value problems
* ''34B09'' Boundary eigenvalue problems
* ''34B10'' Nonlocal and multipoint boundary value problems
* ''34B15'' Nonlinear boundary value problems
* ''34B16'' Singular nonlinear boundary value problems
* ''34B18'' Positive solutions of nonlinear boundary value problems
* ''34B20'' Weyl theory and its generalizations
* ''34B24'' ~Sturm-Liouville theory [See also [[34Lxx|34Lxx]]]
* ''34B27'' Green functions
* ''34B30'' Special equations (Mathieu, Hill, Bessel, etc.)
* ''34B37'' Boundary value problems with impulses
* ''34B40'' Boundary value problems on infinite intervals
* ''34B45'' Boundary value problems on graphs and networks
* ''34B60'' Applications
* ''34B99'' None of the above, but in this section
!!![[34|34-XX]]Cxx  Qualitative theory [See also [[37-XX|37-XX]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/34Cxx.html]]}{{moveright{< [[34Bxx |34Bxx]] | [[34-XX |34-XX]] | [[34Dxx |34Dxx]] >}}}
* ''34C05'' Location of integral curves, singular points, limit cycles
* ''34C07'' Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications)
* ''34C08'' Connections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.)
* ''34C10'' Oscillation theory, zeros, disconjugacy and comparison theory
* ''34C11'' Growth, boundedness
* ''34C12'' Monotone systems
* ''34C14'' Symmetries, invariants
* ''34C15'' Nonlinear oscillations, coupled oscillators
* ''34C20'' Transformation and reduction of equations and systems, normal forms
* ''34C23'' Bifurcation [See also [[37Gxx|37Gxx]]]
* ''34C25'' Periodic solutions
* ''34C26'' Relaxation oscillations
* ''34C27'' Almost and pseudo-almost periodic solutions
* ''34C28'' Complex behavior, chaotic systems [See also [[37Dxx|37Dxx]]]
* ''34C29'' Averaging method
* ''34C37'' Homoclinic and heteroclinic solutions
* ''34C40'' Equations and systems on manifolds
* ''34C41'' Equivalence, asymptotic equivalence
* ''34C45'' Invariant manifolds
* ''34C46'' Multifrequency systems
* ''34C55'' Hysteresis
* ''34C60'' Qualitative investigation and simulation of models
* ''34C99'' None of the above, but in this section
!!![[34|34-XX]]Dxx  Stability theory [See also [[37C75|37Cxx]], [[93Dxx|93Dxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/34Dxx.html]]}{{moveright{< [[34Cxx |34Cxx]] | [[34-XX |34-XX]] | [[34Exx |34Exx]] >}}}
* ''34D05'' Asymptotic properties
* ''34D06'' Synchronization
* ''34D08'' Characteristic and Lyapunov exponents
* ''34D09'' Dichotomy, trichotomy
* ''34D10'' Perturbations
* ''34D15'' Singular perturbations
* ''34D20'' Stability
* ''34D23'' Global stability
* ''34D30'' Structural stability and analogous concepts [See also [[37C20|37Cxx]]]
* ''34D35'' Stability of manifolds of solutions
* ''34D45'' Attractors [See also [[37C70|37Cxx]], [[37D45|37Dxx]]]
* ''34D99'' None of the above, but in this section
!!![[34|34-XX]]Exx  Asymptotic theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/34Exx.html]]}{{moveright{< [[34Dxx |34Dxx]] | [[34-XX |34-XX]] | [[34Fxx |34Fxx]] >}}}
* ''34E05'' Asymptotic expansions
* ''34E10'' Perturbations, asymptotics
* ''34E13'' Multiple scale methods
* ''34E15'' Singular perturbations, general theory
* ''34E17'' Canard solutions
* ''34E18'' Methods of nonstandard analysis
* ''34E20'' Singular perturbations, turning point theory, WKB methods
* ''34E99'' None of the above, but in this section
!!![[34|34-XX]]Fxx  Equations and systems with randomness [See also [[34K50|34Kxx]], [[60H10|60Hxx]], [[93E03|93Exx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/34Fxx.html]]}{{moveright{< [[34Exx |34Exx]] | [[34-XX |34-XX]] | [[34Gxx |34Gxx]] >}}}
* ''34F05'' Equations and systems with randomness [See also [[34K50|34Kxx]], [[60H10|60Hxx]], [[93E03|93Exx]]]
* ''34F10'' Bifurcation
* ''34F15'' Resonance phenomena
* ''34F99'' None of the above, but in this section
!!![[34|34-XX]]Gxx  Differential equations in abstract spaces [See also [[34Lxx|34Lxx]], [[37Kxx|37Kxx]], [[47Dxx|47Dxx]], [[47Hxx|47Hxx]], [[47Jxx|47Jxx]], [[58D25|58Dxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/34Gxx.html]]}{{moveright{< [[34Fxx |34Fxx]] | [[34-XX |34-XX]] | [[34Hxx |34Hxx]] >}}}
* ''34G10'' Linear equations [See also [[47D06|47Dxx]], [[47D09|47Dxx]]]
* ''34G20'' Nonlinear equations [See also [[47Hxx|47Hxx]], [[47Jxx|47Jxx]]]
* ''34G25'' Evolution inclusions
* ''34G99'' None of the above, but in this section
!!![[34|34-XX]]Hxx  Control problems [See also [[49J15|49Jxx]], [[49K15|49Kxx]], [[93C15|93Cxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/34Hxx.html]]}{{moveright{< [[34Gxx |34Gxx]] | [[34-XX |34-XX]] | [[34Kxx |34Kxx]] >}}}
* ''34H05'' Control problems [See also [[49J15|49Jxx]], [[49K15|49Kxx]], [[93C15|93Cxx]]]
* ''34H10'' Chaos control
* ''34H15'' Stabilization
* ''34H20'' Bifurcation control
* ''34H99'' None of the above, but in this section
!!![[34|34-XX]]Kxx  Functional-differential and differential-difference equations [See also [[37-XX|37-XX]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/34Kxx.html]]}{{moveright{< [[34Hxx |34Hxx]] | [[34-XX |34-XX]] | [[34Lxx |34Lxx]] >}}}
* ''34K05'' General theory
* ''34K06'' Linear functional-differential equations
* ''34K07'' Theoretical approximation of solutions
* ''34K08'' Spectral theory of functional-differential operators
* ''34K09'' Functional-differential inclusions
* ''34K10'' Boundary value problems
* ''34K11'' Oscillation theory
* ''34K12'' Growth, boundedness, comparison of solutions
* ''34K13'' Periodic solutions
* ''34K14'' Almost and pseudo-periodic solutions
* ''34K17'' Transformation and reduction of equations and systems, normal forms
* ''34K18'' Bifurcation theory
* ''34K19'' Invariant manifolds
* ''34K20'' Stability theory
* ''34K21'' Stationary solutions
* ''34K23'' Complex (chaotic) behavior of solutions
* ''34K25'' Asymptotic theory
* ''34K26'' Singular perturbations
* ''34K27'' Perturbations
* ''34K28'' Numerical approximation of solutions
* ''34K29'' Inverse problems
* ''34K30'' Equations in abstract spaces [See also [[34Gxx|34Gxx]], [[35R09|35Rxx]], [[35R10|35Rxx]], [[47Jxx|47Jxx]]]
* ''34K31'' Lattice functional-differential equations
* ''34K32'' Implicit equations
* ''34K33'' Averaging
* ''34K34'' Hybrid systems
* ''34K35'' Control problems [See also [[49J21|49Jxx]], [[49K21|49Kxx]], [[93C23|93Cxx]]]
* ''34K36'' Fuzzy functional-differential equations
* ''34K37'' Functional-differential equations with fractional derivatives
* ''34K38'' Functional-differential inequalities
* ''34K40'' Neutral equations
* ''34K45'' Equations with impulses
* ''34K50'' Stochastic functional-differential equations [See also [[60Hxx|60Hxx]]]
* ''34K60'' Qualitative investigation and simulation of models
* ''34K99'' None of the above, but in this section
!!![[34|34-XX]]Lxx  Ordinary differential operators [See also [[47E05|47Exx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/34Lxx.html]]}{{moveright{< [[34Kxx |34Kxx]] | [[34-XX |34-XX]] | [[34Mxx |34Mxx]] >}}}
* ''34L05'' General spectral theory
* ''34L10'' Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions
* ''34L15'' Eigenvalues, estimation of eigenvalues, upper and lower bounds
* ''34L16'' Numerical approximation of eigenvalues and of other parts of the spectrum
* ''34L20'' Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions
* ''34L25'' Scattering theory, inverse scattering
* ''34L30'' Nonlinear ordinary differential operators
* ''34L40'' Particular operators (Dirac, one-dimensional Schrödinger, etc.)
* ''34L99'' None of the above, but in this section
!!![[34|34-XX]]Mxx  Differential equations in the complex domain [See also [[30Dxx|30Dxx]], [[32G34|32Gxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/34Mxx.html]]}{{moveright{< [[34Lxx |34Lxx]] | [[34-XX |34-XX]] | [[34Nxx |34Nxx]] >}}}
* ''34M03'' Linear equations and systems
* ''34M05'' Entire and meromorphic solutions
* ''34M10'' Oscillation, growth of solutions
* ''34M15'' Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical)
* ''34M25'' Formal solutions, transform techniques
* ''34M30'' Asymptotics, summation methods
* ''34M35'' Singularities, monodromy, local behavior of solutions, normal forms
* ''34M40'' Stokes phenomena and connection problems (linear and nonlinear)
* ''34M45'' Differential equations on complex manifolds
* ''34M50'' Inverse problems (~Riemann-Hilbert, inverse differential Galois, etc.)
* ''34M55'' Painlevé and other special equations; classification, hierarchies;
* ''34M56'' Isomonodromic deformations
* ''34M60'' Singular perturbation problems in the complex domain (complex WKB, turning points, steepest descent) [See also [[34E20|34Exx]]]
* ''34M99'' None of the above, but in this section
!!!34-XX Ordinary differential equations {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/34-XX.html]]}{{moveright{< [[33-XX |33-XX]] | [[MSC |MSC2010]] | [[34Axx |34Axx]] >}}}
* ''34-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''34-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''34-02'' Research exposition (monographs, survey articles)
* ''34-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''34-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''34-06'' Proceedings, conferences, collections, etc.
* ''[[34Axx|34Axx]]''  General theory
* ''[[34Bxx|34Bxx]]''  Boundary value problems {For ordinary differential operators, see [[34Lxx|34Lxx]]}
* ''[[34Cxx|34Cxx]]''  Qualitative theory [See also [[37-XX|37-XX]]]
* ''[[34Dxx|34Dxx]]''  Stability theory [See also [[37C75|37Cxx]], [[93Dxx|93Dxx]]]
* ''[[34Exx|34Exx]]''  Asymptotic theory
* ''[[34Fxx|34Fxx]]''  Equations and systems with randomness [See also [[34K50|34Kxx]], [[60H10|60Hxx]], [[93E03|93Exx]]]
* ''[[34Gxx|34Gxx]]''  Differential equations in abstract spaces [See also [[34Lxx|34Lxx]], [[37Kxx|37Kxx]], [[47Dxx|47Dxx]], [[47Hxx|47Hxx]], [[47Jxx|47Jxx]], [[58D25|58Dxx]]]
* ''[[34Hxx|34Hxx]]''  Control problems [See also [[49J15|49Jxx]], [[49K15|49Kxx]], [[93C15|93Cxx]]]
* ''[[34Kxx|34Kxx]]''  Functional-differential and differential-difference equations [See also [[37-XX|37-XX]]]
* ''[[34Lxx|34Lxx]]''  Ordinary differential operators [See also [[47E05|47Exx]]]
* ''[[34Mxx|34Mxx]]''  Differential equations in the complex domain [See also [[30Dxx|30Dxx]], [[32G34|32Gxx]]]
* ''[[34Nxx|34Nxx]]''  Dynamic equations on time scales or measure chains {For real analysis on time scales see [[26E70|26Exx]]}
!!![[34|34-XX]]Nxx  Dynamic equations on time scales or measure chains {For real analysis on time scales see [[26E70|26Exx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/34Nxx.html]]}{{moveright{< [[34Mxx |34Mxx]] | [[34-XX |34-XX]] | [[35-XX |35-XX]] >}}}
* ''34N05'' Dynamic equations on time scales or measure chains {For real analysis on time scales or measure chains, see [[26E70|26Exx]]}
* ''34N99'' None of the above, but in this section
!!![[35|35-XX]]Axx  General topics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/35Axx.html]]}{{moveright{< [[34-XX |34-XX]] | [[35-XX |35-XX]] | [[35Bxx |35Bxx]] >}}}
* ''35A01'' Existence problems: global existence, local existence, non-existence
* ''35A02'' Uniqueness problems: global uniqueness, local uniqueness, non-uniqueness
* ''35A08'' Fundamental solutions
* ''35A09'' Classical solutions
* ''35A10'' ~Cauchy-Kovalevskaya theorems
* ''35A15'' Variational methods
* ''35A16'' Topological and monotonicity methods
* ''35A17'' Parametrices
* ''35A18'' Wave front sets
* ''35A20'' Analytic methods, singularities
* ''35A21'' Propagation of singularities
* ''35A22'' Transform methods (e.g. integral transforms)
* ''35A23'' Inequalities involving derivatives and differential and integral operators, inequalities for integrals
* ''35A24'' Methods of ordinary differential equations
* ''35A25'' Other special methods
* ''35A27'' Microlocal methods; methods of sheaf theory and homological algebra in PDE [See also [[32C38|32Cxx]], [[58J15|58Jxx]]]
* ''35A30'' Geometric theory, characteristics, transformations [See also [[58J70|58Jxx]], [[58J72|58Jxx]]]
* ''35A35'' Theoretical approximation to solutions {For numerical analysis, see [[65Mxx|65Mxx]], [[65Nxx|65Nxx]]}
* ''35A99'' None of the above, but in this section
!!![[35|35-XX]]Bxx  Qualitative properties of solutions {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/35Bxx.html]]}{{moveright{< [[35Axx |35Axx]] | [[35-XX |35-XX]] | [[35Cxx |35Cxx]] >}}}
* ''35B05'' Oscillation, zeros of solutions, mean value theorems, etc.
* ''35B06'' Symmetries, invariants, etc.
* ''35B07'' Axially symmetric solutions
* ''35B08'' Entire solutions
* ''35B09'' Positive solutions
* ''35B10'' Periodic solutions
* ''35B15'' Almost and pseudo-almost periodic solutions
* ''35B20'' Perturbations
* ''35B25'' Singular perturbations
* ''35B27'' Homogenization; equations in media with periodic structure [See also [[74Qxx|74Qxx]], [[76M50|76Mxx]]]
* ''35B30'' Dependence of solutions on initial and boundary data, parameters [See also [[37Cxx|37Cxx]]]
* ''35B32'' Bifurcation [See also [[37Gxx|37Gxx]], [[37K50|37Kxx]]]
* ''35B33'' Critical exponents
* ''35B34'' Resonances
* ''35B35'' Stability
* ''35B36'' Pattern formation
* ''35B38'' Critical points
* ''35B40'' Asymptotic behavior of solutions
* ''35B41'' Attractors
* ''35B42'' Inertial manifolds
* ''35B44'' Blow-up
* ''35B45'' A priori estimates
* ''35B50'' Maximum principles
* ''35B51'' Comparison principles
* ''35B53'' Liouville theorems, ~Phragmén-Lindelöf theorems
* ''35B60'' Continuation and prolongation of solutions [See also [[58A15|58Axx]], [[58A17|58Axx]], [[58Hxx|58Hxx]]]
* ''35B65'' Smoothness and regularity of solutions
* ''35B99'' None of the above, but in this section
!!![[35|35-XX]]Cxx  Representations of solutions {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/35Cxx.html]]}{{moveright{< [[35Bxx |35Bxx]] | [[35-XX |35-XX]] | [[35Dxx |35Dxx]] >}}}
* ''35C05'' Solutions in closed form
* ''35C06'' Self-similar solutions
* ''35C07'' Traveling wave solutions
* ''35C08'' Soliton solutions
* ''35C09'' Trigonometric solutions
* ''35C10'' Series solutions
* ''35C11'' Polynomial solutions
* ''35C15'' Integral representations of solutions
* ''35C20'' Asymptotic expansions
* ''35C99'' None of the above, but in this section
!!![[35|35-XX]]Dxx  Generalized solutions {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/35Dxx.html]]}{{moveright{< [[35Cxx |35Cxx]] | [[35-XX |35-XX]] | [[35Exx |35Exx]] >}}}
* ''35D30'' Weak solutions
* ''35D35'' Strong solutions
* ''35D40'' Viscosity solutions
* ''35D99'' None of the above, but in this section
!!![[35|35-XX]]Exx  Equations and systems with constant coefficients [See also [[35N05|35Nxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/35Exx.html]]}{{moveright{< [[35Dxx |35Dxx]] | [[35-XX |35-XX]] | [[35Fxx |35Fxx]] >}}}
* ''35E05'' Fundamental solutions
* ''35E10'' Convexity properties
* ''35E15'' Initial value problems
* ''35E20'' General theory
* ''35E99'' None of the above, but in this section
!!![[35|35-XX]]Fxx  General first-order equations and systems {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/35Fxx.html]]}{{moveright{< [[35Exx |35Exx]] | [[35-XX |35-XX]] | [[35Gxx |35Gxx]] >}}}
* ''35F05'' Linear first-order equations
* ''35F10'' Initial value problems for linear first-order equations
* ''35F15'' Boundary value problems for linear first-order equations
* ''35F16'' Initial-boundary value problems for linear first-order equations
* ''35F20'' Nonlinear first-order equations
* ''35F21'' ~Hamilton-Jacobi equations
* ''35F25'' Initial value problems for nonlinear first-order equations
* ''35F30'' Boundary value problems for nonlinear first-order equations
* ''35F31'' Initial-boundary value problems for nonlinear first-order equations
* ''35F35'' Linear first-order systems
* ''35F40'' Initial value problems for linear first-order systems
* ''35F45'' Boundary value problems for linear first-order systems
* ''35F46'' Initial-boundary value problems for linear first-order systems
* ''35F50'' Nonlinear first-order systems
* ''35F55'' Initial value problems for nonlinear first-order systems
* ''35F60'' Boundary value problems for nonlinear first-order systems
* ''35F61'' Initial-boundary value problems for nonlinear first-order systems
* ''35F99'' None of the above, but in this section
!!![[35|35-XX]]Gxx  General higher-order equations and systems {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/35Gxx.html]]}{{moveright{< [[35Fxx |35Fxx]] | [[35-XX |35-XX]] | [[35Hxx |35Hxx]] >}}}
* ''35G05'' Linear higher-order equations
* ''35G10'' Initial value problems for linear higher-order equations
* ''35G15'' Boundary value problems for linear higher-order equations
* ''35G16'' Initial-boundary value problems for linear higher-order equations
* ''35G20'' Nonlinear higher-order equations
* ''35G25'' Initial value problems for nonlinear higher-order equations
* ''35G30'' Boundary value problems for nonlinear higher-order equations
* ''35G31'' Initial-boundary value problems for nonlinear higher-order equations
* ''35G35'' Linear higher-order systems
* ''35G40'' Initial value problems for linear higher-order systems
* ''35G45'' Boundary value problems for linear higher-order systems
* ''35G46'' Initial-boundary value problems for linear higher-order systems
* ''35G50'' Nonlinear higher-order systems
* ''35G55'' Initial value problems for nonlinear higher-order systems
* ''35G60'' Boundary value problems for nonlinear higher-order systems
* ''35G61'' Initial-boundary value problems for nonlinear higher-order systems
* ''35G99'' None of the above, but in this section
!!![[35|35-XX]]Hxx  Close-to-elliptic equations and systems {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/35Hxx.html]]}{{moveright{< [[35Gxx |35Gxx]] | [[35-XX |35-XX]] | [[35Jxx |35Jxx]] >}}}
* ''35H10'' Hypoelliptic equations
* ''35H20'' Subelliptic equations
* ''35H30'' Quasi-elliptic equations
* ''35H99'' None of the above, but in this section
!!![[35|35-XX]]Jxx  Elliptic equations and systems [See also [[58J10|58Jxx]], [[58J20|58Jxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/35Jxx.html]]}{{moveright{< [[35Hxx |35Hxx]] | [[35-XX |35-XX]] | [[35Kxx |35Kxx]] >}}}
* ''35J05'' Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also [[31Axx|31Axx]], [[31Bxx|31Bxx]]]
* ''35J08'' Green's functions
* ''35J10'' Schrödinger operator [See also [[35Pxx|35Pxx]]]
* ''35J15'' Second-order elliptic equations
* ''35J20'' Variational methods for second-order elliptic equations
* ''35J25'' Boundary value problems for second-order elliptic equations
* ''35J30'' Higher-order elliptic equations [See also [[31A30|31Axx]], [[31B30|31Bxx]]]
* ''35J35'' Variational methods for higher-order elliptic equations
* ''35J40'' Boundary value problems for higher-order elliptic equations
* ''35J46'' First-order elliptic systems
* ''35J47'' Second-order elliptic systems
* ''35J48'' Higher-order elliptic systems
* ''35J50'' Variational methods for elliptic systems
* ''35J56'' Boundary value problems for first-order elliptic systems
* ''35J57'' Boundary value problems for second-order elliptic systems
* ''35J58'' Boundary value problems for higher-order elliptic systems
* ''35J60'' Nonlinear elliptic equations
* ''35J61'' Semilinear elliptic equations
* ''35J62'' Quasilinear elliptic equations
* ''35J65'' Nonlinear boundary value problems for linear elliptic equations
* ''35J66'' Nonlinear boundary value problems for nonlinear elliptic equations
* ''35J67'' Boundary values of solutions to elliptic equations
* ''35J70'' Degenerate elliptic equations
* ''35J75'' Singular elliptic equations
* ''35J86'' Linear elliptic unilateral problems and linear elliptic variational inequalities [See also [[35R35|35Rxx]], [[49J40|49Jxx]]]
* ''35J87'' Nonlinear elliptic unilateral problems and nonlinear elliptic variational inequalities [See also [[35R35|35Rxx]], [[49J40|49Jxx]]]
* ''35J88'' Systems of elliptic variational inequalities [See also [[35R35|35Rxx]], [[49J40|49Jxx]]]
* ''35J91'' Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian
* ''35J92'' Quasilinear elliptic equations with $p$-Laplacian
* ''35J93'' Quasilinear elliptic equations with mean curvature operator
* ''35J96'' Elliptic ~Monge-Ampère equations
* ''35J99'' None of the above, but in this section
!!![[35|35-XX]]Kxx  Parabolic equations and systems [See also [[35Bxx|35Bxx]], [[35Dxx|35Dxx]], [[35R30|35Rxx]], [[35R35|35Rxx]], [[58J35|58Jxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/35Kxx.html]]}{{moveright{< [[35Jxx |35Jxx]] | [[35-XX |35-XX]] | [[35Lxx |35Lxx]] >}}}
* ''35K05'' Heat equation
* ''35K08'' Heat kernel
* ''35K10'' Second-order parabolic equations
* ''35K15'' Initial value problems for second-order parabolic equations
* ''35K20'' Initial-boundary value problems for second-order parabolic equations
* ''35K25'' Higher-order parabolic equations
* ''35K30'' Initial value problems for higher-order parabolic equations
* ''35K35'' Initial-boundary value problems for higher-order parabolic equations
* ''35K40'' Second-order parabolic systems
* ''35K41'' Higher-order parabolic systems
* ''35K45'' Initial value problems for second-order parabolic systems
* ''35K46'' Initial value problems for higher-order parabolic systems
* ''35K51'' Initial-boundary value problems for second-order parabolic systems
* ''35K52'' Initial-boundary value problems for higher-order parabolic systems
* ''35K55'' Nonlinear parabolic equations
* ''35K57'' Reaction-diffusion equations
* ''35K58'' Semilinear parabolic equations
* ''35K59'' Quasilinear parabolic equations
* ''35K60'' Nonlinear initial value problems for linear parabolic equations
* ''35K61'' Nonlinear initial-boundary value problems for nonlinear parabolic equations
* ''35K65'' Degenerate parabolic equations
* ''35K67'' Singular parabolic equations
* ''35K70'' Ultraparabolic equations, pseudoparabolic equations, etc.
* ''35K85'' Linear parabolic unilateral problems and linear parabolic variational inequalities [See also [[35R35|35Rxx]], [[49J40|49Jxx]]]
* ''35K86'' Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities [See also [[35R35|35Rxx]], [[49J40|49Jxx]]]
* ''35K87'' Systems of parabolic variational inequalities [See also [[35R35|35Rxx]], [[49J40|49Jxx]]]
* ''35K90'' Abstract parabolic equations
* ''35K91'' Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian
* ''35K92'' Quasilinear parabolic equations with $p$-Laplacian
* ''35K93'' Quasilinear parabolic equations with mean curvature operator
* ''35K96'' Parabolic ~Monge-Ampère equations
* ''35K99'' None of the above, but in this section
!!![[35|35-XX]]Lxx  Hyperbolic equations and systems [See also [[58J45|58Jxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/35Lxx.html]]}{{moveright{< [[35Kxx |35Kxx]] | [[35-XX |35-XX]] | [[35Mxx |35Mxx]] >}}}
* ''35L02'' First-order hyperbolic equations
* ''35L03'' Initial value problems for first-order hyperbolic equations
* ''35L04'' Initial-boundary value problems for first-order hyperbolic equations
* ''35L05'' Wave equation
* ''35L10'' Second-order hyperbolic equations
* ''35L15'' Initial value problems for second-order hyperbolic equations
* ''35L20'' Initial-boundary value problems for second-order hyperbolic equations
* ''35L25'' Higher-order hyperbolic equations
* ''35L30'' Initial value problems for higher-order hyperbolic equations
* ''35L35'' Initial-boundary value problems for higher-order hyperbolic equations
* ''35L40'' First-order hyperbolic systems
* ''35L45'' Initial value problems for first-order hyperbolic systems
* ''35L50'' Initial-boundary value problems for first-order hyperbolic systems
* ''35L51'' Second-order hyperbolic systems
* ''35L52'' Initial value problems for second-order hyperbolic systems
* ''35L53'' Initial-boundary value problems for second-order hyperbolic systems
* ''35L55'' Higher-order hyperbolic systems
* ''35L56'' Initial value problems for higher-order hyperbolic systems
* ''35L57'' Initial-boundary value problems for higher-order hyperbolic systems
* ''35L60'' Nonlinear first-order hyperbolic equations
* ''35L65'' Conservation laws
* ''35L67'' Shocks and singularities [See also [[58Kxx|58Kxx]], [[76L05|76Lxx]]]
* ''35L70'' Nonlinear second-order hyperbolic equations
* ''35L71'' Semilinear second-order hyperbolic equations
* ''35L72'' Quasilinear second-order hyperbolic equations
* ''35L75'' Nonlinear higher-order hyperbolic equations
* ''35L76'' Semilinear higher-order hyperbolic equations
* ''35L77'' Quasilinear higher-order hyperbolic equations
* ''35L80'' Degenerate hyperbolic equations
* ''35L81'' Singular hyperbolic equations
* ''35L82'' Pseudohyperbolic equations
* ''35L85'' Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities [See also [[35R35|35Rxx]], [[49J40|49Jxx]]]
* ''35L86'' Nonlinear hyperbolic unilateral problems and nonlinear hyperbolic variational inequalities [See also [[35R35|35Rxx]], [[49J40|49Jxx]]]
* ''35L87'' Unilateral problems and variational inequalities for hyperbolic systems [See also [[35R35|35Rxx]], [[49J40|49Jxx]]]
* ''35L90'' Abstract hyperbolic equations
* ''35L99'' None of the above, but in this section
!!![[35|35-XX]]Mxx  Equations and systems of special type (mixed, composite, etc.) {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/35Mxx.html]]}{{moveright{< [[35Lxx |35Lxx]] | [[35-XX |35-XX]] | [[35Nxx |35Nxx]] >}}}
* ''35M10'' Equations of mixed type
* ''35M11'' Initial value problems for equations of mixed type
* ''35M12'' Boundary value problems for equations of mixed type
* ''35M13'' Initial-boundary value problems for equations of mixed type
* ''35M30'' Systems of mixed type
* ''35M31'' Initial value problems for systems of mixed type
* ''35M32'' Boundary value problems for systems of mixed type
* ''35M33'' Initial-boundary value problems for systems of mixed type
* ''35M85'' Linear unilateral problems and variational inequalities of mixed type [See also [[35R35|35Rxx]], [[49J40|49Jxx]]]
* ''35M86'' Nonlinear unilateral problems and nonlinear variational inequalities of mixed type [See also [[35R35|35Rxx]], [[49J40|49Jxx]]]
* ''35M87'' Systems of variational inequalities of mixed type [See also [[35R35|35Rxx]], [[49J40|49Jxx]]]
* ''35M99'' None of the above, but in this section
!!![[35|35-XX]]Nxx  Overdetermined systems [See also [[58Hxx|58Hxx]], [[58J10|58Jxx]], [[58J15|58Jxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/35Nxx.html]]}{{moveright{< [[35Mxx |35Mxx]] | [[35-XX |35-XX]] | [[35Pxx |35Pxx]] >}}}
* ''35N05'' Overdetermined systems with constant coefficients
* ''35N10'' Overdetermined systems with variable coefficients
* ''35N15'' $\overline\partial$-Neumann problem and generalizations; formal complexes [See also [[32W05|32Wxx]], [[32W10|32Wxx]], [[58J10|58Jxx]]]
* ''35N20'' Overdetermined initial value problems
* ''35N25'' Overdetermined boundary value problems
* ''35N30'' Overdetermined initial-boundary value problems
* ''35N99'' None of the above, but in this section
!!![[35|35-XX]]Pxx  Spectral theory and eigenvalue problems [See also [[47Axx|47Axx]], [[47Bxx|47Bxx]], [[47F05|47Fxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/35Pxx.html]]}{{moveright{< [[35Nxx |35Nxx]] | [[35-XX |35-XX]] | [[35Qxx |35Qxx]] >}}}
* ''35P05'' General topics in linear spectral theory
* ''35P10'' Completeness of eigenfunctions, eigenfunction expansions
* ''35P15'' Estimation of eigenvalues, upper and lower bounds
* ''35P20'' Asymptotic distribution of eigenvalues and eigenfunctions
* ''35P25'' Scattering theory [See also [[47A40|47Axx]]]
* ''35P30'' Nonlinear eigenvalue problems, nonlinear spectral theory
* ''35P99'' None of the above, but in this section
!!![[35|35-XX]]Qxx  Equations of mathematical physics and other areas of application [See also [[35J05|35Jxx]], [[35J10|35Jxx]], [[35K05|35Kxx]], [[35L05|35Lxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/35Qxx.html]]}{{moveright{< [[35Pxx |35Pxx]] | [[35-XX |35-XX]] | [[35Rxx |35Rxx]] >}}}
* ''35Q05'' ~Euler-Poisson-Darboux equations
* ''35Q15'' ~Riemann-Hilbert problems [See also [[30E25|30Exx]], [[31A25|31Axx]], [[31B20|31Bxx]]]
* ''35Q20'' Boltzmann equations
* ''35Q30'' ~Navier-Stokes equations [See also [[76D05|76Dxx]], [[76D07|76Dxx]], [[76N10|76Nxx]]]
* ''35Q31'' Euler equations [See also [[76D05|76Dxx]], [[76D07|76Dxx]], [[76N10|76Nxx]]]
* ''35Q35'' PDEs in connection with fluid mechanics
* ''35Q40'' PDEs in connection with quantum mechanics
* ''35Q41'' Time-dependent Schrödinger equations, Dirac equations
* ''35Q51'' Soliton-like equations [See also [[37K40|37Kxx]]]
* ''35Q53'' ~KdV-like equations (Korteweg-de Vries) [See also [[37K10|37Kxx]]]
* ''35Q55'' ~NLS-like equations (nonlinear Schrödinger) [See also [[37K10|37Kxx]]]
* ''35Q56'' Ginzburg-Landau equations
* ''35Q60'' PDEs in connection with optics and electromagnetic theory
* ''35Q61'' Maxwell equations
* ''35Q62'' PDEs in connection with statistics
* ''35Q68'' PDEs in connection with computer science
* ''35Q70'' PDEs in connection with mechanics of particles and systems
* ''35Q74'' PDEs in connection with mechanics of deformable solids
* ''35Q75'' PDEs in connection with relativity and gravitational theory
* ''35Q76'' Einstein equations
* ''35Q79'' PDEs in connection with classical thermodynamics and heat transfer
* ''35Q82'' PDEs in connection with statistical mechanics
* ''35Q83'' Vlasov-like equations
* ''35Q84'' ~Fokker-Planck equations
* ''35Q85'' PDEs in connection with astronomy and astrophysics
* ''35Q86'' PDEs in connection with geophysics
* ''35Q90'' PDEs in connection with mathematical programming
* ''35Q91'' PDEs in connection with game theory, economics, social and behavioral sciences
* ''35Q92'' PDEs in connection with biology and other natural sciences
* ''35Q93'' PDEs in connection with control and optimization
* ''35Q94'' PDEs in connection with information and communication
* ''35Q99'' None of the above, but in this section
!!![[35|35-XX]]Rxx  Miscellaneous topics {For equations on manifolds, see [[58Jxx|58Jxx]]; for manifolds of solutions, see [[58Bxx|58Bxx]]; for stochastic PDE, see also [[60H15|60Hxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/35Rxx.html]]}{{moveright{< [[35Qxx |35Qxx]] | [[35-XX |35-XX]] | [[35Sxx |35Sxx]] >}}}
* ''35R01'' Partial differential equations on manifolds [See also [[32Wxx|32Wxx]], [[53Cxx|53Cxx]], [[58Jxx|58Jxx]]]
* ''35R02'' Partial differential equations on graphs and networks (ramified or polygonal spaces)
* ''35R03'' Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc.
* ''35R05'' Partial differential equations with discontinuous coefficients or data
* ''35R06'' Partial differential equations with measure
* ''35R09'' Integro-partial differential equations [See also [[45Kxx|45Kxx]]]
* ''35R10'' Partial functional-differential equations
* ''35R11'' Fractional partial differential equations
* ''35R12'' Impulsive partial differential equations
* ''35R13'' Fuzzy partial differential equations
* ''35R15'' Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in infinitely many variables) [See also [[46Gxx|46Gxx]], [[58D25|58Dxx]]]
* ''35R20'' Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for abstract space valued functions) [See also [[34Gxx|34Gxx]], [[47A50|47Axx]], [[47D03|47Dxx]], [[47D06|47Dxx]], [[47D09|47Dxx]], [[47H20|47Hxx]], [[47Jxx|47Jxx]]]
* ''35R25'' Improperly posed problems
* ''35R30'' Inverse problems
* ''35R35'' Free boundary problems
* ''35R37'' Moving boundary problems
* ''35R45'' Partial differential inequalities
* ''35R50'' Partial differential equations of infinite order
* ''35R60'' Partial differential equations with randomness, stochastic partial differential equations [See also [[60H15|60Hxx]]]
* ''35R70'' Partial differential equations with multivalued right-hand sides
* ''35R99'' None of the above, but in this section
!!!35-XX Partial differential equations {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/35-XX.html]]}{{moveright{< [[34-XX |34-XX]] | [[MSC |MSC2010]] | [[35Axx |35Axx]] >}}}
* ''35-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''35-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''35-02'' Research exposition (monographs, survey articles)
* ''35-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''35-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''35-06'' Proceedings, conferences, collections, etc.
* ''[[35Axx|35Axx]]''  General topics
* ''[[35Bxx|35Bxx]]''  Qualitative properties of solutions
* ''[[35Cxx|35Cxx]]''  Representations of solutions
* ''[[35Dxx|35Dxx]]''  Generalized solutions
* ''[[35Exx|35Exx]]''  Equations and systems with constant coefficients [See also [[35N05|35Nxx]]]
* ''[[35Fxx|35Fxx]]''  General first-order equations and systems
* ''[[35Gxx|35Gxx]]''  General higher-order equations and systems
* ''[[35Hxx|35Hxx]]''  Close-to-elliptic equations and systems
* ''[[35Jxx|35Jxx]]''  Elliptic equations and systems [See also [[58J10|58Jxx]], [[58J20|58Jxx]]]
* ''[[35Kxx|35Kxx]]''  Parabolic equations and systems [See also [[35Bxx|35Bxx]], [[35Dxx|35Dxx]], [[35R30|35Rxx]], [[35R35|35Rxx]], [[58J35|58Jxx]]]
* ''[[35Lxx|35Lxx]]''  Hyperbolic equations and systems [See also [[58J45|58Jxx]]]
* ''[[35Mxx|35Mxx]]''  Equations and systems of special type (mixed, composite, etc.)
* ''[[35Nxx|35Nxx]]''  Overdetermined systems [See also [[58Hxx|58Hxx]], [[58J10|58Jxx]], [[58J15|58Jxx]]]
* ''[[35Pxx|35Pxx]]''  Spectral theory and eigenvalue problems [See also [[47Axx|47Axx]], [[47Bxx|47Bxx]], [[47F05|47Fxx]]]
* ''[[35Qxx|35Qxx]]''  Equations of mathematical physics and other areas of application [See also [[35J05|35Jxx]], [[35J10|35Jxx]], [[35K05|35Kxx]], [[35L05|35Lxx]]]
* ''[[35Rxx|35Rxx]]''  Miscellaneous topics {For equations on manifolds, see [[58Jxx|58Jxx]]; for manifolds of solutions, see [[58Bxx|58Bxx]]; for stochastic PDE, see also [[60H15|60Hxx]]}
* ''[[35Sxx|35Sxx]]''  Pseudodifferential operators and other generalizations of partial differential operators [See also [[47G30|47Gxx]], [[58J40|58Jxx]]]
!!![[35|35-XX]]Sxx  Pseudodifferential operators and other generalizations of partial differential operators [See also [[47G30|47Gxx]], [[58J40|58Jxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/35Sxx.html]]}{{moveright{< [[35Rxx |35Rxx]] | [[35-XX |35-XX]] | [[37-XX |37-XX]] >}}}
* ''35S05'' Pseudodifferential operators
* ''35S10'' Initial value problems for pseudodifferential operators
* ''35S11'' Initial-boundary value problems for pseudodifferential operators
* ''35S15'' Boundary value problems for pseudodifferential operators
* ''35S30'' Fourier integral operators
* ''35S35'' Topological aspects: intersection cohomology, stratified sets, etc. [See also [[32C38|32Cxx]], [[32S40|32Sxx]], [[32S60|32Sxx]], [[58J15|58Jxx]]]
* ''35S50'' Paradifferential operators
* ''35S99'' None of the above, but in this section
!!![[37|37-XX]]Axx  Ergodic theory [See also [[28Dxx|28Dxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/37Axx.html]]}{{moveright{< [[35-XX |35-XX]] | [[37-XX |37-XX]] | [[37Bxx |37Bxx]] >}}}
* ''37A05'' Measure-preserving transformations
* ''37A10'' One-parameter continuous families of measure-preserving transformations
* ''37A15'' General groups of measure-preserving transformations [See mainly [[22Fxx|22Fxx]]]
* ''37A17'' Homogeneous flows [See also [[22Fxx|22Fxx]]]
* ''37A20'' Orbit equivalence, cocycles, ergodic equivalence relations
* ''37A25'' Ergodicity, mixing, rates of mixing
* ''37A30'' Ergodic theorems, spectral theory, Markov operators {For operator ergodic theory, see mainly [[47A35|47Axx]]}
* ''37A35'' Entropy and other invariants, isomorphism, classification
* ''37A40'' Nonsingular (and infinite-measure preserving) transformations
* ''37A45'' Relations with number theory and harmonic analysis [See also [[11Kxx|11Kxx]]]
* ''37A50'' Relations with probability theory and stochastic processes [See also [[60Fxx|60Fxx]] and [[60G10|60Gxx]]]
* ''37A55'' Relations with the theory of $C^*$-algebras [See mainly [[46L55|46Lxx]]]
* ''37A60'' Dynamical systems in statistical mechanics [See also [[82Cxx|82Cxx]]]
* ''37A99'' None of the above, but in this section
!!![[37|37-XX]]Bxx  Topological dynamics [See also [[54H20|54Hxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/37Bxx.html]]}{{moveright{< [[37Axx |37Axx]] | [[37-XX |37-XX]] | [[37Cxx |37Cxx]] >}}}
* ''37B05'' Transformations and group actions with special properties (minimality, distality, proximality, etc.)
* ''37B10'' Symbolic dynamics [See also [[37Cxx|37Cxx]], [[37Dxx|37Dxx]]]
* ''37B15'' Cellular automata [See also [[68Q80|68Qxx]]]
* ''37B20'' Notions of recurrence
* ''37B25'' Lyapunov functions and stability; attractors, repellers
* ''37B30'' Index theory, ~Morse-Conley indices
* ''37B35'' Gradient-like and recurrent behavior; isolated (locally maximal) invariant sets
* ''37B40'' Topological entropy
* ''37B45'' Continua theory in dynamics
* ''37B50'' Multi-dimensional shifts of finite type, tiling dynamics
* ''37B55'' Nonautonomous dynamical systems
* ''37B99'' None of the above, but in this section
!!![[37|37-XX]]Cxx  Smooth dynamical systems: general theory [See also [[34Cxx|34Cxx]], [[34Dxx|34Dxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/37Cxx.html]]}{{moveright{< [[37Bxx |37Bxx]] | [[37-XX |37-XX]] | [[37Dxx |37Dxx]] >}}}
* ''37C05'' Smooth mappings and diffeomorphisms
* ''37C10'' Vector fields, flows, ordinary differential equations
* ''37C15'' Topological and differentiable equivalence, conjugacy, invariants, moduli, classification
* ''37C20'' Generic properties, structural stability
* ''37C25'' Fixed points, periodic points, fixed-point index theory
* ''37C27'' Periodic orbits of vector fields and flows
* ''37C29'' Homoclinic and heteroclinic orbits
* ''37C30'' Zeta functions, (~Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems
* ''37C35'' Orbit growth
* ''37C40'' Smooth ergodic theory, invariant measures [See also [[37Dxx|37Dxx]]]
* ''37C45'' Dimension theory of dynamical systems
* ''37C50'' Approximate trajectories (pseudotrajectories, shadowing, etc.)
* ''37C55'' Periodic and quasiperiodic flows and diffeomorphisms
* ''37C60'' Nonautonomous smooth dynamical systems [See also [[37B55|37Bxx]]]
* ''37C65'' Monotone flows
* ''37C70'' Attractors and repellers, topological structure
* ''37C75'' Stability theory
* ''37C80'' Symmetries, equivariant dynamical systems
* ''37C85'' Dynamics of group actions other than ${\bf Z}$ and ${\bf R}$, and foliations [See mainly [[22Fxx|22Fxx]], and also [[57R30|57Rxx]], [[57Sxx|57Sxx]]]
* ''37C99'' None of the above, but in this section
!!![[37|37-XX]]Dxx  Dynamical systems with hyperbolic behavior {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/37Dxx.html]]}{{moveright{< [[37Cxx |37Cxx]] | [[37-XX |37-XX]] | [[37Exx |37Exx]] >}}}
* ''37D05'' Hyperbolic orbits and sets
* ''37D10'' Invariant manifold theory
* ''37D15'' ~Morse-Smale systems
* ''37D20'' Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
* ''37D25'' Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
* ''37D30'' Partially hyperbolic systems and dominated splittings
* ''37D35'' Thermodynamic formalism, variational principles, equilibrium states
* ''37D40'' Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
* ''37D45'' Strange attractors, chaotic dynamics
* ''37D50'' Hyperbolic systems with singularities (billiards, etc.)
* ''37D99'' None of the above, but in this section
!!![[37|37-XX]]Exx  Low-dimensional dynamical systems {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/37Exx.html]]}{{moveright{< [[37Dxx |37Dxx]] | [[37-XX |37-XX]] | [[37Fxx |37Fxx]] >}}}
* ''37E05'' Maps of the interval (piecewise continuous, continuous, smooth)
* ''37E10'' Maps of the circle
* ''37E15'' Combinatorial dynamics (types of periodic orbits)
* ''37E20'' Universality, renormalization [See also [[37F25|37Fxx]]]
* ''37E25'' Maps of trees and graphs
* ''37E30'' Homeomorphisms and diffeomorphisms of planes and surfaces
* ''37E35'' Flows on surfaces
* ''37E40'' Twist maps
* ''37E45'' Rotation numbers and vectors
* ''37E99'' None of the above, but in this section
!!![[37|37-XX]]Fxx  Complex dynamical systems [See also [[30D05|30Dxx]], [[32H50|32Hxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/37Fxx.html]]}{{moveright{< [[37Exx |37Exx]] | [[37-XX |37-XX]] | [[37Gxx |37Gxx]] >}}}
* ''37F05'' Relations and correspondences
* ''37F10'' Polynomials; rational maps; entire and meromorphic functions [See also [[32A10|32Axx]], [[32A20|32Axx]], [[32H02|32Hxx]], [[32H04|32Hxx]]]
* ''37F15'' Expanding maps; hyperbolicity; structural stability
* ''37F20'' Combinatorics and topology
* ''37F25'' Renormalization
* ''37F30'' Quasiconformal methods and Teichmüller theory; Fuchsian and Kleinian groups as dynamical systems
* ''37F35'' Conformal densities and Hausdorff dimension
* ''37F40'' Geometric limits
* ''37F45'' Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations
* ''37F50'' Small divisors, rotation domains and linearization; Fatou and Julia sets
* ''37F75'' Holomorphic foliations and vector fields [See also [[32M25|32Mxx]], [[32S65|32Sxx]], [[34Mxx|34Mxx]]]
* ''37F99'' None of the above, but in this section
!!![[37|37-XX]]Gxx  Local and nonlocal bifurcation theory [See also [[34C23|34Cxx]], [[34K18|34Kxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/37Gxx.html]]}{{moveright{< [[37Fxx |37Fxx]] | [[37-XX |37-XX]] | [[37Hxx |37Hxx]] >}}}
* ''37G05'' Normal forms
* ''37G10'' Bifurcations of singular points
* ''37G15'' Bifurcations of limit cycles and periodic orbits
* ''37G20'' Hyperbolic singular points with homoclinic trajectories
* ''37G25'' Bifurcations connected with nontransversal intersection
* ''37G30'' Infinite nonwandering sets arising in bifurcations
* ''37G35'' Attractors and their bifurcations
* ''37G40'' Symmetries, equivariant bifurcation theory
* ''37G99'' None of the above, but in this section
!!![[37|37-XX]]Hxx  Random dynamical systems [See also [[15B52|15Bxx]], [[34D08|34Dxx]], [[34F05|34Fxx]], [[47B80|47Bxx]], [[70L05|70Lxx]], [[82C05|82Cxx]], [[93Exx|93Exx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/37Hxx.html]]}{{moveright{< [[37Gxx |37Gxx]] | [[37-XX |37-XX]] | [[37Jxx |37Jxx]] >}}}
* ''37H05'' Foundations, general theory of cocycles, algebraic ergodic theory [See also [[37Axx|37Axx]]]
* ''37H10'' Generation, random and stochastic difference and differential equations [See also [[34F05|34Fxx]], [[34K50|34Kxx]], [[60H10|60Hxx]], [[60H15|60Hxx]]]
* ''37H15'' Multiplicative ergodic theory, Lyapunov exponents [See also [[34D08|34Dxx]], [[37Axx|37Axx]], [[37Cxx|37Cxx]], [[37Dxx|37Dxx]]]
* ''37H20'' Bifurcation theory [See also [[37Gxx|37Gxx]]]
* ''37H99'' None of the above, but in this section
!!![[37|37-XX]]Jxx  Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems [See also [[53Dxx|53Dxx]], [[70Fxx|70Fxx]], [[70Hxx|70Hxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/37Jxx.html]]}{{moveright{< [[37Hxx |37Hxx]] | [[37-XX |37-XX]] | [[37Kxx |37Kxx]] >}}}
* ''37J05'' General theory, relations with symplectic geometry and topology
* ''37J10'' Symplectic mappings, fixed points
* ''37J15'' Symmetries, invariants, invariant manifolds, momentum maps, reduction [See also [[53D20|53Dxx]]]
* ''37J20'' Bifurcation problems
* ''37J25'' Stability problems
* ''37J30'' Obstructions to integrability (nonintegrability criteria)
* ''37J35'' Completely integrable systems, topological structure of phase space, integration methods
* ''37J40'' Perturbations, normal forms, small divisors, KAM theory, Arnol'd diffusion
* ''37J45'' Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
* ''37J50'' Action-minimizing orbits and measures
* ''37J55'' Contact systems [See also [[53D10|53Dxx]]]
* ''37J60'' Nonholonomic dynamical systems [See also [[70F25|70Fxx]]]
* ''37J99'' None of the above, but in this section
!!![[37|37-XX]]Kxx  Infinite-dimensional Hamiltonian systems [See also [[35Axx|35Axx]], [[35Qxx|35Qxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/37Kxx.html]]}{{moveright{< [[37Jxx |37Jxx]] | [[37-XX |37-XX]] | [[37Lxx |37Lxx]] >}}}
* ''37K05'' Hamiltonian structures, symmetries, variational principles, conservation laws
* ''37K10'' Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (~KdV, KP, Toda, etc.)
* ''37K15'' Integration of completely integrable systems by inverse spectral and scattering methods
* ''37K20'' Relations with algebraic geometry, complex analysis, special functions [See also [[14H70|14Hxx]]]
* ''37K25'' Relations with differential geometry
* ''37K30'' Relations with infinite-dimensional Lie algebras and other algebraic structures
* ''37K35'' ~Lie-Bäcklund and other transformations
* ''37K40'' Soliton theory, asymptotic behavior of solutions
* ''37K45'' Stability problems
* ''37K50'' Bifurcation problems
* ''37K55'' Perturbations, KAM for infinite-dimensional systems
* ''37K60'' Lattice dynamics [See also [[37L60|37Lxx]]]
* ''37K65'' Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics
* ''37K99'' None of the above, but in this section
!!![[37|37-XX]]Lxx  Infinite-dimensional dissipative dynamical systems [See also [[35Bxx|35Bxx]], [[35Qxx|35Qxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/37Lxx.html]]}{{moveright{< [[37Kxx |37Kxx]] | [[37-XX |37-XX]] | [[37Mxx |37Mxx]] >}}}
* ''37L05'' General theory, nonlinear semigroups, evolution equations
* ''37L10'' Normal forms, center manifold theory, bifurcation theory
* ''37L15'' Stability problems
* ''37L20'' Symmetries
* ''37L25'' Inertial manifolds and other invariant attracting sets
* ''37L30'' Attractors and their dimensions, Lyapunov exponents
* ''37L40'' Invariant measures
* ''37L45'' Hyperbolicity; Lyapunov functions
* ''37L50'' Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systems
* ''37L55'' Infinite-dimensional random dynamical systems; stochastic equations [See also [[35R60|35Rxx]], [[60H10|60Hxx]], [[60H15|60Hxx]]]
* ''37L60'' Lattice dynamics [See also [[37K60|37Kxx]]]
* ''37L65'' Special approximation methods (nonlinear Galerkin, etc.)
* ''37L99'' None of the above, but in this section
!!![[37|37-XX]]Mxx  Approximation methods and numerical treatment of dynamical systems [See also [[65Pxx|65Pxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/37Mxx.html]]}{{moveright{< [[37Lxx |37Lxx]] | [[37-XX |37-XX]] | [[37Nxx |37Nxx]] >}}}
* ''37M05'' Simulation
* ''37M10'' Time series analysis
* ''37M15'' Symplectic integrators
* ''37M20'' Computational methods for bifurcation problems
* ''37M25'' Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy)
* ''37M99'' None of the above, but in this section
!!![[37|37-XX]]Nxx  Applications {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/37Nxx.html]]}{{moveright{< [[37Mxx |37Mxx]] | [[37-XX |37-XX]] | [[37Pxx |37Pxx]] >}}}
* ''37N05'' Dynamical systems in classical and celestial mechanics [See mainly [[70Fxx|70Fxx]], [[70Hxx|70Hxx]], [[70Kxx|70Kxx]]]
* ''37N10'' Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly [[76-XX|76-XX]], especially [[76D05|76Dxx]], [[76F20|76Fxx]], [[86A05|86Axx]], [[86A10|86Axx]]]
* ''37N15'' Dynamical systems in solid mechanics [See mainly [[74Hxx|74Hxx]]]
* ''37N20'' Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
* ''37N25'' Dynamical systems in biology [See mainly [[92-XX|92-XX]], but also [[91-XX|91-XX]]]
* ''37N30'' Dynamical systems in numerical analysis
* ''37N35'' Dynamical systems in control
* ''37N40'' Dynamical systems in optimization and economics
* ''37N99'' None of the above, but in this section
!!!37-XX Dynamical systems and ergodic theory [See also [[26A18|26Axx]], [[28Dxx|28Dxx]], [[34Cxx|34Cxx]], [[34Dxx|34Dxx]], [[35Bxx|35Bxx]], [[46Lxx|46Lxx]], [[58Jxx|58Jxx]], [[70-XX|70-XX]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/37-XX.html]]}{{moveright{< [[35-XX |35-XX]] | [[MSC |MSC2010]] | [[37Axx |37Axx]] >}}}
* ''37-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''37-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''37-02'' Research exposition (monographs, survey articles)
* ''37-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''37-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''37-06'' Proceedings, conferences, collections, etc.
* ''[[37Axx|37Axx]]''  Ergodic theory [See also [[28Dxx|28Dxx]]]
* ''[[37Bxx|37Bxx]]''  Topological dynamics [See also [[54H20|54Hxx]]]
* ''[[37Cxx|37Cxx]]''  Smooth dynamical systems: general theory [See also [[34Cxx|34Cxx]], [[34Dxx|34Dxx]]]
* ''[[37Dxx|37Dxx]]''  Dynamical systems with hyperbolic behavior
* ''[[37Exx|37Exx]]''  Low-dimensional dynamical systems
* ''[[37Fxx|37Fxx]]''  Complex dynamical systems [See also [[30D05|30Dxx]], [[32H50|32Hxx]]]
* ''[[37Gxx|37Gxx]]''  Local and nonlocal bifurcation theory [See also [[34C23|34Cxx]], [[34K18|34Kxx]]]
* ''[[37Hxx|37Hxx]]''  Random dynamical systems [See also [[15B52|15Bxx]], [[34D08|34Dxx]], [[34F05|34Fxx]], [[47B80|47Bxx]], [[70L05|70Lxx]], [[82C05|82Cxx]], [[93Exx|93Exx]]]
* ''[[37Jxx|37Jxx]]''  Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems [See also [[53Dxx|53Dxx]], [[70Fxx|70Fxx]], [[70Hxx|70Hxx]]]
* ''[[37Kxx|37Kxx]]''  Infinite-dimensional Hamiltonian systems [See also [[35Axx|35Axx]], [[35Qxx|35Qxx]]]
* ''[[37Lxx|37Lxx]]''  Infinite-dimensional dissipative dynamical systems [See also [[35Bxx|35Bxx]], [[35Qxx|35Qxx]]]
* ''[[37Mxx|37Mxx]]''  Approximation methods and numerical treatment of dynamical systems [See also [[65Pxx|65Pxx]]]
* ''[[37Nxx|37Nxx]]''  Applications
* ''[[37Pxx|37Pxx]]''  Arithmetic and non-Archimedean dynamical systems [See also [[11S82|11Sxx]], [[37A45|37Axx]]]
!!![[37|37-XX]]Pxx  Arithmetic and non-Archimedean dynamical systems [See also [[11S82|11Sxx]], [[37A45|37Axx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/37Pxx.html]]}{{moveright{< [[37Nxx |37Nxx]] | [[37-XX |37-XX]] | [[39-XX |39-XX]] >}}}
* ''37P05'' Polynomial and rational maps
* ''37P10'' Analytic and meromorphic maps
* ''37P15'' Global ground fields
* ''37P20'' ~Non-Archimedean local ground fields
* ''37P25'' Finite ground fields
* ''37P30'' Height functions; Green functions; invariant measures [See also [[11G50|11Gxx]], [[14G40|14Gxx]]]
* ''37P35'' Arithmetic properties of periodic points
* ''37P40'' ~Non-Archimedean Fatou and Julia sets
* ''37P45'' Families and moduli spaces
* ''37P50'' Dynamical systems on Berkovich spaces
* ''37P55'' Arithmetic dynamics on general algebraic varieties
* ''37P99'' None of the above, but in this section
!!![[39|39-XX]]Axx  Difference equations {For dynamical systems, see [[37-XX|37-XX]]; for dynamic equations on time scales, see [[34N05|34Nxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/39Axx.html]]}{{moveright{< [[37-XX |37-XX]] | [[39-XX |39-XX]] | [[39Bxx |39Bxx]] >}}}
* ''39A05'' General theory
* ''39A06'' Linear equations
* ''39A10'' Difference equations, additive
* ''39A12'' Discrete version of topics in analysis
* ''39A13'' Difference equations, scaling ($q$-differences) [See also [[33Dxx|33Dxx]]]
* ''39A14'' Partial difference equations
* ''39A20'' Multiplicative and other generalized difference equations, e.g. of Lyness type
* ''39A21'' Oscillation theory
* ''39A22'' Growth, boundedness, comparison of solutions
* ''39A23'' Periodic solutions
* ''39A24'' Almost periodic solutions
* ''39A28'' Bifurcation theory
* ''39A30'' Stability theory
* ''39A33'' Complex (chaotic) behavior of solutions
* ''39A45'' Equations in the complex domain
* ''39A50'' Stochastic difference equations
* ''39A60'' Applications
* ''39A70'' Difference operators [See also [[47B39|47Bxx]]]
* ''39A99'' None of the above, but in this section
!!!39-XX Difference and functional equations {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/39-XX.html]]}{{moveright{< [[37-XX |37-XX]] | [[MSC |MSC2010]] | [[39Axx |39Axx]] >}}}
* ''39-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''39-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''39-02'' Research exposition (monographs, survey articles)
* ''39-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''39-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''39-06'' Proceedings, conferences, collections, etc.
* ''[[39Axx|39Axx]]''  Difference equations {For dynamical systems, see [[37-XX|37-XX]]; for dynamic equations on time scales, see [[34N05|34Nxx]]}
* ''[[39Bxx|39Bxx]]''  Functional equations and inequalities [See also [[30D05|30Dxx]]]
!!![[39|39-XX]]Bxx  Functional equations and inequalities [See also [[30D05|30Dxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/39Bxx.html]]}{{moveright{< [[39Axx |39Axx]] | [[39-XX |39-XX]] | [[40-XX |40-XX]] >}}}
* ''39B05'' General
* ''39B12'' Iteration theory, iterative and composite equations [See also [[26A18|26Axx]], [[30D05|30Dxx]], [[37-XX|37-XX]]]
* ''39B22'' Equations for real functions [See also [[26A51|26Axx]], [[26B25|26Bxx]]]
* ''39B32'' Equations for complex functions [See also [[30D05|30Dxx]]]
* ''39B42'' Matrix and operator equations [See also [[47Jxx|47Jxx]]]
* ''39B52'' Equations for functions with more general domains and/or ranges
* ''39B55'' Orthogonal additivity and other conditional equations
* ''39B62'' Functional inequalities, including subadditivity, convexity, etc. [See also [[26A51|26Axx]], [[26B25|26Bxx]], [[26Dxx|26Dxx]]]
* ''39B72'' Systems of functional equations and inequalities
* ''39B82'' Stability, separation, extension, and related topics [See also [[46A22|46Axx]]]
* ''39B99'' None of the above, but in this section
!!![[40|40-XX]]Axx  Convergence and divergence of infinite limiting processes {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/40Axx.html]]}{{moveright{< [[39-XX |39-XX]] | [[40-XX |40-XX]] | [[40Bxx |40Bxx]] >}}}
* ''40A05'' Convergence and divergence of series and sequences
* ''40A10'' Convergence and divergence of integrals
* ''40A15'' Convergence and divergence of continued fractions [See also [[30B70|30Bxx]]]
* ''40A20'' Convergence and divergence of infinite products
* ''40A25'' Approximation to limiting values (summation of series, etc.) {For the ~Euler-Maclaurin summation formula, see [[65B15|65Bxx]]}
* ''40A30'' Convergence and divergence of series and sequences of functions
* ''40A35'' Ideal and statistical convergence [See also [[40G15|40Gxx]]]
* ''40A99'' None of the above, but in this section
!!![[40|40-XX]]Bxx  Multiple sequences and series {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/40Bxx.html]]}{{moveright{< [[40Axx |40Axx]] | [[40-XX |40-XX]] | [[40Cxx |40Cxx]] >}}}
* ''40B05'' Multiple sequences and series (should also be assigned at least one other classification number in this section)
* ''40B99'' None of the above, but in this section
!!![[40|40-XX]]Cxx  General summability methods {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/40Cxx.html]]}{{moveright{< [[40Bxx |40Bxx]] | [[40-XX |40-XX]] | [[40Dxx |40Dxx]] >}}}
* ''40C05'' Matrix methods
* ''40C10'' Integral methods
* ''40C15'' Function-theoretic methods (including power series methods and semicontinuous methods)
* ''40C99'' None of the above, but in this section
!!![[40|40-XX]]Dxx  Direct theorems on summability {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/40Dxx.html]]}{{moveright{< [[40Cxx |40Cxx]] | [[40-XX |40-XX]] | [[40Exx |40Exx]] >}}}
* ''40D05'' General theorems
* ''40D09'' Structure of summability fields
* ''40D10'' Tauberian constants and oscillation limits
* ''40D15'' Convergence factors and summability factors
* ''40D20'' Summability and bounded fields of methods
* ''40D25'' Inclusion and equivalence theorems
* ''40D99'' None of the above, but in this section
!!![[40|40-XX]]Exx  Inversion theorems {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/40Exx.html]]}{{moveright{< [[40Dxx |40Dxx]] | [[40-XX |40-XX]] | [[40Fxx |40Fxx]] >}}}
* ''40E05'' Tauberian theorems, general
* ''40E10'' Growth estimates
* ''40E15'' Lacunary inversion theorems
* ''40E20'' Tauberian constants
* ''40E99'' None of the above, but in this section
!!![[40|40-XX]]Fxx  Absolute and strong summability (should also be assigned at least one other classification number in Section 40) {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/40Fxx.html]]}{{moveright{< [[40Exx |40Exx]] | [[40-XX |40-XX]] | [[40Gxx |40Gxx]] >}}}
* ''40F05'' Absolute and strong summability (should also be assigned at least one other classification number in Section 40)
* ''40F99'' None of the above, but in this section
!!![[40|40-XX]]Gxx  Special methods of summability {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/40Gxx.html]]}{{moveright{< [[40Fxx |40Fxx]] | [[40-XX |40-XX]] | [[40Hxx |40Hxx]] >}}}
* ''40G05'' Cesàro, Euler, Nörlund and Hausdorff methods
* ''40G10'' Abel, Borel and power series methods
* ''40G15'' Summability methods using statistical convergence [See also [[40A35|40Axx]]]
* ''40G99'' None of the above, but in this section
!!![[40|40-XX]]Hxx  Functional analytic methods in summability {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/40Hxx.html]]}{{moveright{< [[40Gxx |40Gxx]] | [[40-XX |40-XX]] | [[40Jxx |40Jxx]] >}}}
* ''40H05'' Functional analytic methods in summability
* ''40H99'' None of the above, but in this section
!!!40-XX Sequences, series, summability {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/40-XX.html]]}{{moveright{< [[39-XX |39-XX]] | [[MSC |MSC2010]] | [[40Axx |40Axx]] >}}}
* ''40-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''40-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''40-02'' Research exposition (monographs, survey articles)
* ''40-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''40-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''40-06'' Proceedings, conferences, collections, etc.
* ''[[40Axx|40Axx]]''  Convergence and divergence of infinite limiting processes
* ''[[40Bxx|40Bxx]]''  Multiple sequences and series
* ''[[40Cxx|40Cxx]]''  General summability methods
* ''[[40Dxx|40Dxx]]''  Direct theorems on summability
* ''[[40Exx|40Exx]]''  Inversion theorems
* ''[[40Fxx|40Fxx]]''  Absolute and strong summability (should also be assigned at least one other classification number in Section 40)
* ''[[40Gxx|40Gxx]]''  Special methods of summability
* ''[[40Hxx|40Hxx]]''  Functional analytic methods in summability
* ''[[40Jxx|40Jxx]]''  Summability in abstract structures [See also [[43A55|43Axx]], [[46A35|46Axx]], [[46B15|46Bxx]]]
!!![[40|40-XX]]Jxx  Summability in abstract structures [See also [[43A55|43Axx]], [[46A35|46Axx]], [[46B15|46Bxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/40Jxx.html]]}{{moveright{< [[40Hxx |40Hxx]] | [[40-XX |40-XX]] | [[41-XX |41-XX]] >}}}
* ''40J05'' Summability in abstract structures [See also [[43A55|43Axx]], [[46A35|46Axx]], [[46B15|46Bxx]]] (should also be assigned at least one other classification number in this section)
* ''40J99'' None of the above, but in this section
!!!41-XX Approximations and expansions {For all approximation theory in the complex domain, see [[30E05|30Exx]] and [[30E10|30Exx]]; for all trigonometric approximation and interpolation, see [[42A10|42Axx]] and [[42A15|42Axx]]; for numerical approximation, see [[65Dxx|65Dxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/41-XX.html]]}{{moveright{< [[40-XX |40-XX]] | [[MSC |MSC2010]] | [[41Axx |41Axx]] >}}}
* ''41-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''41-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''41-02'' Research exposition (monographs, survey articles)
* ''41-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''41-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''41-06'' Proceedings, conferences, collections, etc.
* ''[[41Axx|41Axx]]''  Approximations and expansions {For all approximation theory in the complex domain, see [[30E05|30Exx]] and [[30E10|30Exx]]; for all trigonometric approximation and interpolation, see [[42A10|42Axx]] and [[42A15|42Axx]]; for numerical approximation, see [[65Dxx|65Dxx]]}
!!![[41|41-XX]]Axx  Approximations and expansions {For all approximation theory in the complex domain, see [[30E05|30Exx]] and [[30E10|30Exx]]; for all trigonometric approximation and interpolation, see [[42A10|42Axx]] and [[42A15|42Axx]]; for numerical approximation, see [[65Dxx|65Dxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/41Axx.html]]}{{moveright{< [[40-XX |40-XX]] | [[41-XX |41-XX]] | [[42-XX |42-XX]] >}}}
* ''41A05'' Interpolation [See also [[42A15|42Axx]] and [[65D05|65Dxx]]]
* ''41A10'' Approximation by polynomials {For approximation by trigonometric polynomials, see [[42A10|42Axx]]}
* ''41A15'' Spline approximation
* ''41A17'' Inequalities in approximation (Bernstein, Jackson, Nikol'skiĭ-type inequalities)
* ''41A20'' Approximation by rational functions
* ''41A21'' Padé approximation
* ''41A25'' Rate of convergence, degree of approximation
* ''41A27'' Inverse theorems
* ''41A28'' Simultaneous approximation
* ''41A29'' Approximation with constraints
* ''41A30'' Approximation by other special function classes
* ''41A35'' Approximation by operators (in particular, by integral operators)
* ''41A36'' Approximation by positive operators
* ''41A40'' Saturation
* ''41A44'' Best constants
* ''41A45'' Approximation by arbitrary linear expressions
* ''41A46'' Approximation by arbitrary nonlinear expressions; widths and entropy
* ''41A50'' Best approximation, Chebyshev systems
* ''41A52'' Uniqueness of best approximation
* ''41A55'' Approximate quadratures
* ''41A58'' Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
* ''41A60'' Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also [[30E15|30Exx]]]
* ''41A63'' Multidimensional problems (should also be assigned at least one other classification number in this section)
* ''41A65'' Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
* ''41A80'' Remainders in approximation formulas
* ''41A99'' None of the above, but in this section
!!![[42|42-XX]]Axx  Harmonic analysis in one variable {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/42Axx.html]]}{{moveright{< [[41-XX |41-XX]] | [[42-XX |42-XX]] | [[42Bxx |42Bxx]] >}}}
* ''42A05'' Trigonometric polynomials, inequalities, extremal problems
* ''42A10'' Trigonometric approximation
* ''42A15'' Trigonometric interpolation
* ''42A16'' Fourier coefficients, Fourier series of functions with special properties, special Fourier series {For automorphic theory, see mainly [[11F30|11Fxx]]}
* ''42A20'' Convergence and absolute convergence of Fourier and trigonometric series
* ''42A24'' Summability and absolute summability of Fourier and trigonometric series
* ''42A32'' Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
* ''42A38'' Fourier and ~Fourier-Stieltjes transforms and other transforms of Fourier type
* ''42A45'' Multipliers
* ''42A50'' Conjugate functions, conjugate series, singular integrals
* ''42A55'' Lacunary series of trigonometric and other functions; Riesz products
* ''42A61'' Probabilistic methods
* ''42A63'' Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization
* ''42A65'' Completeness of sets of functions
* ''42A70'' Trigonometric moment problems
* ''42A75'' Classical almost periodic functions, mean periodic functions [See also [[43A60|43Axx]]]
* ''42A82'' Positive definite functions
* ''42A85'' Convolution, factorization
* ''42A99'' None of the above, but in this section
!!![[42|42-XX]]Bxx  Harmonic analysis in several variables {For automorphic theory, see mainly [[11F30|11Fxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/42Bxx.html]]}{{moveright{< [[42Axx |42Axx]] | [[42-XX |42-XX]] | [[42Cxx |42Cxx]] >}}}
* ''42B05'' Fourier series and coefficients
* ''42B08'' Summability
* ''42B10'' Fourier and ~Fourier-Stieltjes transforms and other transforms of Fourier type
* ''42B15'' Multipliers
* ''42B20'' Singular and oscillatory integrals (~Calderón-Zygmund, etc.)
* ''42B25'' Maximal functions, ~Littlewood-Paley theory
* ''42B30'' $H^p$-spaces
* ''42B35'' Function spaces arising in harmonic analysis
* ''42B37'' Harmonic analysis and PDE [See also [[35-XX|35-XX]]]
* ''42B99'' None of the above, but in this section
!!!42-XX Harmonic analysis on Euclidean spaces {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/42-XX.html]]}{{moveright{< [[41-XX |41-XX]] | [[MSC |MSC2010]] | [[42Axx |42Axx]] >}}}
* ''42-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''42-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''42-02'' Research exposition (monographs, survey articles)
* ''42-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''42-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''42-06'' Proceedings, conferences, collections, etc.
* ''[[42Axx|42Axx]]''  Harmonic analysis in one variable
* ''[[42Bxx|42Bxx]]''  Harmonic analysis in several variables {For automorphic theory, see mainly [[11F30|11Fxx]]}
* ''[[42Cxx|42Cxx]]''  Nontrigonometric harmonic analysis
!!![[42|42-XX]]Cxx  Nontrigonometric harmonic analysis {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/42Cxx.html]]}{{moveright{< [[42Bxx |42Bxx]] | [[42-XX |42-XX]] | [[43-XX |43-XX]] >}}}
* ''42C05'' Orthogonal functions and polynomials, general theory [See also [[33C45|33Cxx]], [[33C50|33Cxx]], [[33D45|33Dxx]]]
* ''42C10'' Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
* ''42C15'' General harmonic expansions, frames
* ''42C20'' Other transformations of harmonic type
* ''42C25'' Uniqueness and localization for orthogonal series
* ''42C30'' Completeness of sets of functions
* ''42C40'' Wavelets and other special systems
* ''42C99'' None of the above, but in this section
!!!43-XX Abstract harmonic analysis {For other analysis on topological and Lie groups, see [[22Exx|22Exx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/43-XX.html]]}{{moveright{< [[42-XX |42-XX]] | [[MSC |MSC2010]] | [[43Axx |43Axx]] >}}}
* ''43-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''43-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''43-02'' Research exposition (monographs, survey articles)
* ''43-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''43-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''43-06'' Proceedings, conferences, collections, etc.
* ''[[43Axx|43Axx]]''  Abstract harmonic analysis {For other analysis on topological and Lie groups, see [[22Exx|22Exx]]}
!!![[43|43-XX]]Axx  Abstract harmonic analysis {For other analysis on topological and Lie groups, see [[22Exx|22Exx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/43Axx.html]]}{{moveright{< [[42-XX |42-XX]] | [[43-XX |43-XX]] | [[44-XX |44-XX]] >}}}
* ''43A05'' Measures on groups and semigroups, etc.
* ''43A07'' Means on groups, semigroups, etc.; amenable groups
* ''43A10'' Measure algebras on groups, semigroups, etc.
* ''43A15'' $L^p$-spaces and other function spaces on groups, semigroups, etc.
* ''43A17'' Analysis on ordered groups, $H^p$-theory
* ''43A20'' $L^1$-algebras on groups, semigroups, etc.
* ''43A22'' Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
* ''43A25'' Fourier and ~Fourier-Stieltjes transforms on locally compact and other abelian groups
* ''43A30'' Fourier and ~Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
* ''43A32'' Other transforms and operators of Fourier type
* ''43A35'' Positive definite functions on groups, semigroups, etc.
* ''43A40'' Character groups and dual objects
* ''43A45'' Spectral synthesis on groups, semigroups, etc.
* ''43A46'' Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
* ''43A50'' Convergence of Fourier series and of inverse transforms
* ''43A55'' Summability methods on groups, semigroups, etc. [See also [[40J05|40Jxx]]]
* ''43A60'' Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
* ''43A62'' Hypergroups
* ''43A65'' Representations of groups, semigroups, etc. [See also [[22A10|22Axx]], [[22A20|22Axx]], [[22Dxx|22Dxx]], [[22E45|22Exx]]]
* ''43A70'' Analysis on specific locally compact and other abelian groups [See also [[11R56|11Rxx]], [[22B05|22Bxx]]]
* ''43A75'' Analysis on specific compact groups
* ''43A77'' Analysis on general compact groups
* ''43A80'' Analysis on other specific Lie groups [See also [[22Exx|22Exx]]]
* ''43A85'' Analysis on homogeneous spaces
* ''43A90'' Spherical functions [See also [[22E45|22Exx]], [[22E46|22Exx]], [[33C55|33Cxx]]]
* ''43A95'' Categorical methods [See also [[46Mxx|46Mxx]]]
* ''43A99'' None of the above, but in this section
!!!44-XX Integral transforms, operational calculus {For fractional derivatives and integrals, see [[26A33|26Axx]]. For Fourier transforms, see [[42A38|42Axx]], [[42B10|42Bxx]]. For integral transforms in distribution spaces, see [[46F12|46Fxx]]. For numerical methods, see [[65R10|65Rxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/44-XX.html]]}{{moveright{< [[43-XX |43-XX]] | [[MSC |MSC2010]] | [[44Axx |44Axx]] >}}}
* ''44-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''44-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''44-02'' Research exposition (monographs, survey articles)
* ''44-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''44-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''44-06'' Proceedings, conferences, collections, etc.
* ''[[44Axx|44Axx]]''  Integral transforms, operational calculus {For fractional derivatives and integrals, see [[26A33|26Axx]]. For Fourier transforms, see [[42A38|42Axx]], [[42B10|42Bxx]]. For integral transforms in distribution spaces, see [[46F12|46Fxx]]. For numerical methods, see [[65R10|65Rxx]]}
!!![[44|44-XX]]Axx  Integral transforms, operational calculus {For fractional derivatives and integrals, see [[26A33|26Axx]]. For Fourier transforms, see [[42A38|42Axx]], [[42B10|42Bxx]]. For integral transforms in distribution spaces, see [[46F12|46Fxx]]. For numerical methods, see [[65R10|65Rxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/44Axx.html]]}{{moveright{< [[43-XX |43-XX]] | [[44-XX |44-XX]] | [[45-XX |45-XX]] >}}}
* ''44A05'' General transforms [See also [[42A38|42Axx]]]
* ''44A10'' Laplace transform
* ''44A12'' Radon transform [See also [[92C55|92Cxx]]]
* ''44A15'' Special transforms (Legendre, Hilbert, etc.)
* ''44A20'' Transforms of special functions
* ''44A30'' Multiple transforms
* ''44A35'' Convolution
* ''44A40'' Calculus of Mikusi{ń}ski and other operational calculi
* ''44A45'' Classical operational calculus
* ''44A55'' Discrete operational calculus
* ''44A60'' Moment problems
* ''44A99'' None of the above, but in this section
!!![[45|45-XX]]Axx  Linear integral equations {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/45Axx.html]]}{{moveright{< [[44-XX |44-XX]] | [[45-XX |45-XX]] | [[45Bxx |45Bxx]] >}}}
* ''45A05'' Linear integral equations
* ''45A99'' None of the above, but in this section
!!![[45|45-XX]]Bxx  Fredholm integral equations {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/45Bxx.html]]}{{moveright{< [[45Axx |45Axx]] | [[45-XX |45-XX]] | [[45Cxx |45Cxx]] >}}}
* ''45B05'' Fredholm integral equations
* ''45B99'' None of the above, but in this section
!!![[45|45-XX]]Cxx  Eigenvalue problems [See also [[34Lxx|34Lxx]], [[35Pxx|35Pxx]], [[45P05|45Pxx]], [[47A75|47Axx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/45Cxx.html]]}{{moveright{< [[45Bxx |45Bxx]] | [[45-XX |45-XX]] | [[45Dxx |45Dxx]] >}}}
* ''45C05'' Eigenvalue problems [See also [[34Lxx|34Lxx]], [[35Pxx|35Pxx]], [[45P05|45Pxx]], [[47A75|47Axx]]]
* ''45C99'' None of the above, but in this section
!!![[45|45-XX]]Dxx  Volterra integral equations [See also [[34A12|34Axx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/45Dxx.html]]}{{moveright{< [[45Cxx |45Cxx]] | [[45-XX |45-XX]] | [[45Exx |45Exx]] >}}}
* ''45D05'' Volterra integral equations [See also [[34A12|34Axx]]]
* ''45D99'' None of the above, but in this section
!!![[45|45-XX]]Exx  Singular integral equations [See also [[30E20|30Exx]], [[30E25|30Exx]], [[44A15|44Axx]], [[44A35|44Axx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/45Exx.html]]}{{moveright{< [[45Dxx |45Dxx]] | [[45-XX |45-XX]] | [[45Fxx |45Fxx]] >}}}
* ''45E05'' Integral equations with kernels of Cauchy type [See also [[35J15|35Jxx]]]
* ''45E10'' Integral equations of the convolution type (Abel, Picard, Toeplitz and ~Wiener-Hopf type) [See also [[47B35|47Bxx]]]
* ''45E99'' None of the above, but in this section
!!![[45|45-XX]]Fxx  Systems of linear integral equations {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/45Fxx.html]]}{{moveright{< [[45Exx |45Exx]] | [[45-XX |45-XX]] | [[45Gxx |45Gxx]] >}}}
* ''45F05'' Systems of nonsingular linear integral equations
* ''45F10'' Dual, triple, etc., integral and series equations
* ''45F15'' Systems of singular linear integral equations
* ''45F99'' None of the above, but in this section
!!![[45|45-XX]]Gxx  Nonlinear integral equations [See also [[47H30|47Hxx]], [[47Jxx|47Jxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/45Gxx.html]]}{{moveright{< [[45Fxx |45Fxx]] | [[45-XX |45-XX]] | [[45Hxx |45Hxx]] >}}}
* ''45G05'' Singular nonlinear integral equations
* ''45G10'' Other nonlinear integral equations
* ''45G15'' Systems of nonlinear integral equations
* ''45G99'' None of the above, but in this section
!!![[45|45-XX]]Hxx  Miscellaneous special kernels [See also [[44A15|44Axx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/45Hxx.html]]}{{moveright{< [[45Gxx |45Gxx]] | [[45-XX |45-XX]] | [[45Jxx |45Jxx]] >}}}
* ''45H05'' Miscellaneous special kernels [See also [[44A15|44Axx]]]
* ''45H99'' None of the above, but in this section
!!![[45|45-XX]]Jxx  Integro-ordinary differential equations [See also [[34K05|34Kxx]], [[34K30|34Kxx]], [[47G20|47Gxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/45Jxx.html]]}{{moveright{< [[45Hxx |45Hxx]] | [[45-XX |45-XX]] | [[45Kxx |45Kxx]] >}}}
* ''45J05'' Integro-ordinary differential equations [See also [[34K05|34Kxx]], [[34K30|34Kxx]], [[47G20|47Gxx]]]
* ''45J99'' None of the above, but in this section
!!![[45|45-XX]]Kxx  Integro-partial differential equations [See also [[34K30|34Kxx]], [[35R09|35Rxx]], [[35R10|35Rxx]], [[47G20|47Gxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/45Kxx.html]]}{{moveright{< [[45Jxx |45Jxx]] | [[45-XX |45-XX]] | [[45Lxx |45Lxx]] >}}}
* ''45K05'' Integro-partial differential equations [See also [[34K30|34Kxx]], [[35R09|35Rxx]], [[35R10|35Rxx]], [[47G20|47Gxx]]]
* ''45K99'' None of the above, but in this section
!!![[45|45-XX]]Lxx  Theoretical approximation of solutions {For numerical analysis, see [[65Rxx|65Rxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/45Lxx.html]]}{{moveright{< [[45Kxx |45Kxx]] | [[45-XX |45-XX]] | [[45Mxx |45Mxx]] >}}}
* ''45L05'' Theoretical approximation of solutions {For numerical analysis, see [[65Rxx|65Rxx]]}
* ''45L99'' None of the above, but in this section
!!![[45|45-XX]]Mxx  Qualitative behavior {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/45Mxx.html]]}{{moveright{< [[45Lxx |45Lxx]] | [[45-XX |45-XX]] | [[45Nxx |45Nxx]] >}}}
* ''45M05'' Asymptotics
* ''45M10'' Stability theory
* ''45M15'' Periodic solutions
* ''45M20'' Positive solutions
* ''45M99'' None of the above, but in this section
!!![[45|45-XX]]Nxx  Abstract integral equations, integral equations in abstract spaces {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/45Nxx.html]]}{{moveright{< [[45Mxx |45Mxx]] | [[45-XX |45-XX]] | [[45Pxx |45Pxx]] >}}}
* ''45N05'' Abstract integral equations, integral equations in abstract spaces
* ''45N99'' None of the above, but in this section
!!![[45|45-XX]]Pxx  Integral operators [See also [[47B38|47Bxx]], [[47G10|47Gxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/45Pxx.html]]}{{moveright{< [[45Nxx |45Nxx]] | [[45-XX |45-XX]] | [[45Qxx |45Qxx]] >}}}
* ''45P05'' Integral operators [See also [[47B38|47Bxx]], [[47G10|47Gxx]]]
* ''45P99'' None of the above, but in this section
!!![[45|45-XX]]Qxx  Inverse problems {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/45Qxx.html]]}{{moveright{< [[45Pxx |45Pxx]] | [[45-XX |45-XX]] | [[45Rxx |45Rxx]] >}}}
* ''45Q05'' Inverse problems
* ''45Q99'' None of the above, but in this section
!!!45-XX Integral equations {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/45-XX.html]]}{{moveright{< [[44-XX |44-XX]] | [[MSC |MSC2010]] | [[45Axx |45Axx]] >}}}
* ''45-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''45-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''45-02'' Research exposition (monographs, survey articles)
* ''45-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''45-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''45-06'' Proceedings, conferences, collections, etc.
* ''[[45Axx|45Axx]]''  Linear integral equations
* ''[[45Bxx|45Bxx]]''  Fredholm integral equations
* ''[[45Cxx|45Cxx]]''  Eigenvalue problems [See also [[34Lxx|34Lxx]], [[35Pxx|35Pxx]], [[45P05|45Pxx]], [[47A75|47Axx]]]
* ''[[45Dxx|45Dxx]]''  Volterra integral equations [See also [[34A12|34Axx]]]
* ''[[45Exx|45Exx]]''  Singular integral equations [See also [[30E20|30Exx]], [[30E25|30Exx]], [[44A15|44Axx]], [[44A35|44Axx]]]
* ''[[45Fxx|45Fxx]]''  Systems of linear integral equations
* ''[[45Gxx|45Gxx]]''  Nonlinear integral equations [See also [[47H30|47Hxx]], [[47Jxx|47Jxx]]]
* ''[[45Hxx|45Hxx]]''  Miscellaneous special kernels [See also [[44A15|44Axx]]]
* ''[[45Jxx|45Jxx]]''  Integro-ordinary differential equations [See also [[34K05|34Kxx]], [[34K30|34Kxx]], [[47G20|47Gxx]]]
* ''[[45Kxx|45Kxx]]''  Integro-partial differential equations [See also [[34K30|34Kxx]], [[35R09|35Rxx]], [[35R10|35Rxx]], [[47G20|47Gxx]]]
* ''[[45Lxx|45Lxx]]''  Theoretical approximation of solutions {For numerical analysis, see [[65Rxx|65Rxx]]}
* ''[[45Mxx|45Mxx]]''  Qualitative behavior
* ''[[45Nxx|45Nxx]]''  Abstract integral equations, integral equations in abstract spaces
* ''[[45Pxx|45Pxx]]''  Integral operators [See also [[47B38|47Bxx]], [[47G10|47Gxx]]]
* ''[[45Qxx|45Qxx]]''  Inverse problems
* ''[[45Rxx|45Rxx]]''  Random integral equations [See also [[60H20|60Hxx]]]
!!![[45|45-XX]]Rxx  Random integral equations [See also [[60H20|60Hxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/45Rxx.html]]}{{moveright{< [[45Qxx |45Qxx]] | [[45-XX |45-XX]] | [[46-XX |46-XX]] >}}}
* ''45R05'' Random integral equations [See also [[60H20|60Hxx]]]
* ''45R99'' None of the above, but in this section
!!![[46|46-XX]]Axx  Topological linear spaces and related structures {For function spaces, see [[46Exx|46Exx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/46Axx.html]]}{{moveright{< [[45-XX |45-XX]] | [[46-XX |46-XX]] | [[46Bxx |46Bxx]] >}}}
* ''46A03'' General theory of locally convex spaces
* ''46A04'' Locally convex Fréchet spaces and (DF)-spaces
* ''46A08'' Barrelled spaces, bornological spaces
* ''46A11'' Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
* ''46A13'' Spaces defined by inductive or projective limits (LB, LF, etc.) [See also [[46M40|46Mxx]]]
* ''46A16'' Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
* ''46A17'' Bornologies and related structures; Mackey convergence, etc.
* ''46A19'' Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than ${\bf R}$, etc.)
* ''46A20'' Duality theory
* ''46A22'' Theorems of ~Hahn-Banach type; extension and lifting of functionals and operators [See also [[46M10|46Mxx]]]
* ''46A25'' Reflexivity and semi-reflexivity [See also [[46B10|46Bxx]]]
* ''46A30'' Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness)
* ''46A32'' Spaces of linear operators; topological tensor products; approximation properties [See also [[46B28|46Bxx]], [[46M05|46Mxx]], [[47L05|47Lxx]], [[47L20|47Lxx]]]
* ''46A35'' Summability and bases [See also [[46B15|46Bxx]]]
* ''46A40'' Ordered topological linear spaces, vector lattices [See also [[06F20|06Fxx]], [[46B40|46Bxx]], [[46B42|46Bxx]]]
* ''46A45'' Sequence spaces (including Köthe sequence spaces) [See also [[46B45|46Bxx]]]
* ''46A50'' Compactness in topological linear spaces; angelic spaces, etc.
* ''46A55'' Convex sets in topological linear spaces; Choquet theory [See also [[52A07|52Axx]]]
* ''46A61'' Graded Fréchet spaces and tame operators
* ''46A63'' Topological invariants ((DN), ($\Omega$), etc.)
* ''46A70'' Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)
* ''46A80'' Modular spaces
* ''46A99'' None of the above, but in this section
!!![[46|46-XX]]Bxx  Normed linear spaces and Banach spaces; Banach lattices {For function spaces, see [[46Exx|46Exx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/46Bxx.html]]}{{moveright{< [[46Axx |46Axx]] | [[46-XX |46-XX]] | [[46Cxx |46Cxx]] >}}}
* ''46B03'' Isomorphic theory (including renorming) of Banach spaces
* ''46B04'' Isometric theory of Banach spaces
* ''46B06'' Asymptotic theory of Banach spaces [See also [[52A23|52Axx]]]
* ''46B07'' Local theory of Banach spaces
* ''46B08'' Ultraproduct techniques in Banach space theory [See also [[46M07|46Mxx]]]
* ''46B09'' Probabilistic methods in Banach space theory [See also [[60Bxx|60Bxx]]]
* ''46B10'' Duality and reflexivity [See also [[46A25|46Axx]]]
* ''46B15'' Summability and bases [See also [[46A35|46Axx]]]
* ''46B20'' Geometry and structure of normed linear spaces
* ''46B22'' ~Radon-Nikod{ý}m, Kreĭn-Milman and related properties [See also [[46G10|46Gxx]]]
* ''46B25'' Classical Banach spaces in the general theory
* ''46B26'' Nonseparable Banach spaces
* ''46B28'' Spaces of operators; tensor products; approximation properties [See also [[46A32|46Axx]], [[46M05|46Mxx]], [[47L05|47Lxx]], [[47L20|47Lxx]]]
* ''46B40'' Ordered normed spaces [See also [[46A40|46Axx]], [[46B42|46Bxx]]]
* ''46B42'' Banach lattices [See also [[46A40|46Axx]], [[46B40|46Bxx]]]
* ''46B45'' Banach sequence spaces [See also [[46A45|46Axx]]]
* ''46B50'' Compactness in Banach (or normed) spaces
* ''46B70'' Interpolation between normed linear spaces [See also [[46M35|46Mxx]]]
* ''46B80'' Nonlinear classification of Banach spaces; nonlinear quotients
* ''46B85'' Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science [See also [[05C12|05Cxx]], [[68Rxx|68Rxx]]]
* ''46B99'' None of the above, but in this section
!!![[46|46-XX]]Cxx  Inner product spaces and their generalizations, Hilbert spaces {For function spaces, see [[46Exx|46Exx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/46Cxx.html]]}{{moveright{< [[46Bxx |46Bxx]] | [[46-XX |46-XX]] | [[46Exx |46Exx]] >}}}
* ''46C05'' Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
* ''46C07'' Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) [See also [[46B70|46Bxx]], [[46M35|46Mxx]]]
* ''46C15'' Characterizations of Hilbert spaces
* ''46C20'' Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.) [See also [[47B50|47Bxx]]]
* ''46C50'' Generalizations of inner products (semi-inner products, partial inner products, etc.)
* ''46C99'' None of the above, but in this section
!!![[46|46-XX]]Exx  Linear function spaces and their duals [See also [[30H05|30Hxx]], [[32A38|32Axx]], [[46F05|46Fxx]]] {For function algebras, see [[46J10|46Jxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/46Exx.html]]}{{moveright{< [[46Cxx |46Cxx]] | [[46-XX |46-XX]] | [[46Fxx |46Fxx]] >}}}
* ''46E05'' Lattices of continuous, differentiable or analytic functions
* ''46E10'' Topological linear spaces of continuous, differentiable or analytic functions
* ''46E15'' Banach spaces of continuous, differentiable or analytic functions
* ''46E20'' Hilbert spaces of continuous, differentiable or analytic functions
* ''46E22'' Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de ~Branges-Rovnyak and other structured spaces) [See also [[47B32|47Bxx]]]
* ''46E25'' Rings and algebras of continuous, differentiable or analytic functions {For Banach function algebras, see [[46J10|46Jxx]], [[46J15|46Jxx]]}
* ''46E27'' Spaces of measures [See also [[28A33|28Axx]], [[46Gxx|46Gxx]]]
* ''46E30'' Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
* ''46E35'' Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
* ''46E39'' Sobolev (and similar kinds of) spaces of functions of discrete variables
* ''46E40'' Spaces of vector- and operator-valued functions
* ''46E50'' Spaces of differentiable or holomorphic functions on infinite-dimensional spaces [See also [[46G20|46Gxx]], [[46G25|46Gxx]], [[47H60|47Hxx]]]
* ''46E99'' None of the above, but in this section
!!![[46|46-XX]]Fxx  Distributions, generalized functions, distribution spaces [See also [[46T30|46Txx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/46Fxx.html]]}{{moveright{< [[46Exx |46Exx]] | [[46-XX |46-XX]] | [[46Gxx |46Gxx]] >}}}
* ''46F05'' Topological linear spaces of test functions, distributions and ultradistributions [See also [[46E10|46Exx]], [[46E35|46Exx]]]
* ''46F10'' Operations with distributions
* ''46F12'' Integral transforms in distribution spaces [See also [[42-XX|42-XX]], [[44-XX|44-XX]]]
* ''46F15'' Hyperfunctions, analytic functionals [See also [[32A25|32Axx]], [[32A45|32Axx]], [[32C35|32Cxx]], [[58J15|58Jxx]]]
* ''46F20'' Distributions and ultradistributions as boundary values of analytic functions [See also [[30D40|30Dxx]], [[30E25|30Exx]], [[32A40|32Axx]]]
* ''46F25'' Distributions on infinite-dimensional spaces [See also [[58C35|58Cxx]]]
* ''46F30'' Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
* ''46F99'' None of the above, but in this section
!!![[46|46-XX]]Gxx  Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) [See also [[28-XX|28-XX]], [[46Txx|46Txx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/46Gxx.html]]}{{moveright{< [[46Fxx |46Fxx]] | [[46-XX |46-XX]] | [[46Hxx |46Hxx]] >}}}
* ''46G05'' Derivatives [See also [[46T20|46Txx]], [[58C20|58Cxx]], [[58C25|58Cxx]]]
* ''46G10'' Vector-valued measures and integration [See also [[28Bxx|28Bxx]], [[46B22|46Bxx]]]
* ''46G12'' Measures and integration on abstract linear spaces [See also [[28C20|28Cxx]], [[46T12|46Txx]]]
* ''46G15'' Functional analytic lifting theory [See also [[28A51|28Axx]]]
* ''46G20'' Infinite-dimensional holomorphy [See also [[32-XX|32-XX]], [[46E50|46Exx]], [[46T25|46Txx]], [[58B12|58Bxx]], [[58C10|58Cxx]]]
* ''46G25'' (Spaces of) multilinear mappings, polynomials [See also [[46E50|46Exx]], [[46G20|46Gxx]], [[47H60|47Hxx]]]
* ''46G99'' None of the above, but in this section
!!![[46|46-XX]]Hxx  Topological algebras, normed rings and algebras, Banach algebras {For group algebras, convolution algebras and measure algebras, see [[43A10|43Axx]], [[43A20|43Axx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/46Hxx.html]]}{{moveright{< [[46Gxx |46Gxx]] | [[46-XX |46-XX]] | [[46Jxx |46Jxx]] >}}}
* ''46H05'' General theory of topological algebras
* ''46H10'' Ideals and subalgebras
* ''46H15'' Representations of topological algebras
* ''46H20'' Structure, classification of topological algebras
* ''46H25'' Normed modules and Banach modules, topological modules (if not placed in [[13-XX|13-XX]] or [[16-XX|16-XX]])
* ''46H30'' Functional calculus in topological algebras [See also [[47A60|47Axx]]]
* ''46H35'' Topological algebras of operators [See mainly [[47Lxx|47Lxx]]]
* ''46H40'' Automatic continuity
* ''46H70'' Nonassociative topological algebras [See also [[46K70|46Kxx]], [[46L70|46Lxx]]]
* ''46H99'' None of the above, but in this section
!!![[46|46-XX]]Jxx  Commutative Banach algebras and commutative topological algebras [See also [[46E25|46Exx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/46Jxx.html]]}{{moveright{< [[46Hxx |46Hxx]] | [[46-XX |46-XX]] | [[46Kxx |46Kxx]] >}}}
* ''46J05'' General theory of commutative topological algebras
* ''46J10'' Banach algebras of continuous functions, function algebras [See also [[46E25|46Exx]]]
* ''46J15'' Banach algebras of differentiable or analytic functions, $H^p$-spaces [See also [[30H10|30Hxx]], [[32A35|32Axx]], [[32A37|32Axx]], [[32A38|32Axx]], [[42B30|42Bxx]]]
* ''46J20'' Ideals, maximal ideals, boundaries
* ''46J25'' Representations of commutative topological algebras
* ''46J30'' Subalgebras
* ''46J40'' Structure, classification of commutative topological algebras
* ''46J45'' Radical Banach algebras
* ''46J99'' None of the above, but in this section
!!![[46|46-XX]]Kxx  Topological (rings and) algebras with an involution [See also [[16W10|16Wxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/46Kxx.html]]}{{moveright{< [[46Jxx |46Jxx]] | [[46-XX |46-XX]] | [[46Lxx |46Lxx]] >}}}
* ''46K05'' General theory of topological algebras with involution
* ''46K10'' Representations of topological algebras with involution
* ''46K15'' Hilbert algebras
* ''46K50'' Nonselfadjoint (sub)algebras in algebras with involution
* ''46K70'' Nonassociative topological algebras with an involution [See also [[46H70|46Hxx]], [[46L70|46Lxx]]]
* ''46K99'' None of the above, but in this section
!!![[46|46-XX]]Lxx  Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) [See also [[22D25|22Dxx]], [[47Lxx|47Lxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/46Lxx.html]]}{{moveright{< [[46Kxx |46Kxx]] | [[46-XX |46-XX]] | [[46Mxx |46Mxx]] >}}}
* ''46L05'' General theory of $C^*$-algebras
* ''46L06'' Tensor products of $C^*$-algebras
* ''46L07'' Operator spaces and completely bounded maps [See also [[47L25|47Lxx]]]
* ''46L08'' $C^*$-modules
* ''46L09'' Free products of $C^*$-algebras
* ''46L10'' General theory of von Neumann algebras
* ''46L30'' States
* ''46L35'' Classifications of $C^*$-algebras
* ''46L36'' Classification of factors
* ''46L37'' Subfactors and their classification
* ''46L40'' Automorphisms
* ''46L45'' Decomposition theory for $C^*$-algebras
* ''46L51'' Noncommutative measure and integration
* ''46L52'' Noncommutative function spaces
* ''46L53'' Noncommutative probability and statistics
* ''46L54'' Free probability and free operator algebras
* ''46L55'' Noncommutative dynamical systems [See also [[28Dxx|28Dxx]], [[37Kxx|37Kxx]], [[37Lxx|37Lxx]], [[54H20|54Hxx]]]
* ''46L57'' Derivations, dissipations and positive semigroups in $C^*$-algebras
* ''46L60'' Applications of selfadjoint operator algebras to physics [See also [[46N50|46Nxx]], [[46N55|46Nxx]], [[47L90|47Lxx]], [[81T05|81Txx]], [[82B10|82Bxx]], [[82C10|82Cxx]]]
* ''46L65'' Quantizations, deformations
* ''46L70'' Nonassociative selfadjoint operator algebras [See also [[46H70|46Hxx]], [[46K70|46Kxx]]]
* ''46L80'' $K$-theory and operator algebras (including cyclic theory) [See also [[18F25|18Fxx]], [[19Kxx|19Kxx]], [[46M20|46Mxx]], [[55Rxx|55Rxx]], [[58J22|58Jxx]]]
* ''46L85'' Noncommutative topology [See also [[58B32|58Bxx]], [[58B34|58Bxx]], [[58J22|58Jxx]]]
* ''46L87'' Noncommutative differential geometry [See also [[58B32|58Bxx]], [[58B34|58Bxx]], [[58J22|58Jxx]]]
* ''46L89'' Other “noncommutative” mathematics based on $C^*$-algebra theory [See also [[58B32|58Bxx]], [[58B34|58Bxx]], [[58J22|58Jxx]]]
* ''46L99'' None of the above, but in this section
!!![[46|46-XX]]Mxx  Methods of category theory in functional analysis [See also [[18-XX|18-XX]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/46Mxx.html]]}{{moveright{< [[46Lxx |46Lxx]] | [[46-XX |46-XX]] | [[46Nxx |46Nxx]] >}}}
* ''46M05'' Tensor products [See also [[46A32|46Axx]], [[46B28|46Bxx]], [[47A80|47Axx]]]
* ''46M07'' Ultraproducts [See also [[46B08|46Bxx]], [[46S20|46Sxx]]]
* ''46M10'' Projective and injective objects [See also [[46A22|46Axx]]]
* ''46M15'' Categories, functors {For $K$-theory, EXT, etc., see [[19K33|19Kxx]], [[46L80|46Lxx]], [[46M18|46Mxx]], [[46M20|46Mxx]]}
* ''46M18'' Homological methods (exact sequences, right inverses, lifting, etc.)
* ''46M20'' Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.) [See also [[14F05|14Fxx]], [[18Fxx|18Fxx]], [[19Kxx|19Kxx]], [[32Cxx|32Cxx]], [[32Lxx|32Lxx]], [[46L80|46Lxx]], [[46M15|46Mxx]], [[46M18|46Mxx]], [[55Rxx|55Rxx]]]
* ''46M35'' Abstract interpolation of topological vector spaces [See also [[46B70|46Bxx]]]
* ''46M40'' Inductive and projective limits [See also [[46A13|46Axx]]]
* ''46M99'' None of the above, but in this section
!!![[46|46-XX]]Nxx  Miscellaneous applications of functional analysis [See also [[47Nxx|47Nxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/46Nxx.html]]}{{moveright{< [[46Mxx |46Mxx]] | [[46-XX |46-XX]] | [[46Sxx |46Sxx]] >}}}
* ''46N10'' Applications in optimization, convex analysis, mathematical programming, economics
* ''46N20'' Applications to differential and integral equations
* ''46N30'' Applications in probability theory and statistics
* ''46N40'' Applications in numerical analysis [See also [[65Jxx|65Jxx]]]
* ''46N50'' Applications in quantum physics
* ''46N55'' Applications in statistical physics
* ''46N60'' Applications in biology and other sciences
* ''46N99'' None of the above, but in this section
!!![[46|46-XX]]Sxx  Other (nonclassical) types of functional analysis [See also [[47Sxx|47Sxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/46Sxx.html]]}{{moveright{< [[46Nxx |46Nxx]] | [[46-XX |46-XX]] | [[46Txx |46Txx]] >}}}
* ''46S10'' Functional analysis over fields other than ${\bf R}$ or ${\bf C}$ or the quaternions; non-Archimedean functional analysis [See also [[12J25|12Jxx]], [[32P05|32Pxx]]]
* ''46S20'' Nonstandard functional analysis [See also [[03H05|03Hxx]]]
* ''46S30'' Constructive functional analysis [See also [[03F60|03Fxx]]]
* ''46S40'' Fuzzy functional analysis [See also [[03E72|03Exx]]]
* ''46S50'' Functional analysis in probabilistic metric linear spaces
* ''46S60'' Functional analysis on superspaces (supermanifolds) or graded spaces [See also [[58A50|58Axx]] and [[58C50|58Cxx]]]
* ''46S99'' None of the above, but in this section
!!!46-XX Functional analysis {For manifolds modeled on topological linear spaces, see [[57Nxx|57Nxx]], [[58Bxx|58Bxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/46-XX.html]]}{{moveright{< [[45-XX |45-XX]] | [[MSC |MSC2010]] | [[46Axx |46Axx]] >}}}
* ''46-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''46-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''46-02'' Research exposition (monographs, survey articles)
* ''46-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''46-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''46-06'' Proceedings, conferences, collections, etc.
* ''[[46Axx|46Axx]]''  Topological linear spaces and related structures {For function spaces, see [[46Exx|46Exx]]}
* ''[[46Bxx|46Bxx]]''  Normed linear spaces and Banach spaces; Banach lattices {For function spaces, see [[46Exx|46Exx]]}
* ''[[46Cxx|46Cxx]]''  Inner product spaces and their generalizations, Hilbert spaces {For function spaces, see [[46Exx|46Exx]]}
* ''[[46Exx|46Exx]]''  Linear function spaces and their duals [See also [[30H05|30Hxx]], [[32A38|32Axx]], [[46F05|46Fxx]]] {For function algebras, see [[46J10|46Jxx]]}
* ''[[46Fxx|46Fxx]]''  Distributions, generalized functions, distribution spaces [See also [[46T30|46Txx]]]
* ''[[46Gxx|46Gxx]]''  Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) [See also [[28-XX|28-XX]], [[46Txx|46Txx]]]
* ''[[46Hxx|46Hxx]]''  Topological algebras, normed rings and algebras, Banach algebras {For group algebras, convolution algebras and measure algebras, see [[43A10|43Axx]], [[43A20|43Axx]]}
* ''[[46Jxx|46Jxx]]''  Commutative Banach algebras and commutative topological algebras [See also [[46E25|46Exx]]]
* ''[[46Kxx|46Kxx]]''  Topological (rings and) algebras with an involution [See also [[16W10|16Wxx]]]
* ''[[46Lxx|46Lxx]]''  Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) [See also [[22D25|22Dxx]], [[47Lxx|47Lxx]]]
* ''[[46Mxx|46Mxx]]''  Methods of category theory in functional analysis [See also [[18-XX|18-XX]]]
* ''[[46Nxx|46Nxx]]''  Miscellaneous applications of functional analysis [See also [[47Nxx|47Nxx]]]
* ''[[46Sxx|46Sxx]]''  Other (nonclassical) types of functional analysis [See also [[47Sxx|47Sxx]]]
* ''[[46Txx|46Txx]]''  Nonlinear functional analysis [See also [[47Hxx|47Hxx]], [[47Jxx|47Jxx]], [[58Cxx|58Cxx]], [[58Dxx|58Dxx]]]
!!![[46|46-XX]]Txx  Nonlinear functional analysis [See also [[47Hxx|47Hxx]], [[47Jxx|47Jxx]], [[58Cxx|58Cxx]], [[58Dxx|58Dxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/46Txx.html]]}{{moveright{< [[46Sxx |46Sxx]] | [[46-XX |46-XX]] | [[47-XX |47-XX]] >}}}
* ''46T05'' Infinite-dimensional manifolds [See also [[53Axx|53Axx]], [[57N20|57Nxx]], [[58Bxx|58Bxx]], [[58Dxx|58Dxx]]]
* ''46T10'' Manifolds of mappings
* ''46T12'' Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds [See also [[28Cxx|28Cxx]], [[46G12|46Gxx]], [[60-XX|60-XX]]]
* ''46T20'' Continuous and differentiable maps [See also [[46G05|46Gxx]]]
* ''46T25'' Holomorphic maps [See also [[46G20|46Gxx]]]
* ''46T30'' Distributions and generalized functions on nonlinear spaces [See also [[46Fxx|46Fxx]]]
* ''46T99'' None of the above, but in this section
!!![[47|47-XX]]Axx  General theory of linear operators {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/47Axx.html]]}{{moveright{< [[46-XX |46-XX]] | [[47-XX |47-XX]] | [[47Bxx |47Bxx]] >}}}
* ''47A05'' General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
* ''47A06'' Linear relations (multivalued linear operators)
* ''47A07'' Forms (bilinear, sesquilinear, multilinear)
* ''47A10'' Spectrum, resolvent
* ''47A11'' Local spectral properties
* ''47A12'' Numerical range, numerical radius
* ''47A13'' Several-variable operator theory (spectral, Fredholm, etc.)
* ''47A15'' Invariant subspaces [See also [[47A46|47Axx]]]
* ''47A16'' Cyclic vectors, hypercyclic and chaotic operators
* ''47A20'' Dilations, extensions, compressions
* ''47A25'' Spectral sets
* ''47A30'' Norms (inequalities, more than one norm, etc.)
* ''47A35'' Ergodic theory [See also [[28Dxx|28Dxx]], [[37Axx|37Axx]]]
* ''47A40'' Scattering theory [See also [[34L25|34Lxx]], [[35P25|35Pxx]], [[37K15|37Kxx]], [[58J50|58Jxx]], [[81Uxx|81Uxx]]]
* ''47A45'' Canonical models for contractions and nonselfadjoint operators
* ''47A46'' Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.
* ''47A48'' Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc.
* ''47A50'' Equations and inequalities involving linear operators, with vector unknowns
* ''47A52'' Ill-posed problems, regularization [See also [[35R25|35Rxx]], [[47J06|47Jxx]], [[65F22|65Fxx]], [[65J20|65Jxx]], [[65L08|65Lxx]], [[65M30|65Mxx]], [[65R30|65Rxx]]]
* ''47A53'' (Semi-) Fredholm operators; index theories [See also [[58B15|58Bxx]], [[58J20|58Jxx]]]
* ''47A55'' Perturbation theory [See also [[47H14|47Hxx]], [[58J37|58Jxx]], [[70H09|70Hxx]], [[81Q15|81Qxx]]]
* ''47A56'' Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones)
* ''47A57'' Operator methods in interpolation, moment and extension problems [See also [[30E05|30Exx]], [[42A70|42Axx]], [[42A82|42Axx]], [[44A60|44Axx]]]
* ''47A58'' Operator approximation theory
* ''47A60'' Functional calculus
* ''47A62'' Equations involving linear operators, with operator unknowns
* ''47A63'' Operator inequalities
* ''47A64'' Operator means, shorted operators, etc.
* ''47A65'' Structure theory
* ''47A66'' Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal operators
* ''47A67'' Representation theory
* ''47A68'' Factorization theory (including ~Wiener-Hopf and spectral factorizations)
* ''47A70'' (Generalized) eigenfunction expansions; rigged Hilbert spaces
* ''47A75'' Eigenvalue problems [See also [[47J10|47Jxx]], [[49R05|49Rxx]]]
* ''47A80'' Tensor products of operators [See also [[46M05|46Mxx]]]
* ''47A99'' None of the above, but in this section
!!![[47|47-XX]]Bxx  Special classes of linear operators {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/47Bxx.html]]}{{moveright{< [[47Axx |47Axx]] | [[47-XX |47-XX]] | [[47Cxx |47Cxx]] >}}}
* ''47B06'' Riesz operators; eigenvalue distributions; approximation numbers, $s$-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
* ''47B07'' Operators defined by compactness properties
* ''47B10'' Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.) [See also [[47L20|47Lxx]]]
* ''47B15'' Hermitian and normal operators (spectral measures, functional calculus, etc.)
* ''47B20'' Subnormal operators, hyponormal operators, etc.
* ''47B25'' Symmetric and selfadjoint operators (unbounded)
* ''47B32'' Operators in reproducing-kernel Hilbert spaces (including de Branges, de ~Branges-Rovnyak, and other structured spaces) [See also [[46E22|46Exx]]]
* ''47B33'' Composition operators
* ''47B34'' Kernel operators
* ''47B35'' Toeplitz operators, Hankel operators, ~Wiener-Hopf operators [See also [[45P05|45Pxx]], [[47G10|47Gxx]] for other integral operators; see also [[32A25|32Axx]], [[32M15|32Mxx]]]
* ''47B36'' Jacobi (tridiagonal) operators (matrices) and generalizations
* ''47B37'' Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
* ''47B38'' Operators on function spaces (general)
* ''47B39'' Difference operators [See also [[39A70|39Axx]]]
* ''47B40'' Spectral operators, decomposable operators, well-bounded operators, etc.
* ''47B44'' Accretive operators, dissipative operators, etc.
* ''47B47'' Commutators, derivations, elementary operators, etc.
* ''47B48'' Operators on Banach algebras
* ''47B49'' Transformers, preservers (operators on spaces of operators)
* ''47B50'' Operators on spaces with an indefinite metric [See also [[46C50|46Cxx]]]
* ''47B60'' Operators on ordered spaces
* ''47B65'' Positive operators and order-bounded operators
* ''47B80'' Random operators [See also [[47H40|47Hxx]], [[60H25|60Hxx]]]
* ''47B99'' None of the above, but in this section
!!![[47|47-XX]]Cxx  Individual linear operators as elements of algebraic systems {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/47Cxx.html]]}{{moveright{< [[47Bxx |47Bxx]] | [[47-XX |47-XX]] | [[47Dxx |47Dxx]] >}}}
* ''47C05'' Operators in algebras
* ''47C10'' Operators in ${}^*$-algebras
* ''47C15'' Operators in $C^*$- or von Neumann algebras
* ''47C99'' None of the above, but in this section
!!![[47|47-XX]]Dxx  Groups and semigroups of linear operators, their generalizations and applications {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/47Dxx.html]]}{{moveright{< [[47Cxx |47Cxx]] | [[47-XX |47-XX]] | [[47Exx |47Exx]] >}}}
* ''47D03'' Groups and semigroups of linear operators {For nonlinear operators, see [[47H20|47Hxx]]; see also [[20M20|20Mxx]]}
* ''47D06'' One-parameter semigroups and linear evolution equations [See also [[34G10|34Gxx]], [[34K30|34Kxx]]]
* ''47D07'' Markov semigroups and applications to diffusion processes {For Markov processes, see [[60Jxx|60Jxx]]}
* ''47D08'' Schrödinger and ~Feynman-Kac semigroups
* ''47D09'' Operator sine and cosine functions and higher-order Cauchy problems [See also [[34G10|34Gxx]]]
* ''47D60'' $C$-semigroups, regularized semigroups
* ''47D62'' Integrated semigroups
* ''47D99'' None of the above, but in this section
!!![[47|47-XX]]Exx  Ordinary differential operators [See also [[34Bxx|34Bxx]], [[34Lxx|34Lxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/47Exx.html]]}{{moveright{< [[47Dxx |47Dxx]] | [[47-XX |47-XX]] | [[47Fxx |47Fxx]] >}}}
* ''47E05'' Ordinary differential operators [See also [[34Bxx|34Bxx]], [[34Lxx|34Lxx]]] (should also be assigned at least one other classification number in section 47)
* ''47E99'' None of the above, but in this section
!!![[47|47-XX]]Fxx  Partial differential operators [See also [[35Pxx|35Pxx]], [[58Jxx|58Jxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/47Fxx.html]]}{{moveright{< [[47Exx |47Exx]] | [[47-XX |47-XX]] | [[47Gxx |47Gxx]] >}}}
* ''47F05'' Partial differential operators [See also [[35Pxx|35Pxx]], [[58Jxx|58Jxx]]] (should also be assigned at least one other classification number in section 47)
* ''47F99'' None of the above, but in this section
!!![[47|47-XX]]Gxx  Integral, integro-differential, and pseudodifferential operators [See also [[58Jxx|58Jxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/47Gxx.html]]}{{moveright{< [[47Fxx |47Fxx]] | [[47-XX |47-XX]] | [[47Hxx |47Hxx]] >}}}
* ''47G10'' Integral operators [See also [[45P05|45Pxx]]]
* ''47G20'' Integro-differential operators [See also [[34K30|34Kxx]], [[35R09|35Rxx]], [[35R10|35Rxx]], [[45Jxx|45Jxx]], [[45Kxx|45Kxx]]]
* ''47G30'' Pseudodifferential operators [See also [[35Sxx|35Sxx]], [[58Jxx|58Jxx]]]
* ''47G40'' Potential operators [See also [[31-XX|31-XX]]]
* ''47G99'' None of the above, but in this section
!!![[47|47-XX]]Hxx  Nonlinear operators and their properties {For global and geometric aspects, see [[49J53|49Jxx]], [[58-XX|58-XX]], especially [[58Cxx|58Cxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/47Hxx.html]]}{{moveright{< [[47Gxx |47Gxx]] | [[47-XX |47-XX]] | [[47Jxx |47Jxx]] >}}}
* ''47H04'' Set-valued operators [See also [[28B20|28Bxx]], [[54C60|54Cxx]], [[58C06|58Cxx]]]
* ''47H05'' Monotone operators and generalizations
* ''47H06'' Accretive operators, dissipative operators, etc.
* ''47H07'' Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
* ''47H08'' Measures of noncompactness and condensing mappings, $K$-set contractions, etc.
* ''47H09'' Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc.
* ''47H10'' Fixed-point theorems [See also [[37C25|37Cxx]], [[54H25|54Hxx]], [[55M20|55Mxx]], [[58C30|58Cxx]]]
* ''47H11'' Degree theory [See also [[55M25|55Mxx]], [[58C30|58Cxx]]]
* ''47H14'' Perturbations of nonlinear operators [See also [[47A55|47Axx]], [[58J37|58Jxx]], [[70H09|70Hxx]], [[70K60|70Kxx]], [[81Q15|81Qxx]]]
* ''47H20'' Semigroups of nonlinear operators [See also [[37L05|37Lxx]], [[47J35|47Jxx]], [[54H15|54Hxx]], [[58D07|58Dxx]]]
* ''47H25'' Nonlinear ergodic theorems [See also [[28Dxx|28Dxx]], [[37Axx|37Axx]], [[47A35|47Axx]]]
* ''47H30'' Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) [See also [[45Gxx|45Gxx]], [[45P05|45Pxx]]]
* ''47H40'' Random operators [See also [[47B80|47Bxx]], [[60H25|60Hxx]]]
* ''47H60'' Multilinear and polynomial operators [See also [[46G25|46Gxx]]]
* ''47H99'' None of the above, but in this section
!!![[47|47-XX]]Jxx  Equations and inequalities involving nonlinear operators [See also [[46Txx|46Txx]]] {For global and geometric aspects, see [[58-XX|58-XX]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/47Jxx.html]]}{{moveright{< [[47Hxx |47Hxx]] | [[47-XX |47-XX]] | [[47Lxx |47Lxx]] >}}}
* ''47J05'' Equations involving nonlinear operators (general) [See also [[47H10|47Hxx]], [[47J25|47Jxx]]]
* ''47J06'' Nonlinear ill-posed problems [See also [[35R25|35Rxx]], [[47A52|47Axx]], [[65F22|65Fxx]], [[65J20|65Jxx]], [[65L08|65Lxx]], [[65M30|65Mxx]], [[65R30|65Rxx]]]
* ''47J07'' Abstract inverse mapping and implicit function theorems [See also [[46T20|46Txx]] and [[58C15|58Cxx]]]
* ''47J10'' Nonlinear spectral theory, nonlinear eigenvalue problems [See also [[49R05|49Rxx]]]
* ''47J15'' Abstract bifurcation theory [See also [[34C23|34Cxx]], [[37Gxx|37Gxx]], [[58E07|58Exx]], [[58E09|58Exx]]]
* ''47J20'' Variational and other types of inequalities involving nonlinear operators (general) [See also [[49J40|49Jxx]]]
* ''47J22'' Variational and other types of inclusions [See also [[34A60|34Axx]], [[49J21|49Jxx]], [[49K21|49Kxx]]]
* ''47J25'' Iterative procedures [See also [[65J15|65Jxx]]]
* ''47J30'' Variational methods [See also [[58Exx|58Exx]]]
* ''47J35'' Nonlinear evolution equations [See also [[34G20|34Gxx]], [[35K90|35Kxx]], [[35L90|35Lxx]], [[35Qxx|35Qxx]], [[35R20|35Rxx]], [[37Kxx|37Kxx]], [[37Lxx|37Lxx]], [[47H20|47Hxx]], [[58D25|58Dxx]]]
* ''47J40'' Equations with hysteresis operators [See also [[34C55|34Cxx]], [[74N30|74Nxx]]]
* ''47J99'' None of the above, but in this section
!!![[47|47-XX]]Lxx  Linear spaces and algebras of operators [See also [[46Lxx|46Lxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/47Lxx.html]]}{{moveright{< [[47Jxx |47Jxx]] | [[47-XX |47-XX]] | [[47Nxx |47Nxx]] >}}}
* ''47L05'' Linear spaces of operators [See also [[46A32|46Axx]] and [[46B28|46Bxx]]]
* ''47L07'' Convex sets and cones of operators [See also [[46A55|46Axx]]]
* ''47L10'' Algebras of operators on Banach spaces and other topological linear spaces
* ''47L15'' Operator algebras with symbol structure
* ''47L20'' Operator ideals [See also [[47B10|47Bxx]]]
* ''47L22'' Ideals of polynomials and of multilinear mappings
* ''47L25'' Operator spaces (= matricially normed spaces) [See also [[46L07|46Lxx]]]
* ''47L30'' Abstract operator algebras on Hilbert spaces
* ''47L35'' Nest algebras, CSL algebras
* ''47L40'' Limit algebras, subalgebras of $C^*$-algebras
* ''47L45'' Dual algebras; weakly closed singly generated operator algebras
* ''47L50'' Dual spaces of operator algebras
* ''47L55'' Representations of (nonselfadjoint) operator algebras
* ''47L60'' Algebras of unbounded operators; partial algebras of operators
* ''47L65'' Crossed product algebras (analytic crossed products)
* ''47L70'' Nonassociative nonselfadjoint operator algebras
* ''47L75'' Other nonselfadjoint operator algebras
* ''47L80'' Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)
* ''47L90'' Applications of operator algebras to physics
* ''47L99'' None of the above, but in this section
!!![[47|47-XX]]Nxx  Miscellaneous applications of operator theory [See also [[46Nxx|46Nxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/47Nxx.html]]}{{moveright{< [[47Lxx |47Lxx]] | [[47-XX |47-XX]] | [[47Sxx |47Sxx]] >}}}
* ''47N10'' Applications in optimization, convex analysis, mathematical programming, economics
* ''47N20'' Applications to differential and integral equations
* ''47N30'' Applications in probability theory and statistics
* ''47N40'' Applications in numerical analysis [See also [[65Jxx|65Jxx]]]
* ''47N50'' Applications in the physical sciences
* ''47N60'' Applications in chemistry and life sciences
* ''47N70'' Applications in systems theory, circuits, and control theory
* ''47N99'' None of the above, but in this section
!!!47-XX Operator theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/47-XX.html]]}{{moveright{< [[46-XX |46-XX]] | [[MSC |MSC2010]] | [[47Axx |47Axx]] >}}}
* ''47-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''47-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''47-02'' Research exposition (monographs, survey articles)
* ''47-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''47-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''47-06'' Proceedings, conferences, collections, etc.
* ''[[47Axx|47Axx]]''  General theory of linear operators
* ''[[47Bxx|47Bxx]]''  Special classes of linear operators
* ''[[47Cxx|47Cxx]]''  Individual linear operators as elements of algebraic systems
* ''[[47Dxx|47Dxx]]''  Groups and semigroups of linear operators, their generalizations and applications
* ''[[47Exx|47Exx]]''  Ordinary differential operators [See also [[34Bxx|34Bxx]], [[34Lxx|34Lxx]]]
* ''[[47Fxx|47Fxx]]''  Partial differential operators [See also [[35Pxx|35Pxx]], [[58Jxx|58Jxx]]]
* ''[[47Gxx|47Gxx]]''  Integral, integro-differential, and pseudodifferential operators [See also [[58Jxx|58Jxx]]]
* ''[[47Hxx|47Hxx]]''  Nonlinear operators and their properties {For global and geometric aspects, see [[49J53|49Jxx]], [[58-XX|58-XX]], especially [[58Cxx|58Cxx]]}
* ''[[47Jxx|47Jxx]]''  Equations and inequalities involving nonlinear operators [See also [[46Txx|46Txx]]] {For global and geometric aspects, see [[58-XX|58-XX]]}
* ''[[47Lxx|47Lxx]]''  Linear spaces and algebras of operators [See also [[46Lxx|46Lxx]]]
* ''[[47Nxx|47Nxx]]''  Miscellaneous applications of operator theory [See also [[46Nxx|46Nxx]]]
* ''[[47Sxx|47Sxx]]''  Other (nonclassical) types of operator theory [See also [[46Sxx|46Sxx]]]
!!![[47|47-XX]]Sxx  Other (nonclassical) types of operator theory [See also [[46Sxx|46Sxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/47Sxx.html]]}{{moveright{< [[47Nxx |47Nxx]] | [[47-XX |47-XX]] | [[49-XX |49-XX]] >}}}
* ''47S10'' Operator theory over fields other than ${\bf R}$, ${\bf C}$ or the quaternions; non-Archimedean operator theory
* ''47S20'' Nonstandard operator theory [See also [[03H05|03Hxx]]]
* ''47S30'' Constructive operator theory [See also [[03F60|03Fxx]]]
* ''47S40'' Fuzzy operator theory [See also [[03E72|03Exx]]]
* ''47S50'' Operator theory in probabilistic metric linear spaces [See also [[54E70|54Exx]]]
* ''47S99'' None of the above, but in this section
!!![[49|49-XX]]Jxx  Existence theories {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/49Jxx.html]]}{{moveright{< [[47-XX |47-XX]] | [[49-XX |49-XX]] | [[49Kxx |49Kxx]] >}}}
* ''49J05'' Free problems in one independent variable
* ''49J10'' Free problems in two or more independent variables
* ''49J15'' Optimal control problems involving ordinary differential equations
* ''49J20'' Optimal control problems involving partial differential equations
* ''49J21'' Optimal control problems involving relations other than differential equations
* ''49J27'' Problems in abstract spaces [See also [[90C48|90Cxx]], [[93C25|93Cxx]]]
* ''49J30'' Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
* ''49J35'' Minimax problems
* ''49J40'' Variational methods including variational inequalities [See also [[47J20|47Jxx]]]
* ''49J45'' Methods involving semicontinuity and convergence; relaxation
* ''49J50'' Fréchet and Gateaux differentiability [See also [[46G05|46Gxx]], [[58C20|58Cxx]]]
* ''49J52'' Nonsmooth analysis [See also [[46G05|46Gxx]], [[58C50|58Cxx]], [[90C56|90Cxx]]]
* ''49J53'' Set-valued and variational analysis [See also [[28B20|28Bxx]], [[47H04|47Hxx]], [[54C60|54Cxx]], [[58C06|58Cxx]]]
* ''49J55'' Problems involving randomness [See also [[93E20|93Exx]]]
* ''49J99'' None of the above, but in this section
!!![[49|49-XX]]Kxx  Optimality conditions {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/49Kxx.html]]}{{moveright{< [[49Jxx |49Jxx]] | [[49-XX |49-XX]] | [[49Lxx |49Lxx]] >}}}
* ''49K05'' Free problems in one independent variable
* ''49K10'' Free problems in two or more independent variables
* ''49K15'' Problems involving ordinary differential equations
* ''49K20'' Problems involving partial differential equations
* ''49K21'' Problems involving relations other than differential equations
* ''49K27'' Problems in abstract spaces [See also [[90C48|90Cxx]], [[93C25|93Cxx]]]
* ''49K30'' Optimal solutions belonging to restricted classes
* ''49K35'' Minimax problems
* ''49K40'' Sensitivity, stability, well-posedness [See also [[90C31|90Cxx]]]
* ''49K45'' Problems involving randomness [See also [[93E20|93Exx]]]
* ''49K99'' None of the above, but in this section
!!![[49|49-XX]]Lxx  ~Hamilton-Jacobi theories, including dynamic programming {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/49Lxx.html]]}{{moveright{< [[49Kxx |49Kxx]] | [[49-XX |49-XX]] | [[49Mxx |49Mxx]] >}}}
* ''49L20'' Dynamic programming method
* ''49L25'' Viscosity solutions
* ''49L99'' None of the above, but in this section
!!![[49|49-XX]]Mxx  Numerical methods [See also [[90Cxx|90Cxx]], [[65Kxx|65Kxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/49Mxx.html]]}{{moveright{< [[49Lxx |49Lxx]] | [[49-XX |49-XX]] | [[49Nxx |49Nxx]] >}}}
* ''49M05'' Methods based on necessary conditions
* ''49M15'' Newton-type methods
* ''49M20'' Methods of relaxation type
* ''49M25'' Discrete approximations
* ''49M27'' Decomposition methods
* ''49M29'' Methods involving duality
* ''49M30'' Other methods
* ''49M37'' Methods of nonlinear programming type [See also [[90C30|90Cxx]], [[65Kxx|65Kxx]]]
* ''49M99'' None of the above, but in this section
!!![[49|49-XX]]Nxx  Miscellaneous topics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/49Nxx.html]]}{{moveright{< [[49Mxx |49Mxx]] | [[49-XX |49-XX]] | [[49Qxx |49Qxx]] >}}}
* ''49N05'' Linear optimal control problems [See also [[93C05|93Cxx]]]
* ''49N10'' Linear-quadratic problems
* ''49N15'' Duality theory
* ''49N20'' Periodic optimization
* ''49N25'' Impulsive optimal control problems
* ''49N30'' Problems with incomplete information [See also [[93C41|93Cxx]]]
* ''49N35'' Optimal feedback synthesis [See also [[93B52|93Bxx]]]
* ''49N45'' Inverse problems
* ''49N60'' Regularity of solutions
* ''49N70'' Differential games
* ''49N75'' Pursuit and evasion games
* ''49N90'' Applications of optimal control and differential games [See also [[90C90|90Cxx]], [[93C95|93Cxx]]]
* ''49N99'' None of the above, but in this section
!!![[49|49-XX]]Qxx  Manifolds [See also [[58Exx|58Exx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/49Qxx.html]]}{{moveright{< [[49Nxx |49Nxx]] | [[49-XX |49-XX]] | [[49Rxx |49Rxx]] >}}}
* ''49Q05'' Minimal surfaces [See also [[53A10|53Axx]], [[58E12|58Exx]]]
* ''49Q10'' Optimization of shapes other than minimal surfaces [See also [[90C90|90Cxx]]]
* ''49Q12'' Sensitivity analysis
* ''49Q15'' Geometric measure and integration theory, integral and normal currents [See also [[28A75|28Axx]], [[32C30|32Cxx]], [[58A25|58Axx]], [[58C35|58Cxx]]]
* ''49Q20'' Variational problems in a geometric measure-theoretic setting
* ''49Q99'' None of the above, but in this section
!!![[49|49-XX]]Rxx  Variational methods for eigenvalues of operators [See also [[47A75|47Axx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/49Rxx.html]]}{{moveright{< [[49Qxx |49Qxx]] | [[49-XX |49-XX]] | [[49Sxx |49Sxx]] >}}}
* ''49R05'' Variational methods for eigenvalues of operators [See also [[47A75|47Axx]]] (should also be assigned at least one other classification number in Section 49)
* ''49R99'' None of the above, but in this section
!!!49-XX Calculus of variations and optimal control; optimization [See also [[34H05|34Hxx]], [[34K35|34Kxx]], [[65Kxx|65Kxx]], [[90Cxx|90Cxx]], [[93-XX|93-XX]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/49-XX.html]]}{{moveright{< [[47-XX |47-XX]] | [[MSC |MSC2010]] | [[49Jxx |49Jxx]] >}}}
* ''49-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''49-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''49-02'' Research exposition (monographs, survey articles)
* ''49-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''49-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''49-06'' Proceedings, conferences, collections, etc.
* ''[[49Jxx|49Jxx]]''  Existence theories
* ''[[49Kxx|49Kxx]]''  Optimality conditions
* ''[[49Lxx|49Lxx]]''  ~Hamilton-Jacobi theories, including dynamic programming
* ''[[49Mxx|49Mxx]]''  Numerical methods [See also [[90Cxx|90Cxx]], [[65Kxx|65Kxx]]]
* ''[[49Nxx|49Nxx]]''  Miscellaneous topics
* ''[[49Qxx|49Qxx]]''  Manifolds [See also [[58Exx|58Exx]]]
* ''[[49Rxx|49Rxx]]''  Variational methods for eigenvalues of operators [See also [[47A75|47Axx]]]
* ''[[49Sxx|49Sxx]]''  Variational principles of physics
!!![[49|49-XX]]Sxx  Variational principles of physics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/49Sxx.html]]}{{moveright{< [[49Rxx |49Rxx]] | [[49-XX |49-XX]] | [[51-XX |51-XX]] >}}}
* ''49S05'' Variational principles of physics (should also be assigned at least one other classification number in section 49)
* ''49S99'' None of the above, but in this section
!!![[51|51-XX]]Axx  Linear incidence geometry {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/51Axx.html]]}{{moveright{< [[49-XX |49-XX]] | [[51-XX |51-XX]] | [[51Bxx |51Bxx]] >}}}
* ''51A05'' General theory and projective geometries
* ''51A10'' Homomorphism, automorphism and dualities
* ''51A15'' Structures with parallelism
* ''51A20'' Configuration theorems
* ''51A25'' Algebraization [See also [[12Kxx|12Kxx]], [[20N05|20Nxx]]]
* ''51A30'' Desarguesian and Pappian geometries
* ''51A35'' ~Non-Desarguesian affine and projective planes
* ''51A40'' Translation planes and spreads
* ''51A45'' Incidence structures imbeddable into projective geometries
* ''51A50'' Polar geometry, symplectic spaces, orthogonal spaces
* ''51A99'' None of the above, but in this section
!!![[51|51-XX]]Bxx  Nonlinear incidence geometry {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/51Bxx.html]]}{{moveright{< [[51Axx |51Axx]] | [[51-XX |51-XX]] | [[51Cxx |51Cxx]] >}}}
* ''51B05'' General theory
* ''51B10'' Möbius geometries
* ''51B15'' Laguerre geometries
* ''51B20'' Minkowski geometries
* ''51B25'' Lie geometries
* ''51B99'' None of the above, but in this section
!!![[51|51-XX]]Cxx  Ring geometry (Hjelmslev, Barbilian, etc.) {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/51Cxx.html]]}{{moveright{< [[51Bxx |51Bxx]] | [[51-XX |51-XX]] | [[51Dxx |51Dxx]] >}}}
* ''51C05'' Ring geometry (Hjelmslev, Barbilian, etc.)
* ''51C99'' None of the above, but in this section
!!![[51|51-XX]]Dxx  Geometric closure systems {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/51Dxx.html]]}{{moveright{< [[51Cxx |51Cxx]] | [[51-XX |51-XX]] | [[51Exx |51Exx]] >}}}
* ''51D05'' Abstract (Maeda) geometries
* ''51D10'' Abstract geometries with exchange axiom
* ''51D15'' Abstract geometries with parallelism
* ''51D20'' Combinatorial geometries [See also [[05B25|05Bxx]], [[05B35|05Bxx]]]
* ''51D25'' Lattices of subspaces [See also [[05B35|05Bxx]]]
* ''51D30'' Continuous geometries and related topics [See also [[06Cxx|06Cxx]]]
* ''51D99'' None of the above, but in this section
!!![[51|51-XX]]Exx  Finite geometry and special incidence structures {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/51Exx.html]]}{{moveright{< [[51Dxx |51Dxx]] | [[51-XX |51-XX]] | [[51Fxx |51Fxx]] >}}}
* ''51E05'' General block designs [See also [[05B05|05Bxx]]]
* ''51E10'' Steiner systems
* ''51E12'' Generalized quadrangles, generalized polygons
* ''51E14'' Finite partial geometries (general), nets, partial spreads
* ''51E15'' Affine and projective planes
* ''51E20'' Combinatorial structures in finite projective spaces [See also [[05Bxx|05Bxx]]]
* ''51E21'' Blocking sets, ovals, $k$-arcs
* ''51E22'' Linear codes and caps in Galois spaces [See also [[94B05|94Bxx]]]
* ''51E23'' Spreads and packing problems
* ''51E24'' Buildings and the geometry of diagrams
* ''51E25'' Other finite nonlinear geometries
* ''51E26'' Other finite linear geometries
* ''51E30'' Other finite incidence structures [See also [[05B30|05Bxx]]]
* ''51E99'' None of the above, but in this section
!!![[51|51-XX]]Fxx  Metric geometry {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/51Fxx.html]]}{{moveright{< [[51Exx |51Exx]] | [[51-XX |51-XX]] | [[51Gxx |51Gxx]] >}}}
* ''51F05'' Absolute planes
* ''51F10'' Absolute spaces
* ''51F15'' Reflection groups, reflection geometries [See also [[20H10|20Hxx]], [[20H15|20Hxx]]; for Coxeter groups, see [[20F55|20Fxx]]]
* ''51F20'' Congruence and orthogonality [See also [[20H05|20Hxx]]]
* ''51F25'' Orthogonal and unitary groups [See also [[20H05|20Hxx]]]
* ''51F99'' None of the above, but in this section
!!![[51|51-XX]]Gxx  Ordered geometries (ordered incidence structures, etc.) {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/51Gxx.html]]}{{moveright{< [[51Fxx |51Fxx]] | [[51-XX |51-XX]] | [[51Hxx |51Hxx]] >}}}
* ''51G05'' Ordered geometries (ordered incidence structures, etc.)
* ''51G99'' None of the above, but in this section
!!![[51|51-XX]]Hxx  Topological geometry {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/51Hxx.html]]}{{moveright{< [[51Gxx |51Gxx]] | [[51-XX |51-XX]] | [[51Jxx |51Jxx]] >}}}
* ''51H05'' General theory
* ''51H10'' Topological linear incidence structures
* ''51H15'' Topological nonlinear incidence structures
* ''51H20'' Topological geometries on manifolds [See also [[57-XX|57-XX]]]
* ''51H25'' Geometries with differentiable structure [See also [[53Cxx|53Cxx]], [[53C70|53Cxx]]]
* ''51H30'' Geometries with algebraic manifold structure [See also [[14-XX|14-XX]]]
* ''51H99'' None of the above, but in this section
!!![[51|51-XX]]Jxx  Incidence groups {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/51Jxx.html]]}{{moveright{< [[51Hxx |51Hxx]] | [[51-XX |51-XX]] | [[51Kxx |51Kxx]] >}}}
* ''51J05'' General theory
* ''51J10'' Projective incidence groups
* ''51J15'' Kinematic spaces
* ''51J20'' Representation by near-fields and near-algebras [See also [[12K05|12Kxx]], [[16Y30|16Yxx]]]
* ''51J99'' None of the above, but in this section
!!![[51|51-XX]]Kxx  Distance geometry {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/51Kxx.html]]}{{moveright{< [[51Jxx |51Jxx]] | [[51-XX |51-XX]] | [[51Lxx |51Lxx]] >}}}
* ''51K05'' General theory
* ''51K10'' Synthetic differential geometry
* ''51K99'' None of the above, but in this section
!!![[51|51-XX]]Lxx  Geometric order structures [See also [[53C75|53Cxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/51Lxx.html]]}{{moveright{< [[51Kxx |51Kxx]] | [[51-XX |51-XX]] | [[51Mxx |51Mxx]] >}}}
* ''51L05'' Geometry of orders of nondifferentiable curves
* ''51L10'' Directly differentiable curves
* ''51L15'' $n$-vertex theorems via direct methods
* ''51L20'' Geometry of orders of surfaces
* ''51L99'' None of the above, but in this section
!!![[51|51-XX]]Mxx  Real and complex geometry {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/51Mxx.html]]}{{moveright{< [[51Lxx |51Lxx]] | [[51-XX |51-XX]] | [[51Nxx |51Nxx]] >}}}
* ''51M04'' Elementary problems in Euclidean geometries
* ''51M05'' Euclidean geometries (general) and generalizations
* ''51M09'' Elementary problems in hyperbolic and elliptic geometries
* ''51M10'' Hyperbolic and elliptic geometries (general) and generalizations
* ''51M15'' Geometric constructions
* ''51M16'' Inequalities and extremum problems {For convex problems, see [[52A40|52Axx]]}
* ''51M20'' Polyhedra and polytopes; regular figures, division of spaces [See also [[51F15|51Fxx]]]
* ''51M25'' Length, area and volume [See also [[26B15|26Bxx]]]
* ''51M30'' Line geometries and their generalizations [See also [[53A25|53Axx]]]
* ''51M35'' Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) [See also [[14M15|14Mxx]]]
* ''51M99'' None of the above, but in this section
!!![[51|51-XX]]Nxx  Analytic and descriptive geometry {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/51Nxx.html]]}{{moveright{< [[51Mxx |51Mxx]] | [[51-XX |51-XX]] | [[51Pxx |51Pxx]] >}}}
* ''51N05'' Descriptive geometry [See also [[65D17|65Dxx]], [[68U07|68Uxx]]]
* ''51N10'' Affine analytic geometry
* ''51N15'' Projective analytic geometry
* ''51N20'' Euclidean analytic geometry
* ''51N25'' Analytic geometry with other transformation groups
* ''51N30'' Geometry of classical groups [See also [[20Gxx|20Gxx]], [[14L35|14Lxx]]]
* ''51N35'' Questions of classical algebraic geometry [See also [[14Nxx|14Nxx]]]
* ''51N99'' None of the above, but in this section
!!!51-XX Geometry {For algebraic geometry, see [[14-XX|14-XX]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/51-XX.html]]}{{moveright{< [[49-XX |49-XX]] | [[MSC |MSC2010]] | [[51Axx |51Axx]] >}}}
* ''51-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''51-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''51-02'' Research exposition (monographs, survey articles)
* ''51-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''51-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''51-06'' Proceedings, conferences, collections, etc.
* ''[[51Axx|51Axx]]''  Linear incidence geometry
* ''[[51Bxx|51Bxx]]''  Nonlinear incidence geometry
* ''[[51Cxx|51Cxx]]''  Ring geometry (Hjelmslev, Barbilian, etc.)
* ''[[51Dxx|51Dxx]]''  Geometric closure systems
* ''[[51Exx|51Exx]]''  Finite geometry and special incidence structures
* ''[[51Fxx|51Fxx]]''  Metric geometry
* ''[[51Gxx|51Gxx]]''  Ordered geometries (ordered incidence structures, etc.)
* ''[[51Hxx|51Hxx]]''  Topological geometry
* ''[[51Jxx|51Jxx]]''  Incidence groups
* ''[[51Kxx|51Kxx]]''  Distance geometry
* ''[[51Lxx|51Lxx]]''  Geometric order structures [See also [[53C75|53Cxx]]]
* ''[[51Mxx|51Mxx]]''  Real and complex geometry
* ''[[51Nxx|51Nxx]]''  Analytic and descriptive geometry
* ''[[51Pxx|51Pxx]]''  Geometry and physics (should also be assigned at least one other classification number from Sections 70–086)
!!![[51|51-XX]]Pxx  Geometry and physics (should also be assigned at least one other classification number from Sections 70–086) {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/51Pxx.html]]}{{moveright{< [[51Nxx |51Nxx]] | [[51-XX |51-XX]] | [[52-XX |52-XX]] >}}}
* ''51P05'' Geometry and physics (should also be assigned at least one other classification number from Sections 70–086)
* ''51P99'' None of the above, but in this section
!!![[52|52-XX]]Axx  General convexity {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/52Axx.html]]}{{moveright{< [[51-XX |51-XX]] | [[52-XX |52-XX]] | [[52Bxx |52Bxx]] >}}}
* ''52A01'' Axiomatic and generalized convexity
* ''52A05'' Convex sets without dimension restrictions
* ''52A07'' Convex sets in topological vector spaces [See also [[46A55|46Axx]]]
* ''52A10'' Convex sets in $2$ dimensions (including convex curves) [See also [[53A04|53Axx]]]
* ''52A15'' Convex sets in $3$ dimensions (including convex surfaces) [See also [[53A05|53Axx]], [[53C45|53Cxx]]]
* ''52A20'' Convex sets in $n$ dimensions (including convex hypersurfaces) [See also [[53A07|53Axx]], [[53C45|53Cxx]]]
* ''52A21'' Finite-dimensional Banach spaces (including special norms, zonoids, etc.) [See also [[46Bxx|46Bxx]]]
* ''52A22'' Random convex sets and integral geometry [See also [[53C65|53Cxx]], [[60D05|60Dxx]]]
* ''52A23'' Asymptotic theory of convex bodies [See also [[46B06|46Bxx]]]
* ''52A27'' Approximation by convex sets
* ''52A30'' Variants of convex sets (star-shaped, ($m, n$)-convex, etc.)
* ''52A35'' Helly-type theorems and geometric transversal theory
* ''52A37'' Other problems of combinatorial convexity
* ''52A38'' Length, area, volume [See also [[26B15|26Bxx]], [[28A75|28Axx]], [[49Q20|49Qxx]]]
* ''52A39'' Mixed volumes and related topics
* ''52A40'' Inequalities and extremum problems
* ''52A41'' Convex functions and convex programs [See also [[26B25|26Bxx]], [[90C25|90Cxx]]]
* ''52A55'' Spherical and hyperbolic convexity
* ''52A99'' None of the above, but in this section
!!![[52|52-XX]]Bxx  Polytopes and polyhedra {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/52Bxx.html]]}{{moveright{< [[52Axx |52Axx]] | [[52-XX |52-XX]] | [[52Cxx |52Cxx]] >}}}
* ''52B05'' Combinatorial properties (number of faces, shortest paths, etc.) [See also [[05Cxx|05Cxx]]]
* ''52B10'' Three-dimensional polytopes
* ''52B11'' $n$-dimensional polytopes
* ''52B12'' Special polytopes (linear programming, centrally symmetric, etc.)
* ''52B15'' Symmetry properties of polytopes
* ''52B20'' Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also [[06A11|06Axx]], [[13F20|13Fxx]], [[13Hxx|13Hxx]]]
* ''52B22'' Shellability
* ''52B35'' Gale and other diagrams
* ''52B40'' Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) [See also [[05B35|05Bxx]], [[52Cxx|52Cxx]]]
* ''52B45'' Dissections and valuations (Hilbert's third problem, etc.)
* ''52B55'' Computational aspects related to convexity {For computational geometry and algorithms, see [[68Q25|68Qxx]], [[68U05|68Uxx]]; for numerical algorithms, see [[65Yxx|65Yxx]]} [See also [[68Uxx|68Uxx]]]
* ''52B60'' Isoperimetric problems for polytopes
* ''52B70'' Polyhedral manifolds
* ''52B99'' None of the above, but in this section
!!!52-XX Convex and discrete geometry {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/52-XX.html]]}{{moveright{< [[51-XX |51-XX]] | [[MSC |MSC2010]] | [[52Axx |52Axx]] >}}}
* ''52-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''52-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''52-02'' Research exposition (monographs, survey articles)
* ''52-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''52-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''52-06'' Proceedings, conferences, collections, etc.
* ''[[52Axx|52Axx]]''  General convexity
* ''[[52Bxx|52Bxx]]''  Polytopes and polyhedra
* ''[[52Cxx|52Cxx]]''  Discrete geometry
!!![[52|52-XX]]Cxx  Discrete geometry {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/52Cxx.html]]}{{moveright{< [[52Bxx |52Bxx]] | [[52-XX |52-XX]] | [[53-XX |53-XX]] >}}}
* ''52C05'' Lattices and convex bodies in $2$ dimensions [See also [[11H06|11Hxx]], [[11H31|11Hxx]], [[11P21|11Pxx]]]
* ''52C07'' Lattices and convex bodies in $n$ dimensions [See also [[11H06|11Hxx]], [[11H31|11Hxx]], [[11P21|11Pxx]]]
* ''52C10'' Erdős problems and related topics of discrete geometry [See also [[11Hxx|11Hxx]]]
* ''52C15'' Packing and covering in $2$ dimensions [See also [[05B40|05Bxx]], [[11H31|11Hxx]]]
* ''52C17'' Packing and covering in $n$ dimensions [See also [[05B40|05Bxx]], [[11H31|11Hxx]]]
* ''52C20'' Tilings in $2$ dimensions [See also [[05B45|05Bxx]], [[51M20|51Mxx]]]
* ''52C22'' Tilings in $n$ dimensions [See also [[05B45|05Bxx]], [[51M20|51Mxx]]]
* ''52C23'' Quasicrystals, aperiodic tilings
* ''52C25'' Rigidity and flexibility of structures [See also [[70B15|70Bxx]]]
* ''52C26'' Circle packings and discrete conformal geometry
* ''52C30'' Planar arrangements of lines and pseudolines
* ''52C35'' Arrangements of points, flats, hyperplanes [See also [[32S22|32Sxx]]]
* ''52C40'' Oriented matroids
* ''52C45'' Combinatorial complexity of geometric structures [See also [[68U05|68Uxx]]]
* ''52C99'' None of the above, but in this section
!!![[53|53-XX]]Axx  Classical differential geometry {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/53Axx.html]]}{{moveright{< [[52-XX |52-XX]] | [[53-XX |53-XX]] | [[53Bxx |53Bxx]] >}}}
* ''53A04'' Curves in Euclidean space
* ''53A05'' Surfaces in Euclidean space
* ''53A07'' Higher-dimensional and -codimensional surfaces in Euclidean $n$-space
* ''53A10'' Minimal surfaces, surfaces with prescribed mean curvature [See also [[49Q05|49Qxx]], [[49Q10|49Qxx]], [[53C42|53Cxx]]]
* ''53A15'' Affine differential geometry
* ''53A17'' Kinematics
* ''53A20'' Projective differential geometry
* ''53A25'' Differential line geometry
* ''53A30'' Conformal differential geometry
* ''53A35'' ~Non-Euclidean differential geometry
* ''53A40'' Other special differential geometries
* ''53A45'' Vector and tensor analysis
* ''53A55'' Differential invariants (local theory), geometric objects
* ''53A60'' Geometry of webs [See also [[14C21|14Cxx]], [[20N05|20Nxx]]]
* ''53A99'' None of the above, but in this section
!!![[53|53-XX]]Bxx  Local differential geometry {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/53Bxx.html]]}{{moveright{< [[53Axx |53Axx]] | [[53-XX |53-XX]] | [[53Cxx |53Cxx]] >}}}
* ''53B05'' Linear and affine connections
* ''53B10'' Projective connections
* ''53B15'' Other connections
* ''53B20'' Local Riemannian geometry
* ''53B21'' Methods of Riemannian geometry
* ''53B25'' Local submanifolds [See also [[53C40|53Cxx]]]
* ''53B30'' Lorentz metrics, indefinite metrics
* ''53B35'' Hermitian and Kählerian structures [See also [[32Cxx|32Cxx]]]
* ''53B40'' Finsler spaces and generalizations (areal metrics)
* ''53B50'' Applications to physics
* ''53B99'' None of the above, but in this section
!!![[53|53-XX]]Cxx  Global differential geometry [See also [[51H25|51Hxx]], [[58-XX|58-XX]]; for related bundle theory, see [[55Rxx|55Rxx]], [[57Rxx|57Rxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/53Cxx.html]]}{{moveright{< [[53Bxx |53Bxx]] | [[53-XX |53-XX]] | [[53Dxx |53Dxx]] >}}}
* ''53C05'' Connections, general theory
* ''53C07'' Special connections and metrics on vector bundles (~Hermite-Einstein-~Yang-Mills) [See also [[32Q20|32Qxx]]]
* ''53C08'' Gerbes, differential characters: differential geometric aspects
* ''53C10'' $G$-structures
* ''53C12'' Foliations (differential geometric aspects) [See also [[57R30|57Rxx]], [[57R32|57Rxx]]]
* ''53C15'' General geometric structures on manifolds (almost complex, almost product structures, etc.)
* ''53C17'' ~Sub-Riemannian geometry
* ''53C20'' Global Riemannian geometry, including pinching [See also [[31C12|31Cxx]], [[58B20|58Bxx]]]
* ''53C21'' Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also [[58J60|58Jxx]]]
* ''53C22'' Geodesics [See also [[58E10|58Exx]]]
* ''53C23'' Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
* ''53C24'' Rigidity results
* ''53C25'' Special Riemannian manifolds (Einstein, Sasakian, etc.)
* ''53C26'' ~Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
* ''53C27'' Spin and Spin${}^c$ geometry
* ''53C28'' Twistor methods [See also [[32L25|32Lxx]]]
* ''53C29'' Issues of holonomy
* ''53C30'' Homogeneous manifolds [See also [[14M15|14Mxx]], [[14M17|14Mxx]], [[32M10|32Mxx]], [[57T15|57Txx]]]
* ''53C35'' Symmetric spaces [See also [[32M15|32Mxx]], [[57T15|57Txx]]]
* ''53C38'' Calibrations and calibrated geometries
* ''53C40'' Global submanifolds [See also [[53B25|53Bxx]]]
* ''53C42'' Immersions (minimal, prescribed curvature, tight, etc.) [See also [[49Q05|49Qxx]], [[49Q10|49Qxx]], [[53A10|53Axx]], [[57R40|57Rxx]], [[57R42|57Rxx]]]
* ''53C43'' Differential geometric aspects of harmonic maps [See also [[58E20|58Exx]]]
* ''53C44'' Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
* ''53C45'' Global surface theory (convex surfaces à la A. D. Aleksandrov)
* ''53C50'' Lorentz manifolds, manifolds with indefinite metrics
* ''53C55'' Hermitian and Kählerian manifolds [See also [[32Cxx|32Cxx]]]
* ''53C56'' Other complex differential geometry [See also [[32Cxx|32Cxx]]]
* ''53C60'' Finsler spaces and generalizations (areal metrics) [See also [[58B20|58Bxx]]]
* ''53C65'' Integral geometry [See also [[52A22|52Axx]], [[60D05|60Dxx]]]; differential forms, currents, etc. [See mainly [[58Axx|58Axx]]]
* ''53C70'' Direct methods ($G$-spaces of Busemann, etc.)
* ''53C75'' Geometric orders, order geometry [See also [[51Lxx|51Lxx]]]
* ''53C80'' Applications to physics
* ''53C99'' None of the above, but in this section
!!![[53|53-XX]]Dxx  Symplectic geometry, contact geometry [See also [[37Jxx|37Jxx]], [[70Gxx|70Gxx]], [[70Hxx|70Hxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/53Dxx.html]]}{{moveright{< [[53Cxx |53Cxx]] | [[53-XX |53-XX]] | [[53Zxx |53Zxx]] >}}}
* ''53D05'' Symplectic manifolds, general
* ''53D10'' Contact manifolds, general
* ''53D12'' Lagrangian submanifolds; Maslov index
* ''53D15'' Almost contact and almost symplectic manifolds
* ''53D17'' Poisson manifolds; Poisson groupoids and algebroids
* ''53D18'' Generalized geometries (à la Hitchin)
* ''53D20'' Momentum maps; symplectic reduction
* ''53D22'' Canonical transformations
* ''53D25'' Geodesic flows
* ''53D30'' Symplectic structures of moduli spaces
* ''53D35'' Global theory of symplectic and contact manifolds [See also [[57Rxx|57Rxx]]]
* ''53D37'' Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category [See also [[14J33|14Jxx]]]
* ''53D40'' Floer homology and cohomology, symplectic aspects
* ''53D42'' Symplectic field theory; contact homology
* ''53D45'' ~Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also [[14N35|14Nxx]]]
* ''53D50'' Geometric quantization
* ''53D55'' Deformation quantization, star products
* ''53D99'' None of the above, but in this section
!!!53-XX Differential geometry {For differential topology, see [[57Rxx|57Rxx]]. For foundational questions of differentiable manifolds, see [[58Axx|58Axx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/53-XX.html]]}{{moveright{< [[52-XX |52-XX]] | [[MSC |MSC2010]] | [[53Axx |53Axx]] >}}}
* ''53-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''53-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''53-02'' Research exposition (monographs, survey articles)
* ''53-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''53-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''53-06'' Proceedings, conferences, collections, etc.
* ''[[53Axx|53Axx]]''  Classical differential geometry
* ''[[53Bxx|53Bxx]]''  Local differential geometry
* ''[[53Cxx|53Cxx]]''  Global differential geometry [See also [[51H25|51Hxx]], [[58-XX|58-XX]]; for related bundle theory, see [[55Rxx|55Rxx]], [[57Rxx|57Rxx]]]
* ''[[53Dxx|53Dxx]]''  Symplectic geometry, contact geometry [See also [[37Jxx|37Jxx]], [[70Gxx|70Gxx]], [[70Hxx|70Hxx]]]
* ''[[53Zxx|53Zxx]]''  Applications to physics
!!![[53|53-XX]]Zxx  Applications to physics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/53Zxx.html]]}{{moveright{< [[53Dxx |53Dxx]] | [[53-XX |53-XX]] | [[54-XX |54-XX]] >}}}
* ''53Z05'' Applications to physics
* ''53Z99'' None of the above, but in this section
!!![[54|54-XX]]Axx  Generalities {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/54Axx.html]]}{{moveright{< [[53-XX |53-XX]] | [[54-XX |54-XX]] | [[54Bxx |54Bxx]] >}}}
* ''54A05'' Topological spaces and generalizations (closure spaces, etc.)
* ''54A10'' Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
* ''54A15'' Syntopogeneous structures
* ''54A20'' Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
* ''54A25'' Cardinality properties (cardinal functions and inequalities, discrete subsets) [See also [[03Exx|03Exx]]] {For ultrafilters, see [[54D80|54Dxx]]}
* ''54A35'' Consistency and independence results [See also [[03E35|03Exx]]]
* ''54A40'' Fuzzy topology [See also [[03E72|03Exx]]]
* ''54A99'' None of the above, but in this section
!!![[54|54-XX]]Bxx  Basic constructions {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/54Bxx.html]]}{{moveright{< [[54Axx |54Axx]] | [[54-XX |54-XX]] | [[54Cxx |54Cxx]] >}}}
* ''54B05'' Subspaces
* ''54B10'' Product spaces
* ''54B15'' Quotient spaces, decompositions
* ''54B17'' Adjunction spaces and similar constructions
* ''54B20'' Hyperspaces
* ''54B30'' Categorical methods [See also [[18B30|18Bxx]]]
* ''54B35'' Spectra
* ''54B40'' Presheaves and sheaves [See also [[18F20|18Fxx]]]
* ''54B99'' None of the above, but in this section
!!![[54|54-XX]]Cxx  Maps and general types of spaces defined by maps {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/54Cxx.html]]}{{moveright{< [[54Bxx |54Bxx]] | [[54-XX |54-XX]] | [[54Dxx |54Dxx]] >}}}
* ''54C05'' Continuous maps
* ''54C08'' Weak and generalized continuity
* ''54C10'' Special maps on topological spaces (open, closed, perfect, etc.)
* ''54C15'' Retraction
* ''54C20'' Extension of maps
* ''54C25'' Embedding
* ''54C30'' Real-valued functions [See also [[26-XX|26-XX]]]
* ''54C35'' Function spaces [See also [[46Exx|46Exx]], [[58D15|58Dxx]]]
* ''54C40'' Algebraic properties of function spaces [See also [[46J10|46Jxx]]]
* ''54C45'' $C$- and $C^*$-embedding
* ''54C50'' Special sets defined by functions [See also [[26A21|26Axx]]]
* ''54C55'' Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) [See also [[55M15|55Mxx]]]
* ''54C56'' Shape theory [See also [[55P55|55Pxx]], [[57N25|57Nxx]]]
* ''54C60'' Set-valued maps [See also [[26E25|26Exx]], [[28B20|28Bxx]], [[47H04|47Hxx]], [[58C06|58Cxx]]]
* ''54C65'' Selections [See also [[28B20|28Bxx]]]
* ''54C70'' Entropy
* ''54C99'' None of the above, but in this section
!!![[54|54-XX]]Dxx  Fairly general properties {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/54Dxx.html]]}{{moveright{< [[54Cxx |54Cxx]] | [[54-XX |54-XX]] | [[54Exx |54Exx]] >}}}
* ''54D05'' Connected and locally connected spaces (general aspects)
* ''54D10'' Lower separation axioms ($T_0$--$T_3$, etc.)
* ''54D15'' Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
* ''54D20'' Noncompact covering properties (paracompact, Lindelöf, etc.)
* ''54D25'' “$P$-minimal” and “$P$-closed” spaces
* ''54D30'' Compactness
* ''54D35'' Extensions of spaces (compactifications, supercompactifications, completions, etc.)
* ''54D40'' Remainders
* ''54D45'' Local compactness, $\sigma$-compactness
* ''54D50'' $k$-spaces
* ''54D55'' Sequential spaces
* ''54D60'' Realcompactness and realcompactification
* ''54D65'' Separability
* ''54D70'' Base properties
* ''54D80'' Special constructions of spaces (spaces of ultrafilters, etc.)
* ''54D99'' None of the above, but in this section
!!![[54|54-XX]]Exx  Spaces with richer structures {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/54Exx.html]]}{{moveright{< [[54Dxx |54Dxx]] | [[54-XX |54-XX]] | [[54Fxx |54Fxx]] >}}}
* ''54E05'' Proximity structures and generalizations
* ''54E15'' Uniform structures and generalizations
* ''54E17'' Nearness spaces
* ''54E18'' $p$-spaces, $M$-spaces, $\sigma$-spaces, etc.
* ''54E20'' Stratifiable spaces, cosmic spaces, etc.
* ''54E25'' Semimetric spaces
* ''54E30'' Moore spaces
* ''54E35'' Metric spaces, metrizability
* ''54E40'' Special maps on metric spaces
* ''54E45'' Compact (locally compact) metric spaces
* ''54E50'' Complete metric spaces
* ''54E52'' Baire category, Baire spaces
* ''54E55'' Bitopologies
* ''54E70'' Probabilistic metric spaces
* ''54E99'' None of the above, but in this section
!!![[54|54-XX]]Fxx  Special properties {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/54Fxx.html]]}{{moveright{< [[54Exx |54Exx]] | [[54-XX |54-XX]] | [[54Gxx |54Gxx]] >}}}
* ''54F05'' Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces [See also [[06B30|06Bxx]], [[06F30|06Fxx]]]
* ''54F15'' Continua and generalizations
* ''54F35'' Higher-dimensional local connectedness [See also [[55Mxx|55Mxx]], [[55Nxx|55Nxx]]]
* ''54F45'' Dimension theory [See also [[55M10|55Mxx]]]
* ''54F50'' Spaces of dimension $\leq 1$; curves, dendrites [See also [[26A03|26Axx]]]
* ''54F55'' Unicoherence, multicoherence
* ''54F65'' Topological characterizations of particular spaces
* ''54F99'' None of the above, but in this section
!!![[54|54-XX]]Gxx  Peculiar spaces {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/54Gxx.html]]}{{moveright{< [[54Fxx |54Fxx]] | [[54-XX |54-XX]] | [[54Hxx |54Hxx]] >}}}
* ''54G05'' Extremally disconnected spaces, $F$-spaces, etc.
* ''54G10'' $P$-spaces
* ''54G12'' Scattered spaces
* ''54G15'' Pathological spaces
* ''54G20'' Counterexamples
* ''54G99'' None of the above, but in this section
!!![[54|54-XX]]Hxx  Connections with other structures, applications {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/54Hxx.html]]}{{moveright{< [[54Gxx |54Gxx]] | [[54-XX |54-XX]] | [[54Jxx |54Jxx]] >}}}
* ''54H05'' Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also [[03E15|03Exx]], [[26A21|26Axx]], [[28A05|28Axx]]]
* ''54H10'' Topological representations of algebraic systems [See also [[22-XX|22-XX]]]
* ''54H11'' Topological groups [See also [[22A05|22Axx]]]
* ''54H12'' Topological lattices, etc. [See also [[06B30|06Bxx]], [[06F30|06Fxx]]]
* ''54H13'' Topological fields, rings, etc. [See also [[12Jxx|12Jxx]]] {For algebraic aspects, see [[13Jxx|13Jxx]], [[16W80|16Wxx]]}
* ''54H15'' Transformation groups and semigroups [See also [[20M20|20Mxx]], [[22-XX|22-XX]], [[57Sxx|57Sxx]]]
* ''54H20'' Topological dynamics [See also [[28Dxx|28Dxx]], [[37Bxx|37Bxx]]]
* ''54H25'' Fixed-point and coincidence theorems [See also [[47H10|47Hxx]], [[55M20|55Mxx]]]
* ''54H99'' None of the above, but in this section
!!!54-XX General topology {For the topology of manifolds of all dimensions, see [[57Nxx|57Nxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/54-XX.html]]}{{moveright{< [[53-XX |53-XX]] | [[MSC |MSC2010]] | [[54Axx |54Axx]] >}}}
* ''54-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''54-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''54-02'' Research exposition (monographs, survey articles)
* ''54-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''54-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''54-06'' Proceedings, conferences, collections, etc.
* ''[[54Axx|54Axx]]''  Generalities
* ''[[54Bxx|54Bxx]]''  Basic constructions
* ''[[54Cxx|54Cxx]]''  Maps and general types of spaces defined by maps
* ''[[54Dxx|54Dxx]]''  Fairly general properties
* ''[[54Exx|54Exx]]''  Spaces with richer structures
* ''[[54Fxx|54Fxx]]''  Special properties
* ''[[54Gxx|54Gxx]]''  Peculiar spaces
* ''[[54Hxx|54Hxx]]''  Connections with other structures, applications
* ''[[54Jxx|54Jxx]]''  Nonstandard topology [See also [[03H05|03Hxx]]]
!!![[54|54-XX]]Jxx  Nonstandard topology [See also [[03H05|03Hxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/54Jxx.html]]}{{moveright{< [[54Hxx |54Hxx]] | [[54-XX |54-XX]] | [[55-XX |55-XX]] >}}}
* ''54J05'' Nonstandard topology [See also [[03H05|03Hxx]]]
* ''54J99'' None of the above, but in this section
!!![[55|55-XX]]Mxx  Classical topics {For the topology of Euclidean spaces and manifolds, see [[57Nxx|57Nxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/55Mxx.html]]}{{moveright{< [[54-XX |54-XX]] | [[55-XX |55-XX]] | [[55Nxx |55Nxx]] >}}}
* ''55M05'' Duality
* ''55M10'' Dimension theory [See also [[54F45|54Fxx]]]
* ''55M15'' Absolute neighborhood retracts [See also [[54C55|54Cxx]]]
* ''55M20'' Fixed points and coincidences [See also [[54H25|54Hxx]]]
* ''55M25'' Degree, winding number
* ''55M30'' ~Ljusternik-Schnirelman (~Lyusternik-Shnirel'man) category of a space
* ''55M35'' Finite groups of transformations (including Smith theory) [See also [[57S17|57Sxx]]]
* ''55M99'' None of the above, but in this section
!!![[55|55-XX]]Nxx  Homology and cohomology theories [See also [[57Txx|57Txx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/55Nxx.html]]}{{moveright{< [[55Mxx |55Mxx]] | [[55-XX |55-XX]] | [[55Pxx |55Pxx]] >}}}
* ''55N05'' Čech types
* ''55N07'' ~Steenrod-Sitnikov homologies
* ''55N10'' Singular theory
* ''55N15'' $K$-theory [See also [[19Lxx|19Lxx]]] {For algebraic $K$-theory, see [[18F25|18Fxx]], [[19-XX|19-XX]]}
* ''55N20'' Generalized (extraordinary) homology and cohomology theories
* ''55N22'' Bordism and cobordism theories, formal group laws [See also [[14L05|14Lxx]], [[19L41|19Lxx]], [[57R75|57Rxx]], [[57R77|57Rxx]], [[57R85|57Rxx]], [[57R90|57Rxx]]]
* ''55N25'' Homology with local coefficients, equivariant cohomology
* ''55N30'' Sheaf cohomology [See also [[18F20|18Fxx]], [[32C35|32Cxx]], [[32L10|32Lxx]]]
* ''55N32'' Orbifold cohomology
* ''55N33'' Intersection homology and cohomology
* ''55N34'' Elliptic cohomology
* ''55N35'' Other homology theories
* ''55N40'' Axioms for homology theory and uniqueness theorems
* ''55N45'' Products and intersections
* ''55N91'' Equivariant homology and cohomology [See also [[19L47|19Lxx]]]
* ''55N99'' None of the above, but in this section
!!![[55|55-XX]]Pxx  Homotopy theory {For simple homotopy type, see [[57Q10|57Qxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/55Pxx.html]]}{{moveright{< [[55Nxx |55Nxx]] | [[55-XX |55-XX]] | [[55Qxx |55Qxx]] >}}}
* ''55P05'' Homotopy extension properties, cofibrations
* ''55P10'' Homotopy equivalences
* ''55P15'' Classification of homotopy type
* ''55P20'' ~Eilenberg-Mac Lane spaces
* ''55P25'' ~Spanier-Whitehead duality
* ''55P30'' ~Eckmann-Hilton duality
* ''55P35'' Loop spaces
* ''55P40'' Suspensions
* ''55P42'' Stable homotopy theory, spectra
* ''55P43'' Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.)
* ''55P45'' $H$-spaces and duals
* ''55P47'' Infinite loop spaces
* ''55P48'' Loop space machines, operads [See also [[18D50|18Dxx]]]
* ''55P50'' String topology
* ''55P55'' Shape theory [See also [[54C56|54Cxx]], [[55Q07|55Qxx]]]
* ''55P57'' Proper homotopy theory
* ''55P60'' Localization and completion
* ''55P62'' Rational homotopy theory
* ''55P65'' Homotopy functors
* ''55P91'' Equivariant homotopy theory [See also [[19L47|19Lxx]]]
* ''55P92'' Relations between equivariant and nonequivariant homotopy theory
* ''55P99'' None of the above, but in this section
!!![[55|55-XX]]Qxx  Homotopy groups {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/55Qxx.html]]}{{moveright{< [[55Pxx |55Pxx]] | [[55-XX |55-XX]] | [[55Rxx |55Rxx]] >}}}
* ''55Q05'' Homotopy groups, general; sets of homotopy classes
* ''55Q07'' Shape groups
* ''55Q10'' Stable homotopy groups
* ''55Q15'' Whitehead products and generalizations
* ''55Q20'' Homotopy groups of wedges, joins, and simple spaces
* ''55Q25'' Hopf invariants
* ''55Q35'' Operations in homotopy groups
* ''55Q40'' Homotopy groups of spheres
* ''55Q45'' Stable homotopy of spheres
* ''55Q50'' $J$-morphism [See also [[19L20|19Lxx]]]
* ''55Q51'' $v_n$-periodicity
* ''55Q52'' Homotopy groups of special spaces
* ''55Q55'' Cohomotopy groups
* ''55Q70'' Homotopy groups of special types [See also [[55N05|55Nxx]], [[55N07|55Nxx]]]
* ''55Q91'' Equivariant homotopy groups [See also [[19L47|19Lxx]]]
* ''55Q99'' None of the above, but in this section
!!![[55|55-XX]]Rxx  Fiber spaces and bundles [See also [[18F15|18Fxx]], [[32Lxx|32Lxx]], [[46M20|46Mxx]], [[57R20|57Rxx]], [[57R22|57Rxx]], [[57R25|57Rxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/55Rxx.html]]}{{moveright{< [[55Qxx |55Qxx]] | [[55-XX |55-XX]] | [[55Sxx |55Sxx]] >}}}
* ''55R05'' Fiber spaces
* ''55R10'' Fiber bundles
* ''55R12'' Transfer
* ''55R15'' Classification
* ''55R20'' Spectral sequences and homology of fiber spaces [See also [[55Txx|55Txx]]]
* ''55R25'' Sphere bundles and vector bundles
* ''55R35'' Classifying spaces of groups and $H$-spaces
* ''55R37'' Maps between classifying spaces
* ''55R40'' Homology of classifying spaces, characteristic classes [See also [[57Txx|57Txx]], [[57R20|57Rxx]]]
* ''55R45'' Homology and homotopy of $B{\rm O}$ and $B{\rm U}$; Bott periodicity
* ''55R50'' Stable classes of vector space bundles, $K$-theory [See also [[19Lxx|19Lxx]]] {For algebraic $K$-theory, see [[18F25|18Fxx]], [[19-XX|19-XX]]}
* ''55R55'' Fiberings with singularities
* ''55R60'' Microbundles and block bundles [See also [[57N55|57Nxx]], [[57Q50|57Qxx]]]
* ''55R65'' Generalizations of fiber spaces and bundles
* ''55R70'' Fibrewise topology
* ''55R80'' Discriminantal varieties, configuration spaces
* ''55R91'' Equivariant fiber spaces and bundles [See also [[19L47|19Lxx]]]
* ''55R99'' None of the above, but in this section
!!![[55|55-XX]]Sxx  Operations and obstructions {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/55Sxx.html]]}{{moveright{< [[55Rxx |55Rxx]] | [[55-XX |55-XX]] | [[55Txx |55Txx]] >}}}
* ''55S05'' Primary cohomology operations
* ''55S10'' Steenrod algebra
* ''55S12'' ~Dyer-Lashof operations
* ''55S15'' Symmetric products, cyclic products
* ''55S20'' Secondary and higher cohomology operations
* ''55S25'' $K$-theory operations and generalized cohomology operations [See also [[19D55|19Dxx]], [[19Lxx|19Lxx]]]
* ''55S30'' Massey products
* ''55S35'' Obstruction theory
* ''55S36'' Extension and compression of mappings
* ''55S37'' Classification of mappings
* ''55S40'' Sectioning fiber spaces and bundles
* ''55S45'' Postnikov systems, $k$-invariants
* ''55S91'' Equivariant operations and obstructions [See also [[19L47|19Lxx]]]
* ''55S99'' None of the above, but in this section
!!![[55|55-XX]]Txx  Spectral sequences [See also [[18G40|18Gxx]], [[55R20|55Rxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/55Txx.html]]}{{moveright{< [[55Sxx |55Sxx]] | [[55-XX |55-XX]] | [[55Uxx |55Uxx]] >}}}
* ''55T05'' General
* ''55T10'' Serre spectral sequences
* ''55T15'' Adams spectral sequences
* ''55T20'' ~Eilenberg-Moore spectral sequences [See also [[57T35|57Txx]]]
* ''55T25'' Generalized cohomology
* ''55T99'' None of the above, but in this section
!!!55-XX Algebraic topology {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/55-XX.html]]}{{moveright{< [[54-XX |54-XX]] | [[MSC |MSC2010]] | [[55Mxx |55Mxx]] >}}}
* ''55-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''55-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''55-02'' Research exposition (monographs, survey articles)
* ''55-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''55-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''55-06'' Proceedings, conferences, collections, etc.
* ''[[55Mxx|55Mxx]]''  Classical topics {For the topology of Euclidean spaces and manifolds, see [[57Nxx|57Nxx]]}
* ''[[55Nxx|55Nxx]]''  Homology and cohomology theories [See also [[57Txx|57Txx]]]
* ''[[55Pxx|55Pxx]]''  Homotopy theory {For simple homotopy type, see [[57Q10|57Qxx]]}
* ''[[55Qxx|55Qxx]]''  Homotopy groups
* ''[[55Rxx|55Rxx]]''  Fiber spaces and bundles [See also [[18F15|18Fxx]], [[32Lxx|32Lxx]], [[46M20|46Mxx]], [[57R20|57Rxx]], [[57R22|57Rxx]], [[57R25|57Rxx]]]
* ''[[55Sxx|55Sxx]]''  Operations and obstructions
* ''[[55Txx|55Txx]]''  Spectral sequences [See also [[18G40|18Gxx]], [[55R20|55Rxx]]]
* ''[[55Uxx|55Uxx]]''  Applied homological algebra and category theory [See also [[18Gxx|18Gxx]]]
!!![[55|55-XX]]Uxx  Applied homological algebra and category theory [See also [[18Gxx|18Gxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/55Uxx.html]]}{{moveright{< [[55Txx |55Txx]] | [[55-XX |55-XX]] | [[57-XX |57-XX]] >}}}
* ''55U05'' Abstract complexes
* ''55U10'' Simplicial sets and complexes
* ''55U15'' Chain complexes
* ''55U20'' Universal coefficient theorems, Bockstein operator
* ''55U25'' Homology of a product, Künneth formula
* ''55U30'' Duality
* ''55U35'' Abstract and axiomatic homotopy theory
* ''55U40'' Topological categories, foundations of homotopy theory
* ''55U99'' None of the above, but in this section
!!![[57|57-XX]]Mxx  Low-dimensional topology {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/57Mxx.html]]}{{moveright{< [[55-XX |55-XX]] | [[57-XX |57-XX]] | [[57Nxx |57Nxx]] >}}}
* ''57M05'' Fundamental group, presentations, free differential calculus
* ''57M07'' Topological methods in group theory
* ''57M10'' Covering spaces
* ''57M12'' Special coverings, e.g. branched
* ''57M15'' Relations with graph theory [See also [[05Cxx|05Cxx]]]
* ''57M20'' Two-dimensional complexes
* ''57M25'' Knots and links in $S^3$ {For higher dimensions, see [[57Q45|57Qxx]]}
* ''57M27'' Invariants of knots and 3-manifolds
* ''57M30'' Wild knots and surfaces, etc., wild embeddings
* ''57M35'' Dehn's lemma, sphere theorem, loop theorem, asphericity
* ''57M40'' Characterizations of $E^3$ and $S^3$ (Poincaré conjecture) [See also [[57N12|57Nxx]]]
* ''57M50'' Geometric structures on low-dimensional manifolds
* ''57M60'' Group actions in low dimensions
* ''57M99'' None of the above, but in this section
!!![[57|57-XX]]Nxx  Topological manifolds {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/57Nxx.html]]}{{moveright{< [[57Mxx |57Mxx]] | [[57-XX |57-XX]] | [[57Pxx |57Pxx]] >}}}
* ''57N05'' Topology of $E^2$, $2$-manifolds
* ''57N10'' Topology of general $3$-manifolds [See also [[57Mxx|57Mxx]]]
* ''57N12'' Topology of $E^3$ and $S^3$ [See also [[57M40|57Mxx]]]
* ''57N13'' Topology of $E^4$, $4$-manifolds [See also [[14Jxx|14Jxx]], [[32Jxx|32Jxx]]]
* ''57N15'' Topology of $E^n$, $n$-manifolds ($4 \less n \less \infty$)
* ''57N16'' Geometric structures on manifolds [See also [[57M50|57Mxx]]]
* ''57N17'' Topology of topological vector spaces
* ''57N20'' Topology of infinite-dimensional manifolds [See also [[58Bxx|58Bxx]]]
* ''57N25'' Shapes [See also [[54C56|54Cxx]], [[55P55|55Pxx]], [[55Q07|55Qxx]]]
* ''57N30'' Engulfing
* ''57N35'' Embeddings and immersions
* ''57N37'' Isotopy and pseudo-isotopy
* ''57N40'' Neighborhoods of submanifolds
* ''57N45'' Flatness and tameness
* ''57N50'' $S^{n-1}\subset E^n$, Schoenflies problem
* ''57N55'' Microbundles and block bundles [See also [[55R60|55Rxx]], [[57Q50|57Qxx]]]
* ''57N60'' Cellularity
* ''57N65'' Algebraic topology of manifolds
* ''57N70'' Cobordism and concordance
* ''57N75'' General position and transversality
* ''57N80'' Stratifications
* ''57N99'' None of the above, but in this section
!!![[57|57-XX]]Pxx  Generalized manifolds [See also [[18F15|18Fxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/57Pxx.html]]}{{moveright{< [[57Nxx |57Nxx]] | [[57-XX |57-XX]] | [[57Qxx |57Qxx]] >}}}
* ''57P05'' Local properties of generalized manifolds
* ''57P10'' Poincaré duality spaces
* ''57P99'' None of the above, but in this section
!!![[57|57-XX]]Qxx  ~PL-topology {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/57Qxx.html]]}{{moveright{< [[57Pxx |57Pxx]] | [[57-XX |57-XX]] | [[57Rxx |57Rxx]] >}}}
* ''57Q05'' General topology of complexes
* ''57Q10'' Simple homotopy type, Whitehead torsion, ~Reidemeister-Franz torsion, etc. [See also [[19B28|19Bxx]]]
* ''57Q12'' Wall finiteness obstruction for ~CW-cmplexes
* ''57Q15'' Triangulating manifolds
* ''57Q20'' Cobordism
* ''57Q25'' Comparison of ~PL-structures: classification, Hauptvermutung
* ''57Q30'' Engulfing
* ''57Q35'' Embeddings and immersions
* ''57Q37'' Isotopy
* ''57Q40'' Regular neighborhoods
* ''57Q45'' Knots and links (in high dimensions) {For the low-dimensional case, see [[57M25|57Mxx]]}
* ''57Q50'' Microbundles and block bundles [See also [[55R60|55Rxx]], [[57N55|57Nxx]]]
* ''57Q55'' Approximations
* ''57Q60'' Cobordism and concordance
* ''57Q65'' General position and transversality
* ''57Q91'' Equivariant ~PL-topology
* ''57Q99'' None of the above, but in this section
!!![[57|57-XX]]Rxx  Differential topology {For foundational questions of differentiable manifolds, see [[58Axx|58Axx]]; for infinite-dimensional manifolds, see [[58Bxx|58Bxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/57Rxx.html]]}{{moveright{< [[57Qxx |57Qxx]] | [[57-XX |57-XX]] | [[57Sxx |57Sxx]] >}}}
* ''57R05'' Triangulating
* ''57R10'' Smoothing
* ''57R12'' Smooth approximations
* ''57R15'' Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
* ''57R17'' Symplectic and contact topology
* ''57R18'' Topology and geometry of orbifolds
* ''57R19'' Algebraic topology on manifolds
* ''57R20'' Characteristic classes and numbers
* ''57R22'' Topology of vector bundles and fiber bundles [See also [[55Rxx|55Rxx]]]
* ''57R25'' Vector fields, frame fields
* ''57R27'' Controllability of vector fields on $C^\infty$ and real-analytic manifolds [See also [[49Qxx|49Qxx]], [[37C10|37Cxx]], [[93B05|93Bxx]]]
* ''57R30'' Foliations; geometric theory
* ''57R32'' Classifying spaces for foliations; Gelfand-Fuks cohomology [See also [[58H10|58Hxx]]]
* ''57R35'' Differentiable mappings
* ''57R40'' Embeddings
* ''57R42'' Immersions
* ''57R45'' Singularities of differentiable mappings
* ''57R50'' Diffeomorphisms
* ''57R52'' Isotopy
* ''57R55'' Differentiable structures
* ''57R56'' Topological quantum field theories
* ''57R57'' Applications of global analysis to structures on manifolds, Donaldson and ~Seiberg-Witten invariants [See also [[58-XX|58-XX]]]
* ''57R58'' Floer homology
* ''57R60'' Homotopy spheres, Poincaré conjecture
* ''57R65'' Surgery and handlebodies
* ''57R67'' Surgery obstructions, Wall groups [See also [[19J25|19Jxx]]]
* ''57R70'' Critical points and critical submanifolds
* ''57R75'' ${\rm O}$- and ${\rm SO}$-cobordism
* ''57R77'' Complex cobordism (${\rm U}$- and ${\rm SU}$-cobordism) [See also [[55N22|55Nxx]]]
* ''57R80'' $h$- and $s$-cobordism
* ''57R85'' Equivariant cobordism
* ''57R90'' Other types of cobordism [See also [[55N22|55Nxx]]]
* ''57R91'' Equivariant algebraic topology of manifolds
* ''57R95'' Realizing cycles by submanifolds
* ''57R99'' None of the above, but in this section
!!![[57|57-XX]]Sxx  Topological transformation groups [See also [[20F34|20Fxx]], [[22-XX|22-XX]], [[37-XX|37-XX]], [[54H15|54Hxx]], [[58D05|58Dxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/57Sxx.html]]}{{moveright{< [[57Rxx |57Rxx]] | [[57-XX |57-XX]] | [[57Txx |57Txx]] >}}}
* ''57S05'' Topological properties of groups of homeomorphisms or diffeomorphisms
* ''57S10'' Compact groups of homeomorphisms
* ''57S15'' Compact Lie groups of differentiable transformations
* ''57S17'' Finite transformation groups
* ''57S20'' Noncompact Lie groups of transformations
* ''57S25'' Groups acting on specific manifolds
* ''57S30'' Discontinuous groups of transformations
* ''57S99'' None of the above, but in this section
!!!57-XX Manifolds and cell complexes {For complex manifolds, see [[32Qxx|32Qxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/57-XX.html]]}{{moveright{< [[55-XX |55-XX]] | [[MSC |MSC2010]] | [[57Mxx |57Mxx]] >}}}
* ''57-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''57-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''57-02'' Research exposition (monographs, survey articles)
* ''57-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''57-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''57-06'' Proceedings, conferences, collections, etc.
* ''[[57Mxx|57Mxx]]''  Low-dimensional topology
* ''[[57Nxx|57Nxx]]''  Topological manifolds
* ''[[57Pxx|57Pxx]]''  Generalized manifolds [See also [[18F15|18Fxx]]]
* ''[[57Qxx|57Qxx]]''  ~PL-topology
* ''[[57Rxx|57Rxx]]''  Differential topology {For foundational questions of differentiable manifolds, see [[58Axx|58Axx]]; for infinite-dimensional manifolds, see [[58Bxx|58Bxx]]}
* ''[[57Sxx|57Sxx]]''  Topological transformation groups [See also [[20F34|20Fxx]], [[22-XX|22-XX]], [[37-XX|37-XX]], [[54H15|54Hxx]], [[58D05|58Dxx]]]
* ''[[57Txx|57Txx]]''  Homology and homotopy of topological groups and related structures
!!![[57|57-XX]]Txx  Homology and homotopy of topological groups and related structures {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/57Txx.html]]}{{moveright{< [[57Sxx |57Sxx]] | [[57-XX |57-XX]] | [[58-XX |58-XX]] >}}}
* ''57T05'' Hopf algebras [See also [[16T05|16Txx]]]
* ''57T10'' Homology and cohomology of Lie groups
* ''57T15'' Homology and cohomology of homogeneous spaces of Lie groups
* ''57T20'' Homotopy groups of topological groups and homogeneous spaces
* ''57T25'' Homology and cohomology of $H$-spaces
* ''57T30'' Bar and cobar constructions [See also [[18G55|18Gxx]], [[55Uxx|55Uxx]]]
* ''57T35'' Applications of ~Eilenberg-Moore spectral sequences [See also [[55R20|55Rxx]], [[55T20|55Txx]]]
* ''57T99'' None of the above, but in this section
!!![[58|58-XX]]Axx  General theory of differentiable manifolds [See also [[32Cxx|32Cxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/58Axx.html]]}{{moveright{< [[57-XX |57-XX]] | [[58-XX |58-XX]] | [[58Bxx |58Bxx]] >}}}
* ''58A03'' Topos-theoretic approach to differentiable manifolds
* ''58A05'' Differentiable manifolds, foundations
* ''58A07'' Real-analytic and Nash manifolds [See also [[14P20|14Pxx]], [[32C07|32Cxx]]]
* ''58A10'' Differential forms
* ''58A12'' de Rham theory [See also [[14Fxx|14Fxx]]]
* ''58A14'' Hodge theory [See also [[14C30|14Cxx]], [[14Fxx|14Fxx]], [[32J25|32Jxx]], [[32S35|32Sxx]]]
* ''58A15'' Exterior differential systems (Cartan theory)
* ''58A17'' Pfaffian systems
* ''58A20'' Jets
* ''58A25'' Currents [See also [[32C30|32Cxx]], [[53C65|53Cxx]]]
* ''58A30'' Vector distributions (subbundles of the tangent bundles)
* ''58A32'' Natural bundles
* ''58A35'' Stratified sets [See also [[32S60|32Sxx]]]
* ''58A40'' Differential spaces
* ''58A50'' Supermanifolds and graded manifolds [See also [[14A22|14Axx]], [[32C11|32Cxx]]]
* ''58A99'' None of the above, but in this section
!!![[58|58-XX]]Bxx  Infinite-dimensional manifolds {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/58Bxx.html]]}{{moveright{< [[58Axx |58Axx]] | [[58-XX |58-XX]] | [[58Cxx |58Cxx]] >}}}
* ''58B05'' Homotopy and topological questions
* ''58B10'' Differentiability questions
* ''58B12'' Questions of holomorphy [See also [[32-XX|32-XX]], [[46G20|46Gxx]]]
* ''58B15'' Fredholm structures [See also [[47A53|47Axx]]]
* ''58B20'' Riemannian, Finsler and other geometric structures [See also [[53C20|53Cxx]], [[53C60|53Cxx]]]
* ''58B25'' Group structures and generalizations on infinite-dimensional manifolds [See also [[22E65|22Exx]], [[58D05|58Dxx]]]
* ''58B32'' Geometry of quantum groups
* ''58B34'' Noncommutative geometry (à la Connes)
* ''58B99'' None of the above, but in this section
!!![[58|58-XX]]Cxx  Calculus on manifolds; nonlinear operators [See also [[46Txx|46Txx]], [[47Hxx|47Hxx]], [[47Jxx|47Jxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/58Cxx.html]]}{{moveright{< [[58Bxx |58Bxx]] | [[58-XX |58-XX]] | [[58Dxx |58Dxx]] >}}}
* ''58C05'' Real-valued functions
* ''58C06'' Set valued and function-space valued mappings [See also [[47H04|47Hxx]], [[54C60|54Cxx]]]
* ''58C07'' Continuity properties of mappings
* ''58C10'' Holomorphic maps [See also [[32-XX|32-XX]]]
* ''58C15'' Implicit function theorems; global Newton methods
* ''58C20'' Differentiation theory (Gateaux, Fréchet, etc.) [See also [[26Exx|26Exx]], [[46G05|46Gxx]]]
* ''58C25'' Differentiable maps
* ''58C30'' Fixed point theorems on manifolds [See also [[47H10|47Hxx]]]
* ''58C35'' Integration on manifolds; measures on manifolds [See also [[28Cxx|28Cxx]]]
* ''58C40'' Spectral theory; eigenvalue problems [See also [[47J10|47Jxx]], [[58E07|58Exx]]]
* ''58C50'' Analysis on supermanifolds or graded manifolds
* ''58C99'' None of the above, but in this section
!!![[58|58-XX]]Dxx  Spaces and manifolds of mappings (including nonlinear versions of [[46Exx|46Exx]]) [See also [[46Txx|46Txx]], [[53Cxx|53Cxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/58Dxx.html]]}{{moveright{< [[58Cxx |58Cxx]] | [[58-XX |58-XX]] | [[58Exx |58Exx]] >}}}
* ''58D05'' Groups of diffeomorphisms and homeomorphisms as manifolds [See also [[22E65|22Exx]], [[57S05|57Sxx]]]
* ''58D07'' Groups and semigroups of nonlinear operators [See also [[17B65|17Bxx]], [[47H20|47Hxx]]]
* ''58D10'' Spaces of imbeddings and immersions
* ''58D15'' Manifolds of mappings [See also [[46T10|46Txx]], [[54C35|54Cxx]]]
* ''58D17'' Manifolds of metrics (esp. Riemannian)
* ''58D19'' Group actions and symmetry properties
* ''58D20'' Measures (Gaussian, cylindrical, etc.) on manifolds of maps [See also [[28Cxx|28Cxx]], [[46T12|46Txx]]]
* ''58D25'' Equations in function spaces; evolution equations [See also [[34Gxx|34Gxx]], [[35K90|35Kxx]], [[35L90|35Lxx]], [[35R15|35Rxx]], [[37Lxx|37Lxx]], [[47Jxx|47Jxx]]]
* ''58D27'' Moduli problems for differential geometric structures
* ''58D29'' Moduli problems for topological structures
* ''58D30'' Applications (in quantum mechanics (Feynman path integrals), relativity, fluid dynamics, etc.)
* ''58D99'' None of the above, but in this section
!!![[58|58-XX]]Exx  Variational problems in infinite-dimensional spaces {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/58Exx.html]]}{{moveright{< [[58Dxx |58Dxx]] | [[58-XX |58-XX]] | [[58Hxx |58Hxx]] >}}}
* ''58E05'' Abstract critical point theory (Morse theory, ~Ljusternik-Schnirelman (~Lyusternik-Shnirel'man) theory, etc.)
* ''58E07'' Abstract bifurcation theory
* ''58E09'' Group-invariant bifurcation theory
* ''58E10'' Applications to the theory of geodesics (problems in one independent variable)
* ''58E11'' Critical metrics
* ''58E12'' Applications to minimal surfaces (problems in two independent variables) [See also [[49Q05|49Qxx]]]
* ''58E15'' Application to extremal problems in several variables; ~Yang-Mills functionals [See also [[81T13|81Txx]]], etc.
* ''58E17'' Pareto optimality, etc., applications to economics [See also [[90C29|90Cxx]]]
* ''58E20'' Harmonic maps [See also [[53C43|53Cxx]]], etc.
* ''58E25'' Applications to control theory [See also [[49-XX|49-XX]], [[93-XX|93-XX]]]
* ''58E30'' Variational principles
* ''58E35'' Variational inequalities (global problems)
* ''58E40'' Group actions
* ''58E50'' Applications
* ''58E99'' None of the above, but in this section
!!![[58|58-XX]]Hxx  Pseudogroups, differentiable groupoids and general structures on manifolds {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/58Hxx.html]]}{{moveright{< [[58Exx |58Exx]] | [[58-XX |58-XX]] | [[58Jxx |58Jxx]] >}}}
* ''58H05'' Pseudogroups and differentiable groupoids [See also [[22A22|22Axx]], [[22E65|22Exx]]]
* ''58H10'' Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) [See also [[57R32|57Rxx]]]
* ''58H15'' Deformations of structures [See also [[32Gxx|32Gxx]], [[58J10|58Jxx]]]
* ''58H99'' None of the above, but in this section
!!![[58|58-XX]]Jxx  Partial differential equations on manifolds; differential operators [See also [[32Wxx|32Wxx]], [[35-XX|35-XX]], [[53Cxx|53Cxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/58Jxx.html]]}{{moveright{< [[58Hxx |58Hxx]] | [[58-XX |58-XX]] | [[58Kxx |58Kxx]] >}}}
* ''58J05'' Elliptic equations on manifolds, general theory [See also [[35-XX|35-XX]]]
* ''58J10'' Differential complexes [See also [[35Nxx|35Nxx]]]; elliptic complexes
* ''58J15'' Relations with hyperfunctions
* ''58J20'' Index theory and related fixed point theorems [See also [[19K56|19Kxx]], [[46L80|46Lxx]]]
* ''58J22'' Exotic index theories [See also [[19K56|19Kxx]], [[46L05|46Lxx]], [[46L10|46Lxx]], [[46L80|46Lxx]], [[46M20|46Mxx]]]
* ''58J26'' Elliptic genera
* ''58J28'' Eta-invariants, ~Chern-Simons invariants
* ''58J30'' Spectral flows
* ''58J32'' Boundary value problems on manifolds
* ''58J35'' Heat and other parabolic equation methods
* ''58J37'' Perturbations; asymptotics
* ''58J40'' Pseudodifferential and Fourier integral operators on manifolds [See also [[35Sxx|35Sxx]]]
* ''58J42'' Noncommutative global analysis, noncommutative residues
* ''58J45'' Hyperbolic equations [See also [[35Lxx|35Lxx]]]
* ''58J47'' Propagation of singularities; initial value problems
* ''58J50'' Spectral problems; spectral geometry; scattering theory [See also [[35Pxx|35Pxx]]]
* ''58J51'' Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicity
* ''58J52'' Determinants and determinant bundles, analytic torsion
* ''58J53'' Isospectrality
* ''58J55'' Bifurcation [See also [[35B32|35Bxx]]]
* ''58J60'' Relations with special manifold structures (Riemannian, Finsler, etc.)
* ''58J65'' Diffusion processes and stochastic analysis on manifolds [See also [[35R60|35Rxx]], [[60H10|60Hxx]], [[60J60|60Jxx]]]
* ''58J70'' Invariance and symmetry properties [See also [[35A30|35Axx]]]
* ''58J72'' Correspondences and other transformation methods (e.g. ~Lie-Bäcklund) [See also [[35A22|35Axx]]]
* ''58J90'' Applications
* ''58J99'' None of the above, but in this section
!!![[58|58-XX]]Kxx  Theory of singularities and catastrophe theory [See also [[32Sxx|32Sxx]], [[37-XX|37-XX]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/58Kxx.html]]}{{moveright{< [[58Jxx |58Jxx]] | [[58-XX |58-XX]] | [[58Zxx |58Zxx]] >}}}
* ''58K05'' Critical points of functions and mappings
* ''58K10'' Monodromy
* ''58K15'' Topological properties of mappings
* ''58K20'' Algebraic and analytic properties of mappings
* ''58K25'' Stability
* ''58K30'' Global theory
* ''58K35'' Catastrophe theory
* ''58K40'' Classification; finite determinacy of map germs
* ''58K45'' Singularities of vector fields, topological aspects
* ''58K50'' Normal forms
* ''58K55'' Asymptotic behavior
* ''58K60'' Deformation of singularities
* ''58K65'' Topological invariants
* ''58K70'' Symmetries, equivariance
* ''58K99'' None of the above, but in this section
!!!58-XX Global analysis, analysis on manifolds [See also [[32Cxx|32Cxx]], [[32Fxx|32Fxx]], [[32Wxx|32Wxx]], [[46-XX|46-XX]], [[47Hxx|47Hxx]], [[53Cxx|53Cxx]]] {For geometric integration theory, see [[49Q15|49Qxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/58-XX.html]]}{{moveright{< [[57-XX |57-XX]] | [[MSC |MSC2010]] | [[58Axx |58Axx]] >}}}
* ''58-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''58-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''58-02'' Research exposition (monographs, survey articles)
* ''58-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''58-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''58-06'' Proceedings, conferences, collections, etc.
* ''[[58Axx|58Axx]]''  General theory of differentiable manifolds [See also [[32Cxx|32Cxx]]]
* ''[[58Bxx|58Bxx]]''  Infinite-dimensional manifolds
* ''[[58Cxx|58Cxx]]''  Calculus on manifolds; nonlinear operators [See also [[46Txx|46Txx]], [[47Hxx|47Hxx]], [[47Jxx|47Jxx]]]
* ''[[58Dxx|58Dxx]]''  Spaces and manifolds of mappings (including nonlinear versions of [[46Exx|46Exx]]) [See also [[46Txx|46Txx]], [[53Cxx|53Cxx]]]
* ''[[58Exx|58Exx]]''  Variational problems in infinite-dimensional spaces
* ''[[58Hxx|58Hxx]]''  Pseudogroups, differentiable groupoids and general structures on manifolds
* ''[[58Jxx|58Jxx]]''  Partial differential equations on manifolds; differential operators [See also [[32Wxx|32Wxx]], [[35-XX|35-XX]], [[53Cxx|53Cxx]]]
* ''[[58Kxx|58Kxx]]''  Theory of singularities and catastrophe theory [See also [[32Sxx|32Sxx]], [[37-XX|37-XX]]]
* ''[[58Zxx|58Zxx]]''  Applications to physics
!!![[58|58-XX]]Zxx  Applications to physics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/58Zxx.html]]}{{moveright{< [[58Kxx |58Kxx]] | [[58-XX |58-XX]] | [[60-XX |60-XX]] >}}}
* ''58Z05'' Applications to physics
* ''58Z99'' None of the above, but in this section
!!![[60|60-XX]]Axx  Foundations of probability theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/60Axx.html]]}{{moveright{< [[58-XX |58-XX]] | [[60-XX |60-XX]] | [[60Bxx |60Bxx]] >}}}
* ''60A05'' Axioms; other general questions
* ''60A10'' Probabilistic measure theory {For ergodic theory, see [[28Dxx|28Dxx]] and [[60Fxx|60Fxx]]}
* ''60A86'' Fuzzy probability
* ''60A99'' None of the above, but in this section
!!![[60|60-XX]]Bxx  Probability theory on algebraic and topological structures {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/60Bxx.html]]}{{moveright{< [[60Axx |60Axx]] | [[60-XX |60-XX]] | [[60Cxx |60Cxx]] >}}}
* ''60B05'' Probability measures on topological spaces
* ''60B10'' Convergence of probability measures
* ''60B11'' Probability theory on linear topological spaces [See also [[28C20|28Cxx]]]
* ''60B12'' Limit theorems for vector-valued random variables (infinite-dimensional case)
* ''60B15'' Probability measures on groups or semigroups, Fourier transforms, factorization
* ''60B20'' Random matrices (probabilistic aspects; for algebraic aspects see [[15B52|15Bxx]])
* ''60B99'' None of the above, but in this section
!!![[60|60-XX]]Cxx  Combinatorial probability {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/60Cxx.html]]}{{moveright{< [[60Bxx |60Bxx]] | [[60-XX |60-XX]] | [[60Dxx |60Dxx]] >}}}
* ''60C05'' Combinatorial probability
* ''60C99'' None of the above, but in this section
!!![[60|60-XX]]Dxx  Geometric probability and stochastic geometry [See also [[52A22|52Axx]], [[53C65|53Cxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/60Dxx.html]]}{{moveright{< [[60Cxx |60Cxx]] | [[60-XX |60-XX]] | [[60Exx |60Exx]] >}}}
* ''60D05'' Geometric probability and stochastic geometry [See also [[52A22|52Axx]], [[53C65|53Cxx]]]
* ''60D99'' None of the above, but in this section
!!![[60|60-XX]]Exx  Distribution theory [See also [[62Exx|62Exx]], [[62Hxx|62Hxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/60Exx.html]]}{{moveright{< [[60Dxx |60Dxx]] | [[60-XX |60-XX]] | [[60Fxx |60Fxx]] >}}}
* ''60E05'' Distributions: general theory
* ''60E07'' Infinitely divisible distributions; stable distributions
* ''60E10'' Characteristic functions; other transforms
* ''60E15'' Inequalities; stochastic orderings
* ''60E99'' None of the above, but in this section
!!![[60|60-XX]]Fxx  Limit theorems [See also [[28Dxx|28Dxx]], [[60B12|60Bxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/60Fxx.html]]}{{moveright{< [[60Exx |60Exx]] | [[60-XX |60-XX]] | [[60Gxx |60Gxx]] >}}}
* ''60F05'' Central limit and other weak theorems
* ''60F10'' Large deviations
* ''60F15'' Strong theorems
* ''60F17'' Functional limit theorems; invariance principles
* ''60F20'' Zero-one laws
* ''60F25'' $L^p$-limit theorems
* ''60F99'' None of the above, but in this section
!!![[60|60-XX]]Gxx  Stochastic processes {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/60Gxx.html]]}{{moveright{< [[60Fxx |60Fxx]] | [[60-XX |60-XX]] | [[60Hxx |60Hxx]] >}}}
* ''60G05'' Foundations of stochastic processes
* ''60G07'' General theory of processes
* ''60G09'' Exchangeability
* ''60G10'' Stationary processes
* ''60G12'' General second-order processes
* ''60G15'' Gaussian processes
* ''60G17'' Sample path properties
* ''60G18'' Self-similar processes
* ''60G20'' Generalized stochastic processes
* ''60G22'' Fractional processes, including fractional Brownian motion
* ''60G25'' Prediction theory [See also [[62M20|62Mxx]]]
* ''60G30'' Continuity and singularity of induced measures
* ''60G35'' Signal detection and filtering [See also [[62M20|62Mxx]], [[93E10|93Exx]], [[93E11|93Exx]], [[94Axx|94Axx]]]
* ''60G40'' Stopping times; optimal stopping problems; gambling theory [See also [[62L15|62Lxx]], [[91A60|91Axx]]]
* ''60G42'' Martingales with discrete parameter
* ''60G44'' Martingales with continuous parameter
* ''60G46'' Martingales and classical analysis
* ''60G48'' Generalizations of martingales
* ''60G50'' Sums of independent random variables; random walks
* ''60G51'' Processes with independent increments; Lévy processes
* ''60G52'' Stable processes
* ''60G55'' Point processes
* ''60G57'' Random measures
* ''60G60'' Random fields
* ''60G70'' Extreme value theory; extremal processes
* ''60G99'' None of the above, but in this section
!!![[60|60-XX]]Hxx  Stochastic analysis [See also [[58J65|58Jxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/60Hxx.html]]}{{moveright{< [[60Gxx |60Gxx]] | [[60-XX |60-XX]] | [[60Jxx |60Jxx]] >}}}
* ''60H05'' Stochastic integrals
* ''60H07'' Stochastic calculus of variations and the Malliavin calculus
* ''60H10'' Stochastic ordinary differential equations [See also [[34F05|34Fxx]]]
* ''60H15'' Stochastic partial differential equations [See also [[35R60|35Rxx]]]
* ''60H20'' Stochastic integral equations
* ''60H25'' Random operators and equations [See also [[47B80|47Bxx]]]
* ''60H30'' Applications of stochastic analysis (to PDE, etc.)
* ''60H35'' Computational methods for stochastic equations [See also [[65C30|65Cxx]]]
* ''60H40'' White noise theory
* ''60H99'' None of the above, but in this section
!!![[60|60-XX]]Jxx  Markov processes {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/60Jxx.html]]}{{moveright{< [[60Hxx |60Hxx]] | [[60-XX |60-XX]] | [[60Kxx |60Kxx]] >}}}
* ''60J05'' Discrete-time Markov processes on general state spaces
* ''60J10'' Markov chains (discrete-time Markov processes on discrete state spaces)
* ''60J20'' Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also [[90B30|90Bxx]], [[91D10|91Dxx]], [[91D35|91Dxx]], [[91E40|91Exx]]]
* ''60J22'' Computational methods in Markov chains [See also [[65C40|65Cxx]]]
* ''60J25'' Continuous-time Markov processes on general state spaces
* ''60J27'' Continuous-time Markov processes on discrete state spaces
* ''60J28'' Applications of continuous-time Markov processes on discrete state spaces
* ''60J35'' Transition functions, generators and resolvents [See also [[47D03|47Dxx]], [[47D07|47Dxx]]]
* ''60J40'' Right processes
* ''60J45'' Probabilistic potential theory [See also [[31Cxx|31Cxx]], [[31D05|31Dxx]]]
* ''60J50'' Boundary theory
* ''60J55'' Local time and additive functionals
* ''60J57'' Multiplicative functionals
* ''60J60'' Diffusion processes [See also [[58J65|58Jxx]]]
* ''60J65'' Brownian motion [See also [[58J65|58Jxx]]]
* ''60J67'' Stochastic (Schramm-)Loewner evolution (SLE)
* ''60J68'' Superprocesses
* ''60J70'' Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also [[92Dxx|92Dxx]]]
* ''60J75'' Jump processes
* ''60J80'' Branching processes (~Galton-Watson, birth-and-death, etc.)
* ''60J85'' Applications of branching processes [See also [[92Dxx|92Dxx]]]
* ''60J99'' None of the above, but in this section
!!!60-XX Probability theory and stochastic processes {For additional applications, see [[11Kxx|11Kxx]], [[62-XX|62-XX]], [[90-XX|90-XX]], [[91-XX|91-XX]], [[92-XX|92-XX]], [[93-XX|93-XX]], [[94-XX|94-XX]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/60-XX.html]]}{{moveright{< [[58-XX |58-XX]] | [[MSC |MSC2010]] | [[60Axx |60Axx]] >}}}
* ''60-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''60-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''60-02'' Research exposition (monographs, survey articles)
* ''60-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''60-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''60-06'' Proceedings, conferences, collections, etc.
* ''60-08'' Computational methods (not classified at a more specific level) [See also [[65C50|65Cxx]]]
* ''[[60Axx|60Axx]]''  Foundations of probability theory
* ''[[60Bxx|60Bxx]]''  Probability theory on algebraic and topological structures
* ''[[60Cxx|60Cxx]]''  Combinatorial probability
* ''[[60Dxx|60Dxx]]''  Geometric probability and stochastic geometry [See also [[52A22|52Axx]], [[53C65|53Cxx]]]
* ''[[60Exx|60Exx]]''  Distribution theory [See also [[62Exx|62Exx]], [[62Hxx|62Hxx]]]
* ''[[60Fxx|60Fxx]]''  Limit theorems [See also [[28Dxx|28Dxx]], [[60B12|60Bxx]]]
* ''[[60Gxx|60Gxx]]''  Stochastic processes
* ''[[60Hxx|60Hxx]]''  Stochastic analysis [See also [[58J65|58Jxx]]]
* ''[[60Jxx|60Jxx]]''  Markov processes
* ''[[60Kxx|60Kxx]]''  Special processes
!!![[60|60-XX]]Kxx  Special processes {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/60Kxx.html]]}{{moveright{< [[60Jxx |60Jxx]] | [[60-XX |60-XX]] | [[62-XX |62-XX]] >}}}
* ''60K05'' Renewal theory
* ''60K10'' Applications (reliability, demand theory, etc.)
* ''60K15'' Markov renewal processes, semi-Markov processes
* ''60K20'' Applications of Markov renewal processes (reliability, queueing networks, etc.) [See also [[90Bxx|90Bxx]]]
* ''60K25'' Queueing theory [See also [[68M20|68Mxx]], [[90B22|90Bxx]]]
* ''60K30'' Applications (congestion, allocation, storage, traffic, etc.) [See also [[90Bxx|90Bxx]]]
* ''60K35'' Interacting random processes; statistical mechanics type models; percolation theory [See also [[82B43|82Bxx]], [[82C43|82Cxx]]]
* ''60K37'' Processes in random environments
* ''60K40'' Other physical applications of random processes
* ''60K99'' None of the above, but in this section
!!![[62|62-XX]]Axx  Foundational and philosophical topics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/62Axx.html]]}{{moveright{< [[60-XX |60-XX]] | [[62-XX |62-XX]] | [[62Bxx |62Bxx]] >}}}
* ''62A01'' Foundations and philosophical topics
* ''62A86'' Fuzzy analysis in statistics
* ''62A99'' None of the above, but in this section
!!![[62|62-XX]]Bxx  Sufficiency and information {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/62Bxx.html]]}{{moveright{< [[62Axx |62Axx]] | [[62-XX |62-XX]] | [[62Cxx |62Cxx]] >}}}
* ''62B05'' Sufficient statistics and fields
* ''62B10'' Information-theoretic topics [See also [[94A17|94Axx]]]
* ''62B15'' Theory of statistical experiments
* ''62B86'' Fuzziness, sufficiency, and information
* ''62B99'' None of the above, but in this section
!!![[62|62-XX]]Cxx  Decision theory [See also [[90B50|90Bxx]], [[91B06|91Bxx]]; for game theory, see [[91A35|91Axx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/62Cxx.html]]}{{moveright{< [[62Bxx |62Bxx]] | [[62-XX |62-XX]] | [[62Dxx |62Dxx]] >}}}
* ''62C05'' General considerations
* ''62C07'' Complete class results
* ''62C10'' Bayesian problems; characterization of Bayes procedures
* ''62C12'' Empirical decision procedures; empirical Bayes procedures
* ''62C15'' Admissibility
* ''62C20'' Minimax procedures
* ''62C25'' Compound decision problems
* ''62C86'' Decision theory and fuzziness
* ''62C99'' None of the above, but in this section
!!![[62|62-XX]]Dxx  Sampling theory, sample surveys {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/62Dxx.html]]}{{moveright{< [[62Cxx |62Cxx]] | [[62-XX |62-XX]] | [[62Exx |62Exx]] >}}}
* ''62D05'' Sampling theory, sample surveys
* ''62D99'' None of the above, but in this section
!!![[62|62-XX]]Exx  Distribution theory [See also [[60Exx|60Exx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/62Exx.html]]}{{moveright{< [[62Dxx |62Dxx]] | [[62-XX |62-XX]] | [[62Fxx |62Fxx]] >}}}
* ''62E10'' Characterization and structure theory
* ''62E15'' Exact distribution theory
* ''62E17'' Approximations to distributions (nonasymptotic)
* ''62E20'' Asymptotic distribution theory
* ''62E86'' Fuzziness in connection with the topics on distributions in this section
* ''62E99'' None of the above, but in this section
!!![[62|62-XX]]Fxx  Parametric inference {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/62Fxx.html]]}{{moveright{< [[62Exx |62Exx]] | [[62-XX |62-XX]] | [[62Gxx |62Gxx]] >}}}
* ''62F03'' Hypothesis testing
* ''62F05'' Asymptotic properties of tests
* ''62F07'' Ranking and selection
* ''62F10'' Point estimation
* ''62F12'' Asymptotic properties of estimators
* ''62F15'' Bayesian inference
* ''62F25'' Tolerance and confidence regions
* ''62F30'' Inference under constraints
* ''62F35'' Robustness and adaptive procedures
* ''62F40'' Bootstrap, jackknife and other resampling methods
* ''62F86'' Parametric inference and fuzziness
* ''62F99'' None of the above, but in this section
!!![[62|62-XX]]Gxx  Nonparametric inference {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/62Gxx.html]]}{{moveright{< [[62Fxx |62Fxx]] | [[62-XX |62-XX]] | [[62Hxx |62Hxx]] >}}}
* ''62G05'' Estimation
* ''62G07'' Density estimation
* ''62G08'' Nonparametric regression
* ''62G09'' Resampling methods
* ''62G10'' Hypothesis testing
* ''62G15'' Tolerance and confidence regions
* ''62G20'' Asymptotic properties
* ''62G30'' Order statistics; empirical distribution functions
* ''62G32'' Statistics of extreme values; tail inference
* ''62G35'' Robustness
* ''62G86'' Nonparametric inference and fuzziness
* ''62G99'' None of the above, but in this section
!!![[62|62-XX]]Hxx  Multivariate analysis [See also [[60Exx|60Exx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/62Hxx.html]]}{{moveright{< [[62Gxx |62Gxx]] | [[62-XX |62-XX]] | [[62Jxx |62Jxx]] >}}}
* ''62H05'' Characterization and structure theory
* ''62H10'' Distribution of statistics
* ''62H11'' Directional data; spatial statistics
* ''62H12'' Estimation
* ''62H15'' Hypothesis testing
* ''62H17'' Contingency tables
* ''62H20'' Measures of association (correlation, canonical correlation, etc.)
* ''62H25'' Factor analysis and principal components; correspondence analysis
* ''62H30'' Classification and discrimination; cluster analysis [See also [[68T10|68Txx]], [[91C20|91Cxx]]]
* ''62H35'' Image analysis
* ''62H86'' Multivariate analysis and fuzziness
* ''62H99'' None of the above, but in this section
!!![[62|62-XX]]Jxx  Linear inference, regression {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/62Jxx.html]]}{{moveright{< [[62Hxx |62Hxx]] | [[62-XX |62-XX]] | [[62Kxx |62Kxx]] >}}}
* ''62J02'' General nonlinear regression
* ''62J05'' Linear regression
* ''62J07'' Ridge regression; shrinkage estimators
* ''62J10'' Analysis of variance and covariance
* ''62J12'' Generalized linear models
* ''62J15'' Paired and multiple comparisons
* ''62J20'' Diagnostics
* ''62J86'' Fuzziness, and linear inference and regression
* ''62J99'' None of the above, but in this section
!!![[62|62-XX]]Kxx  Design of experiments [See also [[05Bxx|05Bxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/62Kxx.html]]}{{moveright{< [[62Jxx |62Jxx]] | [[62-XX |62-XX]] | [[62Lxx |62Lxx]] >}}}
* ''62K05'' Optimal designs
* ''62K10'' Block designs
* ''62K15'' Factorial designs
* ''62K20'' Response surface designs
* ''62K25'' Robust parameter designs
* ''62K86'' Fuzziness and design of experiments
* ''62K99'' None of the above, but in this section
!!![[62|62-XX]]Lxx  Sequential methods {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/62Lxx.html]]}{{moveright{< [[62Kxx |62Kxx]] | [[62-XX |62-XX]] | [[62Mxx |62Mxx]] >}}}
* ''62L05'' Sequential design
* ''62L10'' Sequential analysis
* ''62L12'' Sequential estimation
* ''62L15'' Optimal stopping [See also [[60G40|60Gxx]], [[91A60|91Axx]]]
* ''62L20'' Stochastic approximation
* ''62L86'' Fuzziness and sequential methods
* ''62L99'' None of the above, but in this section
!!![[62|62-XX]]Mxx  Inference from stochastic processes {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/62Mxx.html]]}{{moveright{< [[62Lxx |62Lxx]] | [[62-XX |62-XX]] | [[62Nxx |62Nxx]] >}}}
* ''62M02'' Markov processes: hypothesis testing
* ''62M05'' Markov processes: estimation
* ''62M07'' ~Non-Markovian processes: hypothesis testing
* ''62M09'' ~Non-Markovian processes: estimation
* ''62M10'' Time series, auto-correlation, regression, etc. [See also [[91B84|91Bxx]]]
* ''62M15'' Spectral analysis
* ''62M20'' Prediction [See also [[60G25|60Gxx]]]; filtering [See also [[60G35|60Gxx]], [[93E10|93Exx]], [[93E11|93Exx]]]
* ''62M30'' Spatial processes
* ''62M40'' Random fields; image analysis
* ''62M45'' Neural nets and related approaches
* ''62M86'' Inference from stochastic processes and fuzziness
* ''62M99'' None of the above, but in this section
!!![[62|62-XX]]Nxx  Survival analysis and censored data {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/62Nxx.html]]}{{moveright{< [[62Mxx |62Mxx]] | [[62-XX |62-XX]] | [[62Pxx |62Pxx]] >}}}
* ''62N01'' Censored data models
* ''62N02'' Estimation
* ''62N03'' Testing
* ''62N05'' Reliability and life testing [See also [[90B25|90Bxx]]]
* ''62N86'' Fuzziness, and survival analysis and censored data
* ''62N99'' None of the above, but in this section
!!![[62|62-XX]]Pxx  Applications [See also [[90-XX|90-XX]], [[91-XX|91-XX]], [[92-XX|92-XX]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/62Pxx.html]]}{{moveright{< [[62Nxx |62Nxx]] | [[62-XX |62-XX]] | [[62Qxx |62Qxx]] >}}}
* ''62P05'' Applications to actuarial sciences and financial mathematics
* ''62P10'' Applications to biology and medical sciences
* ''62P12'' Applications to environmental and related topics
* ''62P15'' Applications to psychology
* ''62P20'' Applications to economics [See also [[91Bxx|91Bxx]]]
* ''62P25'' Applications to social sciences
* ''62P30'' Applications in engineering and industry
* ''62P35'' Applications to physics
* ''62P99'' None of the above, but in this section
!!!62-XX Statistics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/62-XX.html]]}{{moveright{< [[60-XX |60-XX]] | [[MSC |MSC2010]] | [[62Axx |62Axx]] >}}}
* ''62-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''62-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''62-02'' Research exposition (monographs, survey articles)
* ''62-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''62-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''62-06'' Proceedings, conferences, collections, etc.
* ''62-07'' Data analysis
* ''62-09'' Graphical methods
* ''[[62Axx|62Axx]]''  Foundational and philosophical topics
* ''[[62Bxx|62Bxx]]''  Sufficiency and information
* ''[[62Cxx|62Cxx]]''  Decision theory [See also [[90B50|90Bxx]], [[91B06|91Bxx]]; for game theory, see [[91A35|91Axx]]]
* ''[[62Dxx|62Dxx]]''  Sampling theory, sample surveys
* ''[[62Exx|62Exx]]''  Distribution theory [See also [[60Exx|60Exx]]]
* ''[[62Fxx|62Fxx]]''  Parametric inference
* ''[[62Gxx|62Gxx]]''  Nonparametric inference
* ''[[62Hxx|62Hxx]]''  Multivariate analysis [See also [[60Exx|60Exx]]]
* ''[[62Jxx|62Jxx]]''  Linear inference, regression
* ''[[62Kxx|62Kxx]]''  Design of experiments [See also [[05Bxx|05Bxx]]]
* ''[[62Lxx|62Lxx]]''  Sequential methods
* ''[[62Mxx|62Mxx]]''  Inference from stochastic processes
* ''[[62Nxx|62Nxx]]''  Survival analysis and censored data
* ''[[62Pxx|62Pxx]]''  Applications [See also [[90-XX|90-XX]], [[91-XX|91-XX]], [[92-XX|92-XX]]]
* ''[[62Qxx|62Qxx]]''  Statistical tables
!!![[62|62-XX]]Qxx  Statistical tables {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/62Qxx.html]]}{{moveright{< [[62Pxx |62Pxx]] | [[62-XX |62-XX]] | [[65-XX |65-XX]] >}}}
* ''62Q05'' Statistical tables
* ''62Q99'' None of the above, but in this section
!!![[65|65-XX]]Axx  Tables {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/65Axx.html]]}{{moveright{< [[62-XX |62-XX]] | [[65-XX |65-XX]] | [[65Bxx |65Bxx]] >}}}
* ''65A05'' Tables
* ''65A99'' None of the above, but in this section
!!![[65|65-XX]]Bxx  Acceleration of convergence {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/65Bxx.html]]}{{moveright{< [[65Axx |65Axx]] | [[65-XX |65-XX]] | [[65Cxx |65Cxx]] >}}}
* ''65B05'' Extrapolation to the limit, deferred corrections
* ''65B10'' Summation of series
* ''65B15'' ~Euler-Maclaurin formula
* ''65B99'' None of the above, but in this section
!!![[65|65-XX]]Cxx  Probabilistic methods, simulation and stochastic differential equations {For theoretical aspects, see [[68U20|68Uxx]] and [[60H35|60Hxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/65Cxx.html]]}{{moveright{< [[65Bxx |65Bxx]] | [[65-XX |65-XX]] | [[65Dxx |65Dxx]] >}}}
* ''65C05'' Monte Carlo methods
* ''65C10'' Random number generation
* ''65C20'' Models, numerical methods [See also [[68U20|68Uxx]]]
* ''65C30'' Stochastic differential and integral equations
* ''65C35'' Stochastic particle methods [See also [[82C80|82Cxx]]]
* ''65C40'' Computational Markov chains
* ''65C50'' Other computational problems in probability
* ''65C60'' Computational problems in statistics
* ''65C99'' None of the above, but in this section
!!![[65|65-XX]]Dxx  Numerical approximation and computational geometry (primarily algorithms) {For theory, see [[41-XX|41-XX]] and [[68Uxx|68Uxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/65Dxx.html]]}{{moveright{< [[65Cxx |65Cxx]] | [[65-XX |65-XX]] | [[65Exx |65Exx]] >}}}
* ''65D05'' Interpolation
* ''65D07'' Splines
* ''65D10'' Smoothing, curve fitting
* ''65D15'' Algorithms for functional approximation
* ''65D17'' Computer aided design (modeling of curves and surfaces) [See also [[68U07|68Uxx]]]
* ''65D18'' Computer graphics, image analysis, and computational geometry [See also [[51N05|51Nxx]], [[68U05|68Uxx]]]
* ''65D19'' Computational issues in computer and robotic vision
* ''65D20'' Computation of special functions, construction of tables [See also [[33F05|33Fxx]]]
* ''65D25'' Numerical differentiation
* ''65D30'' Numerical integration
* ''65D32'' Quadrature and cubature formulas
* ''65D99'' None of the above, but in this section
!!![[65|65-XX]]Exx  Numerical methods in complex analysis (potential theory, etc.) {For numerical methods in conformal mapping, see also [[30C30|30Cxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/65Exx.html]]}{{moveright{< [[65Dxx |65Dxx]] | [[65-XX |65-XX]] | [[65Fxx |65Fxx]] >}}}
* ''65E05'' Numerical methods in complex analysis (potential theory, etc.) {For numerical methods in conformal mapping, see also [[30C30|30Cxx]]}
* ''65E99'' None of the above, but in this section
!!![[65|65-XX]]Fxx  Numerical linear algebra {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/65Fxx.html]]}{{moveright{< [[65Exx |65Exx]] | [[65-XX |65-XX]] | [[65Gxx |65Gxx]] >}}}
* ''65F05'' Direct methods for linear systems and matrix inversion
* ''65F08'' Preconditioners for iterative methods
* ''65F10'' Iterative methods for linear systems [See also [[65N22|65Nxx]]]
* ''65F15'' Eigenvalues, eigenvectors
* ''65F18'' Inverse eigenvalue problems
* ''65F20'' Overdetermined systems, pseudoinverses
* ''65F22'' Ill-posedness, regularization
* ''65F25'' Orthogonalization
* ''65F30'' Other matrix algorithms
* ''65F35'' Matrix norms, conditioning, scaling [See also [[15A12|15Axx]], [[15A60|15Axx]]]
* ''65F40'' Determinants
* ''65F50'' Sparse matrices
* ''65F60'' Matrix exponential and similar matrix functions
* ''65F99'' None of the above, but in this section
!!![[65|65-XX]]Gxx  Error analysis and interval analysis {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/65Gxx.html]]}{{moveright{< [[65Fxx |65Fxx]] | [[65-XX |65-XX]] | [[65Hxx |65Hxx]] >}}}
* ''65G20'' Algorithms with automatic result verification
* ''65G30'' Interval and finite arithmetic
* ''65G40'' General methods in interval analysis
* ''65G50'' Roundoff error
* ''65G99'' None of the above, but in this section
!!![[65|65-XX]]Hxx  Nonlinear algebraic or transcendental equations {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/65Hxx.html]]}{{moveright{< [[65Gxx |65Gxx]] | [[65-XX |65-XX]] | [[65Jxx |65Jxx]] >}}}
* ''65H04'' Roots of polynomial equations
* ''65H05'' Single equations
* ''65H10'' Systems of equations
* ''65H17'' Eigenvalues, eigenvectors [See also [[47Hxx|47Hxx]], [[47Jxx|47Jxx]], [[58C40|58Cxx]], [[58E07|58Exx]], [[90C30|90Cxx]]]
* ''65H20'' Global methods, including homotopy approaches [See also [[58C30|58Cxx]], [[90C30|90Cxx]]]
* ''65H99'' None of the above, but in this section
!!![[65|65-XX]]Jxx  Numerical analysis in abstract spaces {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/65Jxx.html]]}{{moveright{< [[65Hxx |65Hxx]] | [[65-XX |65-XX]] | [[65Kxx |65Kxx]] >}}}
* ''65J05'' General theory
* ''65J08'' Abstract evolution equations
* ''65J10'' Equations with linear operators (do not use [[65Fxx|65Fxx]])
* ''65J15'' Equations with nonlinear operators (do not use [[65Hxx|65Hxx]])
* ''65J20'' Improperly posed problems; regularization
* ''65J22'' Inverse problems
* ''65J99'' None of the above, but in this section
!!![[65|65-XX]]Kxx  Mathematical programming, optimization and variational techniques {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/65Kxx.html]]}{{moveright{< [[65Jxx |65Jxx]] | [[65-XX |65-XX]] | [[65Lxx |65Lxx]] >}}}
* ''65K05'' Mathematical programming methods [See also [[90Cxx|90Cxx]]]
* ''65K10'' Optimization and variational techniques [See also [[49Mxx|49Mxx]], [[93B40|93Bxx]]]
* ''65K15'' Numerical methods for variational inequalities and related problems
* ''65K99'' None of the above, but in this section
!!![[65|65-XX]]Lxx  Ordinary differential equations {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/65Lxx.html]]}{{moveright{< [[65Kxx |65Kxx]] | [[65-XX |65-XX]] | [[65Mxx |65Mxx]] >}}}
* ''65L03'' Functional-differential equations
* ''65L04'' Stiff equations
* ''65L05'' Initial value problems
* ''65L06'' Multistep, ~Runge-Kutta and extrapolation methods
* ''65L07'' Numerical investigation of stability of solutions
* ''65L08'' Improperly posed problems
* ''65L09'' Inverse problems
* ''65L10'' Boundary value problems
* ''65L11'' Singularly perturbed problems
* ''65L12'' Finite difference methods
* ''65L15'' Eigenvalue problems
* ''65L20'' Stability and convergence of numerical methods
* ''65L50'' Mesh generation and refinement
* ''65L60'' Finite elements, ~Rayleigh-Ritz, Galerkin and collocation methods
* ''65L70'' Error bounds
* ''65L80'' Methods for differential-algebraic equations
* ''65L99'' None of the above, but in this section
!!![[65|65-XX]]Mxx  Partial differential equations, initial value and time-dependent initial-boundary value problems {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/65Mxx.html]]}{{moveright{< [[65Lxx |65Lxx]] | [[65-XX |65-XX]] | [[65Nxx |65Nxx]] >}}}
* ''65M06'' Finite difference methods
* ''65M08'' Finite volume methods
* ''65M12'' Stability and convergence of numerical methods
* ''65M15'' Error bounds
* ''65M20'' Method of lines
* ''65M22'' Solution of discretized equations [See also 65Fxx, 65Hxx]
* ''65M25'' Method of characteristics
* ''65M30'' Improperly posed problems
* ''65M32'' Inverse problems
* ''65M38'' Boundary element methods
* ''65M50'' Mesh generation and refinement
* ''65M55'' Multigrid methods; domain decomposition
* ''65M60'' Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
* ''65M70'' Spectral, collocation and related methods
* ''65M75'' Probabilistic methods, particle methods, etc.
* ''65M80'' Fundamental solutions, Green's function methods, etc.
* ''65M85'' Fictitious domain methods
* ''65M99'' None of the above, but in this section
!!![[65|65-XX]]Nxx  Partial differential equations, boundary value problems {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/65Nxx.html]]}{{moveright{< [[65Mxx |65Mxx]] | [[65-XX |65-XX]] | [[65Pxx |65Pxx]] >}}}
* ''65N06'' Finite difference methods
* ''65N08'' Finite volume methods
* ''65N12'' Stability and convergence of numerical methods
* ''65N15'' Error bounds
* ''65N20'' Ill-posed problems
* ''65N21'' Inverse problems
* ''65N22'' Solution of discretized equations [See also [[65Fxx|65Fxx]], [[65Hxx|65Hxx]]]
* ''65N25'' Eigenvalue problems
* ''65N30'' Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
* ''65N35'' Spectral, collocation and related methods
* ''65N38'' Boundary element methods
* ''65N40'' Method of lines
* ''65N45'' Method of contraction of the boundary
* ''65N50'' Mesh generation and refinement
* ''65N55'' Multigrid methods; domain decomposition
* ''65N75'' Probabilistic methods, particle methods, etc.
* ''65N80'' Fundamental solutions, Green's function methods, etc.
* ''65N85'' Fictitious domain methods
* ''65N99'' None of the above, but in this section
!!![[65|65-XX]]Pxx  Numerical problems in dynamical systems [See also [[37Mxx|37Mxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/65Pxx.html]]}{{moveright{< [[65Nxx |65Nxx]] | [[65-XX |65-XX]] | [[65Qxx |65Qxx]] >}}}
* ''65P10'' Hamiltonian systems including symplectic integrators
* ''65P20'' Numerical chaos
* ''65P30'' Bifurcation problems
* ''65P40'' Nonlinear stabilities
* ''65P99'' None of the above, but in this section
!!![[65|65-XX]]Qxx  Difference and functional equations, recurrence relations {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/65Qxx.html]]}{{moveright{< [[65Pxx |65Pxx]] | [[65-XX |65-XX]] | [[65Rxx |65Rxx]] >}}}
* ''65Q10'' Difference equations
* ''65Q20'' Functional equations
* ''65Q30'' Recurrence relations
* ''65Q99'' None of the above, but in this section
!!![[65|65-XX]]Rxx  Integral equations, integral transforms {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/65Rxx.html]]}{{moveright{< [[65Qxx |65Qxx]] | [[65-XX |65-XX]] | [[65Sxx |65Sxx]] >}}}
* ''65R10'' Integral transforms
* ''65R20'' Integral equations
* ''65R30'' Improperly posed problems
* ''65R32'' Inverse problems
* ''65R99'' None of the above, but in this section
!!![[65|65-XX]]Sxx  Graphical methods {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/65Sxx.html]]}{{moveright{< [[65Rxx |65Rxx]] | [[65-XX |65-XX]] | [[65Txx |65Txx]] >}}}
* ''65S05'' Graphical methods
* ''65S99'' None of the above, but in this section
!!![[65|65-XX]]Txx  Numerical methods in Fourier analysis {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/65Txx.html]]}{{moveright{< [[65Sxx |65Sxx]] | [[65-XX |65-XX]] | [[65Yxx |65Yxx]] >}}}
* ''65T40'' Trigonometric approximation and interpolation
* ''65T50'' Discrete and fast Fourier transforms
* ''65T60'' Wavelets
* ''65T99'' None of the above, but in this section
!!![[65|65-XX]]Yxx  Computer aspects of numerical algorithms {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/65Yxx.html]]}{{moveright{< [[65Txx |65Txx]] | [[65-XX |65-XX]] | [[65Zxx |65Zxx]] >}}}
* ''65Y04'' Algorithms for computer arithmetic, etc. [See also [[68M07|68Mxx]]]
* ''65Y05'' Parallel computation
* ''65Y10'' Algorithms for specific classes of architectures
* ''65Y15'' Packaged methods
* ''65Y20'' Complexity and performance of numerical algorithms [See also [[68Q25|68Qxx]]]
* ''65Y99'' None of the above, but in this section
!!!65-XX Numerical analysis {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/65-XX.html]]}{{moveright{< [[62-XX |62-XX]] | [[MSC |MSC2010]] | [[65Axx |65Axx]] >}}}
* ''65-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''65-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''65-02'' Research exposition (monographs, survey articles)
* ''65-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''65-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''65-05'' Experimental papers
* ''65-06'' Proceedings, conferences, collections, etc.
* ''[[65Axx|65Axx]]''  Tables
* ''[[65Bxx|65Bxx]]''  Acceleration of convergence
* ''[[65Cxx|65Cxx]]''  Probabilistic methods, simulation and stochastic differential equations {For theoretical aspects, see [[68U20|68Uxx]] and [[60H35|60Hxx]]}
* ''[[65Dxx|65Dxx]]''  Numerical approximation and computational geometry (primarily algorithms) {For theory, see [[41-XX|41-XX]] and [[68Uxx|68Uxx]]}
* ''[[65Exx|65Exx]]''  Numerical methods in complex analysis (potential theory, etc.) {For numerical methods in conformal mapping, see also [[30C30|30Cxx]]}
* ''[[65Fxx|65Fxx]]''  Numerical linear algebra
* ''[[65Gxx|65Gxx]]''  Error analysis and interval analysis
* ''[[65Hxx|65Hxx]]''  Nonlinear algebraic or transcendental equations
* ''[[65Jxx|65Jxx]]''  Numerical analysis in abstract spaces
* ''[[65Kxx|65Kxx]]''  Mathematical programming, optimization and variational techniques
* ''[[65Lxx|65Lxx]]''  Ordinary differential equations
* ''[[65Mxx|65Mxx]]''  Partial differential equations, initial value and time-dependent initial-boundary value problems
* ''[[65Nxx|65Nxx]]''  Partial differential equations, boundary value problems
* ''[[65Pxx|65Pxx]]''  Numerical problems in dynamical systems [See also [[37Mxx|37Mxx]]]
* ''[[65Qxx|65Qxx]]''  Difference and functional equations, recurrence relations
* ''[[65Rxx|65Rxx]]''  Integral equations, integral transforms
* ''[[65Sxx|65Sxx]]''  Graphical methods
* ''[[65Txx|65Txx]]''  Numerical methods in Fourier analysis
* ''[[65Yxx|65Yxx]]''  Computer aspects of numerical algorithms
* ''[[65Zxx|65Zxx]]''  Applications to physics
!!![[65|65-XX]]Zxx  Applications to physics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/65Zxx.html]]}{{moveright{< [[65Yxx |65Yxx]] | [[65-XX |65-XX]] | [[68-XX |68-XX]] >}}}
* ''65Z05'' Applications to physics
* ''65Z99'' None of the above, but in this section
!!![[68|68-XX]]Mxx  Computer system organization {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/68Mxx.html]]}{{moveright{< [[65-XX |65-XX]] | [[68-XX |68-XX]] | [[68Nxx |68Nxx]] >}}}
* ''68M01'' General
* ''68M07'' Mathematical problems of computer architecture
* ''68M10'' Network design and communication [See also [[68R10|68Rxx]], [[90B18|90Bxx]]]
* ''68M11'' Internet topics [See also [[68U35|68Uxx]]]
* ''68M12'' Network protocols
* ''68M14'' Distributed systems
* ''68M15'' Reliability, testing and fault tolerance [See also [[94C12|94Cxx]]]
* ''68M20'' Performance evaluation; queueing; scheduling [See also [[60K25|60Kxx]], [[90Bxx|90Bxx]]]
* ''68M99'' None of the above, but in this section
!!![[68|68-XX]]Nxx  Software {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/68Nxx.html]]}{{moveright{< [[68Mxx |68Mxx]] | [[68-XX |68-XX]] | [[68Pxx |68Pxx]] >}}}
* ''68N01'' General
* ''68N15'' Programming languages
* ''68N17'' Logic programming
* ''68N18'' Functional programming and lambda calculus [See also [[03B40|03Bxx]]]
* ''68N19'' Other programming techniques (object-oriented, sequential, concurrent, automatic, etc.)
* ''68N20'' Compilers and interpreters
* ''68N25'' Operating systems
* ''68N30'' Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)
* ''68N99'' None of the above, but in this section
!!![[68|68-XX]]Pxx  Theory of data {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/68Pxx.html]]}{{moveright{< [[68Nxx |68Nxx]] | [[68-XX |68-XX]] | [[68Qxx |68Qxx]] >}}}
* ''68P01'' General
* ''68P05'' Data structures
* ''68P10'' Searching and sorting
* ''68P15'' Database theory
* ''68P20'' Information storage and retrieval
* ''68P25'' Data encryption [See also [[94A60|94Axx]], [[81P94|81Pxx]]]
* ''68P30'' Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) [See also [[94Axx|94Axx]]]
* ''68P99'' None of the above, but in this section
!!![[68|68-XX]]Qxx  Theory of computing {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/68Qxx.html]]}{{moveright{< [[68Pxx |68Pxx]] | [[68-XX |68-XX]] | [[68Rxx |68Rxx]] >}}}
* ''68Q01'' General
* ''68Q05'' Models of computation (Turing machines, etc.) [See also [[03D10|03Dxx]], [[68Q12|68Qxx]], [[81P68|81Pxx]]]
* ''68Q10'' Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.) [See also [[68Q85|68Qxx]]]
* ''68Q12'' Quantum algorithms and complexity [See also [[68Q05|68Qxx]], [[81P68|81Pxx]]]
* ''68Q15'' Complexity classes (hierarchies, relations among complexity classes, etc.) [See also [[03D15|03Dxx]], [[68Q17|68Qxx]], [[68Q19|68Qxx]]]
* ''68Q17'' Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) [See also [[68Q15|68Qxx]]]
* ''68Q19'' Descriptive complexity and finite models [See also [[03C13|03Cxx]]]
* ''68Q25'' Analysis of algorithms and problem complexity [See also [[68W40|68Wxx]]]
* ''68Q30'' Algorithmic information theory (Kolmogorov complexity, etc.) [See also [[03D32|03Dxx]]]
* ''68Q32'' Computational learning theory [See also [[68T05|68Txx]]]
* ''68Q42'' Grammars and rewriting systems
* ''68Q45'' Formal languages and automata [See also [[03D05|03Dxx]], [[68Q70|68Qxx]], [[94A45|94Axx]]]
* ''68Q55'' Semantics [See also [[03B70|03Bxx]], [[06B35|06Bxx]], [[18C50|18Cxx]]]
* ''68Q60'' Specification and verification (program logics, model checking, etc.) [See also [[03B70|03Bxx]]]
* ''68Q65'' Abstract data types; algebraic specification [See also [[18C50|18Cxx]]]
* ''68Q70'' Algebraic theory of languages and automata [See also [[18B20|18Bxx]], [[20M35|20Mxx]]]
* ''68Q80'' Cellular automata [See also [[37B15|37Bxx]]]
* ''68Q85'' Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
* ''68Q87'' Probability in computer science (algorithm analysis, random structures, phase transitions, etc.) [See also [[68W20|68Wxx]], [[68W40|68Wxx]]]
* ''68Q99'' None of the above, but in this section
!!![[68|68-XX]]Rxx  Discrete mathematics in relation to computer science {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/68Rxx.html]]}{{moveright{< [[68Qxx |68Qxx]] | [[68-XX |68-XX]] | [[68Txx |68Txx]] >}}}
* ''68R01'' General
* ''68R05'' Combinatorics
* ''68R10'' Graph theory (including graph drawing) [See also [[05Cxx|05Cxx]], [[90B10|90Bxx]], [[90B35|90Bxx]], [[90C35|90Cxx]]]
* ''68R15'' Combinatorics on words
* ''68R99'' None of the above, but in this section
!!![[68|68-XX]]Txx  Artificial intelligence {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/68Txx.html]]}{{moveright{< [[68Rxx |68Rxx]] | [[68-XX |68-XX]] | [[68Uxx |68Uxx]] >}}}
* ''68T01'' General
* ''68T05'' Learning and adaptive systems [See also [[68Q32|68Qxx]], [[91E40|91Exx]]]
* ''68T10'' Pattern recognition, speech recognition {For cluster analysis, see [[62H30|62Hxx]]}
* ''68T15'' Theorem proving (deduction, resolution, etc.) [See also [[03B35|03Bxx]]]
* ''68T20'' Problem solving (heuristics, search strategies, etc.)
* ''68T27'' Logic in artificial intelligence
* ''68T30'' Knowledge representation
* ''68T35'' Languages and software systems (knowledge-based systems, expert systems, etc.)
* ''68T37'' Reasoning under uncertainty
* ''68T40'' Robotics [See also [[93C85|93Cxx]]]
* ''68T42'' Agent technology
* ''68T45'' Machine vision and scene understanding
* ''68T50'' Natural language processing [See also [[03B65|03Bxx]]]
* ''68T99'' None of the above, but in this section
!!![[68|68-XX]]Uxx  Computing methodologies and applications {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/68Uxx.html]]}{{moveright{< [[68Txx |68Txx]] | [[68-XX |68-XX]] | [[68Wxx |68Wxx]] >}}}
* ''68U01'' General
* ''68U05'' Computer graphics; computational geometry [See also [[65D18|65Dxx]]]
* ''68U07'' Computer-aided design [See also [[65D17|65Dxx]]]
* ''68U10'' Image processing
* ''68U15'' Text processing; mathematical typography
* ''68U20'' Simulation [See also [[65Cxx|65Cxx]]]
* ''68U35'' Information systems (hypertext navigation, interfaces, decision support, etc.) [See also [[68M11|68Mxx]]]
* ''68U99'' None of the above, but in this section
!!!68-XX Computer science {For papers involving machine computations and programs in a specific mathematical area, see Section–04 in that area} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/68-XX.html]]}{{moveright{< [[65-XX |65-XX]] | [[MSC |MSC2010]] | [[68Mxx |68Mxx]] >}}}
* ''68-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''68-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''68-02'' Research exposition (monographs, survey articles)
* ''68-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''68-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''68-06'' Proceedings, conferences, collections, etc.
* ''[[68Mxx|68Mxx]]''  Computer system organization
* ''[[68Nxx|68Nxx]]''  Software
* ''[[68Pxx|68Pxx]]''  Theory of data
* ''[[68Qxx|68Qxx]]''  Theory of computing
* ''[[68Rxx|68Rxx]]''  Discrete mathematics in relation to computer science
* ''[[68Txx|68Txx]]''  Artificial intelligence
* ''[[68Uxx|68Uxx]]''  Computing methodologies and applications
* ''[[68Wxx|68Wxx]]''  Algorithms {For numerical algorithms, see [[65-XX|65-XX]]; for combinatorics and graph theory, see [[05C85|05Cxx]], [[68Rxx|68Rxx]]}
!!![[68|68-XX]]Wxx  Algorithms {For numerical algorithms, see [[65-XX|65-XX]]; for combinatorics and graph theory, see [[05C85|05Cxx]], [[68Rxx|68Rxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/68Wxx.html]]}{{moveright{< [[68Uxx |68Uxx]] | [[68-XX |68-XX]] | [[70-XX |70-XX]] >}}}
* ''68W01'' General
* ''68W05'' Nonnumerical algorithms
* ''68W10'' Parallel algorithms
* ''68W15'' Distributed algorithms
* ''68W20'' Randomized algorithms
* ''68W25'' Approximation algorithms
* ''68W27'' Online algorithms
* ''68W30'' Symbolic computation and algebraic computation [See also [[11Yxx|11Yxx]], [[12Y05|12Yxx]], [[13Pxx|13Pxx]], [[14Qxx|14Qxx]], [[16Z05|16Zxx]], [[17-08|17-XX]], [[33F10|33Fxx]]]
* ''68W32'' Algorithms on strings
* ''68W35'' VLSI algorithms
* ''68W40'' Analysis of algorithms [See also [[68Q25|68Qxx]]]
* ''68W99'' None of the above, but in this section
!!![[70|70-XX]]Axx  Axiomatics, foundations {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/70Axx.html]]}{{moveright{< [[68-XX |68-XX]] | [[70-XX |70-XX]] | [[70Bxx |70Bxx]] >}}}
* ''70A05'' Axiomatics, foundations
* ''70A99'' None of the above, but in this section
!!![[70|70-XX]]Bxx  Kinematics [See also [[53A17|53Axx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/70Bxx.html]]}{{moveright{< [[70Axx |70Axx]] | [[70-XX |70-XX]] | [[70Cxx |70Cxx]] >}}}
* ''70B05'' Kinematics of a particle
* ''70B10'' Kinematics of a rigid body
* ''70B15'' Mechanisms, robots [See also [[68T40|68Txx]], [[70Q05|70Qxx]], [[93C85|93Cxx]]]
* ''70B99'' None of the above, but in this section
!!![[70|70-XX]]Cxx  Statics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/70Cxx.html]]}{{moveright{< [[70Bxx |70Bxx]] | [[70-XX |70-XX]] | [[70Exx |70Exx]] >}}}
* ''70C20'' Statics
* ''70C99'' None of the above, but in this section
!!![[70|70-XX]]Exx  Dynamics of a rigid body and of multibody systems {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/70Exx.html]]}{{moveright{< [[70Cxx |70Cxx]] | [[70-XX |70-XX]] | [[70Fxx |70Fxx]] >}}}
* ''70E05'' Motion of the gyroscope
* ''70E15'' Free motion of a rigid body [See also [[70M20|70Mxx]]]
* ''70E17'' Motion of a rigid body with a fixed point
* ''70E18'' Motion of a rigid body in contact with a solid surface [See also [[70F25|70Fxx]]]
* ''70E20'' Perturbation methods for rigid body dynamics
* ''70E40'' Integrable cases of motion
* ''70E45'' Higher-dimensional generalizations
* ''70E50'' Stability problems
* ''70E55'' Dynamics of multibody systems
* ''70E60'' Robot dynamics and control [See also [[68T40|68Txx]], [[70Q05|70Qxx]], [[93C85|93Cxx]]]
* ''70E99'' None of the above, but in this section
!!![[70|70-XX]]Fxx  Dynamics of a system of particles, including celestial mechanics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/70Fxx.html]]}{{moveright{< [[70Exx |70Exx]] | [[70-XX |70-XX]] | [[70Gxx |70Gxx]] >}}}
* ''70F05'' Two-body problems
* ''70F07'' Three-body problems
* ''70F10'' $n$-body problems
* ''70F15'' Celestial mechanics
* ''70F16'' Collisions in celestial mechanics, regularization
* ''70F17'' Inverse problems
* ''70F20'' Holonomic systems
* ''70F25'' Nonholonomic systems
* ''70F35'' Collision of rigid or pseudo-rigid bodies
* ''70F40'' Problems with friction
* ''70F45'' Infinite particle systems
* ''70F99'' None of the above, but in this section
!!![[70|70-XX]]Gxx  General models, approaches, and methods [See also [[37-XX|37-XX]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/70Gxx.html]]}{{moveright{< [[70Fxx |70Fxx]] | [[70-XX |70-XX]] | [[70Hxx |70Hxx]] >}}}
* ''70G10'' Generalized coordinates; event, impulse-energy, configuration, state, or phase space
* ''70G40'' Topological and differential-topological methods
* ''70G45'' Differential-geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) [See also [[53Cxx|53Cxx]], [[53Dxx|53Dxx]], [[58Axx|58Axx]]]
* ''70G55'' Algebraic geometry methods
* ''70G60'' Dynamical systems methods
* ''70G65'' Symmetries, Lie-group and Lie-algebra methods
* ''70G70'' Functional-analytic methods
* ''70G75'' Variational methods
* ''70G99'' None of the above, but in this section
!!![[70|70-XX]]Hxx  Hamiltonian and Lagrangian mechanics [See also [[37Jxx|37Jxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/70Hxx.html]]}{{moveright{< [[70Gxx |70Gxx]] | [[70-XX |70-XX]] | [[70Jxx |70Jxx]] >}}}
* ''70H03'' Lagrange's equations
* ''70H05'' Hamilton's equations
* ''70H06'' Completely integrable systems and methods of integration
* ''70H07'' Nonintegrable systems
* ''70H08'' Nearly integrable Hamiltonian systems, KAM theory
* ''70H09'' Perturbation theories
* ''70H11'' Adiabatic invariants
* ''70H12'' Periodic and almost periodic solutions
* ''70H14'' Stability problems
* ''70H15'' Canonical and symplectic transformations
* ''70H20'' ~Hamilton-Jacobi equations
* ''70H25'' Hamilton's principle
* ''70H30'' Other variational principles
* ''70H33'' Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction
* ''70H40'' Relativistic dynamics
* ''70H45'' Constrained dynamics, Dirac's theory of constraints [See also [[70F20|70Fxx]], [[70F25|70Fxx]], [[70Gxx|70Gxx]]]
* ''70H50'' Higher-order theories
* ''70H99'' None of the above, but in this section
!!![[70|70-XX]]Jxx  Linear vibration theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/70Jxx.html]]}{{moveright{< [[70Hxx |70Hxx]] | [[70-XX |70-XX]] | [[70Kxx |70Kxx]] >}}}
* ''70J10'' Modal analysis
* ''70J25'' Stability
* ''70J30'' Free motions
* ''70J35'' Forced motions
* ''70J40'' Parametric resonances
* ''70J50'' Systems arising from the discretization of structural vibration problems
* ''70J99'' None of the above, but in this section
!!![[70|70-XX]]Kxx  Nonlinear dynamics [See also [[34Cxx|34Cxx]], [[37-XX|37-XX]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/70Kxx.html]]}{{moveright{< [[70Jxx |70Jxx]] | [[70-XX |70-XX]] | [[70Lxx |70Lxx]] >}}}
* ''70K05'' Phase plane analysis, limit cycles
* ''70K20'' Stability
* ''70K25'' Free motions
* ''70K28'' Parametric resonances
* ''70K30'' Nonlinear resonances
* ''70K40'' Forced motions
* ''70K42'' Equilibria and periodic trajectories
* ''70K43'' Quasi-periodic motions and invariant tori
* ''70K44'' Homoclinic and heteroclinic trajectories
* ''70K45'' Normal forms
* ''70K50'' Bifurcations and instability
* ''70K55'' Transition to stochasticity (chaotic behavior) [See also [[37D45|37Dxx]]]
* ''70K60'' General perturbation schemes
* ''70K65'' Averaging of perturbations
* ''70K70'' Systems with slow and fast motions
* ''70K75'' Nonlinear modes
* ''70K99'' None of the above, but in this section
!!![[70|70-XX]]Lxx  Random vibrations [See also [[74H50|74Hxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/70Lxx.html]]}{{moveright{< [[70Kxx |70Kxx]] | [[70-XX |70-XX]] | [[70Mxx |70Mxx]] >}}}
* ''70L05'' Random vibrations [See also [[74H50|74Hxx]]]
* ''70L99'' None of the above, but in this section
!!![[70|70-XX]]Mxx  Orbital mechanics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/70Mxx.html]]}{{moveright{< [[70Lxx |70Lxx]] | [[70-XX |70-XX]] | [[70Pxx |70Pxx]] >}}}
* ''70M20'' Orbital mechanics
* ''70M99'' None of the above, but in this section
!!![[70|70-XX]]Pxx  Variable mass, rockets {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/70Pxx.html]]}{{moveright{< [[70Mxx |70Mxx]] | [[70-XX |70-XX]] | [[70Qxx |70Qxx]] >}}}
* ''70P05'' Variable mass, rockets
* ''70P99'' None of the above, but in this section
!!![[70|70-XX]]Qxx  Control of mechanical systems [See also [[60Gxx|60Gxx]], [[60Jxx|60Jxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/70Qxx.html]]}{{moveright{< [[70Pxx |70Pxx]] | [[70-XX |70-XX]] | [[70Sxx |70Sxx]] >}}}
* ''70Q05'' Control of mechanical systems
* ''70Q99'' None of the above, but in this section
!!!70-XX Mechanics of particles and systems {For relativistic mechanics, see [[83A05|83Axx]] and [[83C10|83Cxx]]; for statistical mechanics, see [[82-XX|82-XX]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/70-XX.html]]}{{moveright{< [[68-XX |68-XX]] | [[MSC |MSC2010]] | [[70Axx |70Axx]] >}}}
* ''70-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''70-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''70-02'' Research exposition (monographs, survey articles)
* ''70-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''70-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''70-05'' Experimental work
* ''70-06'' Proceedings, conferences, collections, etc.
* ''70-08'' Computational methods
* ''[[70Axx|70Axx]]''  Axiomatics, foundations
* ''[[70Bxx|70Bxx]]''  Kinematics [See also [[53A17|53Axx]]]
* ''[[70Cxx|70Cxx]]''  Statics
* ''[[70Exx|70Exx]]''  Dynamics of a rigid body and of multibody systems
* ''[[70Fxx|70Fxx]]''  Dynamics of a system of particles, including celestial mechanics
* ''[[70Gxx|70Gxx]]''  General models, approaches, and methods [See also [[37-XX|37-XX]]]
* ''[[70Hxx|70Hxx]]''  Hamiltonian and Lagrangian mechanics [See also [[37Jxx|37Jxx]]]
* ''[[70Jxx|70Jxx]]''  Linear vibration theory
* ''[[70Kxx|70Kxx]]''  Nonlinear dynamics [See also [[34Cxx|34Cxx]], [[37-XX|37-XX]]]
* ''[[70Lxx|70Lxx]]''  Random vibrations [See also [[74H50|74Hxx]]]
* ''[[70Mxx|70Mxx]]''  Orbital mechanics
* ''[[70Pxx|70Pxx]]''  Variable mass, rockets
* ''[[70Qxx|70Qxx]]''  Control of mechanical systems [See also [[60Gxx|60Gxx]], [[60Jxx|60Jxx]]]
* ''[[70Sxx|70Sxx]]''  Classical field theories [See also [[37Kxx|37Kxx]], [[37Lxx|37Lxx]], [[78-XX|78-XX]], [[81Txx|81Txx]], [[83-XX|83-XX]]]
!!![[70|70-XX]]Sxx  Classical field theories [See also [[37Kxx|37Kxx]], [[37Lxx|37Lxx]], [[78-XX|78-XX]], [[81Txx|81Txx]], [[83-XX|83-XX]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/70Sxx.html]]}{{moveright{< [[70Qxx |70Qxx]] | [[70-XX |70-XX]] | [[74-XX |74-XX]] >}}}
* ''70S05'' Lagrangian formalism and Hamiltonian formalism
* ''70S10'' Symmetries and conservation laws
* ''70S15'' ~Yang-Mills and other gauge theories
* ''70S20'' More general nonquantum field theories
* ''70S99'' None of the above, but in this section
!!![[74|74-XX]]Axx  Generalities, axiomatics, foundations of continuum mechanics of solids {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/74Axx.html]]}{{moveright{< [[70-XX |70-XX]] | [[74-XX |74-XX]] | [[74Bxx |74Bxx]] >}}}
* ''74A05'' Kinematics of deformation
* ''74A10'' Stress
* ''74A15'' Thermodynamics
* ''74A20'' Theory of constitutive functions
* ''74A25'' Molecular, statistical, and kinetic theories
* ''74A30'' Nonsimple materials
* ''74A35'' Polar materials
* ''74A40'' Random materials and composite materials
* ''74A45'' Theories of fracture and damage
* ''74A50'' Structured surfaces and interfaces, coexistent phases
* ''74A55'' Theories of friction (tribology)
* ''74A60'' Micromechanical theories
* ''74A65'' Reactive materials
* ''74A99'' None of the above, but in this section
!!![[74|74-XX]]Bxx  Elastic materials {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/74Bxx.html]]}{{moveright{< [[74Axx |74Axx]] | [[74-XX |74-XX]] | [[74Cxx |74Cxx]] >}}}
* ''74B05'' Classical linear elasticity
* ''74B10'' Linear elasticity with initial stresses
* ''74B15'' Equations linearized about a deformed state (small deformations superposed on large)
* ''74B20'' Nonlinear elasticity
* ''74B99'' None of the above, but in this section
!!![[74|74-XX]]Cxx  Plastic materials, materials of stress-rate and internal-variable type {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/74Cxx.html]]}{{moveright{< [[74Bxx |74Bxx]] | [[74-XX |74-XX]] | [[74Dxx |74Dxx]] >}}}
* ''74C05'' Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials)
* ''74C10'' Small-strain, rate-dependent theories (including theories of viscoplasticity)
* ''74C15'' Large-strain, rate-independent theories (including nonlinear plasticity)
* ''74C20'' Large-strain, rate-dependent theories
* ''74C99'' None of the above, but in this section
!!![[74|74-XX]]Dxx  Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/74Dxx.html]]}{{moveright{< [[74Cxx |74Cxx]] | [[74-XX |74-XX]] | [[74Exx |74Exx]] >}}}
* ''74D05'' Linear constitutive equations
* ''74D10'' Nonlinear constitutive equations
* ''74D99'' None of the above, but in this section
!!![[74|74-XX]]Exx  Material properties given special treatment {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/74Exx.html]]}{{moveright{< [[74Dxx |74Dxx]] | [[74-XX |74-XX]] | [[74Fxx |74Fxx]] >}}}
* ''74E05'' Inhomogeneity
* ''74E10'' Anisotropy
* ''74E15'' Crystalline structure
* ''74E20'' Granularity
* ''74E25'' Texture
* ''74E30'' Composite and mixture properties
* ''74E35'' Random structure
* ''74E40'' Chemical structure
* ''74E99'' None of the above, but in this section
!!![[74|74-XX]]Fxx  Coupling of solid mechanics with other effects {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/74Fxx.html]]}{{moveright{< [[74Exx |74Exx]] | [[74-XX |74-XX]] | [[74Gxx |74Gxx]] >}}}
* ''74F05'' Thermal effects
* ''74F10'' Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
* ''74F15'' Electromagnetic effects
* ''74F20'' Mixture effects
* ''74F25'' Chemical and reactive effects
* ''74F99'' None of the above, but in this section
!!![[74|74-XX]]Gxx  Equilibrium (steady-state) problems {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/74Gxx.html]]}{{moveright{< [[74Fxx |74Fxx]] | [[74-XX |74-XX]] | [[74Hxx |74Hxx]] >}}}
* ''74G05'' Explicit solutions
* ''74G10'' Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.)
* ''74G15'' Numerical approximation of solutions
* ''74G20'' Local existence of solutions (near a given solution)
* ''74G25'' Global existence of solutions
* ''74G30'' Uniqueness of solutions
* ''74G35'' Multiplicity of solutions
* ''74G40'' Regularity of solutions
* ''74G45'' Bounds for solutions
* ''74G50'' ~Saint-Venant's principle
* ''74G55'' Qualitative behavior of solutions
* ''74G60'' Bifurcation and buckling
* ''74G65'' Energy minimization
* ''74G70'' Stress concentrations, singularities
* ''74G75'' Inverse problems
* ''74G99'' None of the above, but in this section
!!![[74|74-XX]]Hxx  Dynamical problems {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/74Hxx.html]]}{{moveright{< [[74Gxx |74Gxx]] | [[74-XX |74-XX]] | [[74Jxx |74Jxx]] >}}}
* ''74H05'' Explicit solutions
* ''74H10'' Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.)
* ''74H15'' Numerical approximation of solutions
* ''74H20'' Existence of solutions
* ''74H25'' Uniqueness of solutions
* ''74H30'' Regularity of solutions
* ''74H35'' Singularities, blowup, stress concentrations
* ''74H40'' Long-time behavior of solutions
* ''74H45'' Vibrations
* ''74H50'' Random vibrations
* ''74H55'' Stability
* ''74H60'' Dynamical bifurcation
* ''74H65'' Chaotic behavior
* ''74H99'' None of the above, but in this section
!!![[74|74-XX]]Jxx  Waves {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/74Jxx.html]]}{{moveright{< [[74Hxx |74Hxx]] | [[74-XX |74-XX]] | [[74Kxx |74Kxx]] >}}}
* ''74J05'' Linear waves
* ''74J10'' Bulk waves
* ''74J15'' Surface waves
* ''74J20'' Wave scattering
* ''74J25'' Inverse problems
* ''74J30'' Nonlinear waves
* ''74J35'' Solitary waves
* ''74J40'' Shocks and related discontinuities
* ''74J99'' None of the above, but in this section
!!![[74|74-XX]]Kxx  Thin bodies, structures {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/74Kxx.html]]}{{moveright{< [[74Jxx |74Jxx]] | [[74-XX |74-XX]] | [[74Lxx |74Lxx]] >}}}
* ''74K05'' Strings
* ''74K10'' Rods (beams, columns, shafts, arches, rings, etc.)
* ''74K15'' Membranes
* ''74K20'' Plates
* ''74K25'' Shells
* ''74K30'' Junctions
* ''74K35'' Thin films
* ''74K99'' None of the above, but in this section
!!![[74|74-XX]]Lxx  Special subfields of solid mechanics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/74Lxx.html]]}{{moveright{< [[74Kxx |74Kxx]] | [[74-XX |74-XX]] | [[74Mxx |74Mxx]] >}}}
* ''74L05'' Geophysical solid mechanics [See also [[86-XX|86-XX]]]
* ''74L10'' Soil and rock mechanics
* ''74L15'' Biomechanical solid mechanics [See also [[92C10|92Cxx]]]
* ''74L99'' None of the above, but in this section
!!![[74|74-XX]]Mxx  Special kinds of problems {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/74Mxx.html]]}{{moveright{< [[74Lxx |74Lxx]] | [[74-XX |74-XX]] | [[74Nxx |74Nxx]] >}}}
* ''74M05'' Control, switches and devices (“smart materials”) [See also [[93Cxx|93Cxx]]]
* ''74M10'' Friction
* ''74M15'' Contact
* ''74M20'' Impact
* ''74M25'' Micromechanics
* ''74M99'' None of the above, but in this section
!!![[74|74-XX]]Nxx  Phase transformations in solids [See also [[74A50|74Axx]], [[80Axx|80Axx]], [[82B26|82Bxx]], [[82C26|82Cxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/74Nxx.html]]}{{moveright{< [[74Mxx |74Mxx]] | [[74-XX |74-XX]] | [[74Pxx |74Pxx]] >}}}
* ''74N05'' Crystals
* ''74N10'' Displacive transformations
* ''74N15'' Analysis of microstructure
* ''74N20'' Dynamics of phase boundaries
* ''74N25'' Transformations involving diffusion
* ''74N30'' Problems involving hysteresis
* ''74N99'' None of the above, but in this section
!!![[74|74-XX]]Pxx  Optimization [See also [[49Qxx|49Qxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/74Pxx.html]]}{{moveright{< [[74Nxx |74Nxx]] | [[74-XX |74-XX]] | [[74Qxx |74Qxx]] >}}}
* ''74P05'' Compliance or weight optimization
* ''74P10'' Optimization of other properties
* ''74P15'' Topological methods
* ''74P20'' Geometrical methods
* ''74P99'' None of the above, but in this section
!!![[74|74-XX]]Qxx  Homogenization, determination of effective properties {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/74Qxx.html]]}{{moveright{< [[74Pxx |74Pxx]] | [[74-XX |74-XX]] | [[74Rxx |74Rxx]] >}}}
* ''74Q05'' Homogenization in equilibrium problems
* ''74Q10'' Homogenization and oscillations in dynamical problems
* ''74Q15'' Effective constitutive equations
* ''74Q20'' Bounds on effective properties
* ''74Q99'' None of the above, but in this section
!!![[74|74-XX]]Rxx  Fracture and damage {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/74Rxx.html]]}{{moveright{< [[74Qxx |74Qxx]] | [[74-XX |74-XX]] | [[74Sxx |74Sxx]] >}}}
* ''74R05'' Brittle damage
* ''74R10'' Brittle fracture
* ''74R15'' High-velocity fracture
* ''74R20'' Anelastic fracture and damage
* ''74R99'' None of the above, but in this section
!!!74-XX Mechanics of deformable solids {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/74-XX.html]]}{{moveright{< [[70-XX |70-XX]] | [[MSC |MSC2010]] | [[74Axx |74Axx]] >}}}
* ''74-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''74-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''74-02'' Research exposition (monographs, survey articles)
* ''74-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''74-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''74-05'' Experimental work
* ''74-06'' Proceedings, conferences, collections, etc.
* ''[[74Axx|74Axx]]''  Generalities, axiomatics, foundations of continuum mechanics of solids
* ''[[74Bxx|74Bxx]]''  Elastic materials
* ''[[74Cxx|74Cxx]]''  Plastic materials, materials of stress-rate and internal-variable type
* ''[[74Dxx|74Dxx]]''  Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
* ''[[74Exx|74Exx]]''  Material properties given special treatment
* ''[[74Fxx|74Fxx]]''  Coupling of solid mechanics with other effects
* ''[[74Gxx|74Gxx]]''  Equilibrium (steady-state) problems
* ''[[74Hxx|74Hxx]]''  Dynamical problems
* ''[[74Jxx|74Jxx]]''  Waves
* ''[[74Kxx|74Kxx]]''  Thin bodies, structures
* ''[[74Lxx|74Lxx]]''  Special subfields of solid mechanics
* ''[[74Mxx|74Mxx]]''  Special kinds of problems
* ''[[74Nxx|74Nxx]]''  Phase transformations in solids [See also [[74A50|74Axx]], [[80Axx|80Axx]], [[82B26|82Bxx]], [[82C26|82Cxx]]]
* ''[[74Pxx|74Pxx]]''  Optimization [See also [[49Qxx|49Qxx]]]
* ''[[74Qxx|74Qxx]]''  Homogenization, determination of effective properties
* ''[[74Rxx|74Rxx]]''  Fracture and damage
* ''[[74Sxx|74Sxx]]''  Numerical methods [See also [[65-XX|65-XX]], [[74G15|74Gxx]], [[74H15|74Hxx]]]
!!![[74|74-XX]]Sxx  Numerical methods [See also [[65-XX|65-XX]], [[74G15|74Gxx]], [[74H15|74Hxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/74Sxx.html]]}{{moveright{< [[74Rxx |74Rxx]] | [[74-XX |74-XX]] | [[76-XX |76-XX]] >}}}
* ''74S05'' Finite element methods
* ''74S10'' Finite volume methods
* ''74S15'' Boundary element methods
* ''74S20'' Finite difference methods
* ''74S25'' Spectral and related methods
* ''74S30'' Other numerical methods
* ''74S60'' Stochastic methods
* ''74S70'' Complex variable methods
* ''74S99'' None of the above, but in this section
!!![[76|76-XX]]Axx  Foundations, constitutive equations, rheology {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Axx.html]]}{{moveright{< [[74-XX |74-XX]] | [[76-XX |76-XX]] | [[76Bxx |76Bxx]] >}}}
* ''76A02'' Foundations of fluid mechanics
* ''76A05'' ~Non-Newtonian fluids
* ''76A10'' Viscoelastic fluids
* ''76A15'' Liquid crystals [See also [[82D30|82Dxx]]]
* ''76A20'' Thin fluid films
* ''76A25'' Superfluids (classical aspects)
* ''76A99'' None of the above, but in this section
!!![[76|76-XX]]Bxx  Incompressible inviscid fluids {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Bxx.html]]}{{moveright{< [[76Axx |76Axx]] | [[76-XX |76-XX]] | [[76Dxx |76Dxx]] >}}}
* ''76B03'' Existence, uniqueness, and regularity theory [See also [[35Q35|35Qxx]]]
* ''76B07'' Free-surface potential flows
* ''76B10'' Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
* ''76B15'' Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also [[35Q30|35Qxx]]]
* ''76B20'' Ship waves
* ''76B25'' Solitary waves [See also [[35C11|35Cxx]]]
* ''76B45'' Capillarity (surface tension) [See also [[76D45|76Dxx]]]
* ''76B47'' Vortex flows
* ''76B55'' Internal waves
* ''76B60'' Atmospheric waves [See also [[86A10|86Axx]]]
* ''76B65'' Rossby waves [See also [[86A05|86Axx]], [[86A10|86Axx]]]
* ''76B70'' Stratification effects in inviscid fluids
* ''76B75'' Flow control and optimization [See also [[49Q10|49Qxx]], [[93C20|93Cxx]], [[93C95|93Cxx]]]
* ''76B99'' None of the above, but in this section
!!![[76|76-XX]]Dxx  Incompressible viscous fluids {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Dxx.html]]}{{moveright{< [[76Bxx |76Bxx]] | [[76-XX |76-XX]] | [[76Exx |76Exx]] >}}}
* ''76D03'' Existence, uniqueness, and regularity theory [See also [[35Q30|35Qxx]]]
* ''76D05'' ~Navier-Stokes equations [See also [[35Q30|35Qxx]]]
* ''76D06'' Statistical solutions of ~Navier-Stokes and related equations [See also [[60H30|60Hxx]], [[76M35|76Mxx]]]
* ''76D07'' Stokes and related (Oseen, etc.) flows
* ''76D08'' Lubrication theory
* ''76D09'' Viscous-inviscid interaction
* ''76D10'' Boundary-layer theory, separation and reattachment, higher-order effects
* ''76D17'' Viscous vortex flows
* ''76D25'' Wakes and jets
* ''76D27'' Other free-boundary flows; ~Hele-Shaw flows
* ''76D33'' Waves
* ''76D45'' Capillarity (surface tension) [See also [[76B45|76Bxx]]]
* ''76D50'' Stratification effects in viscous fluids
* ''76D55'' Flow control and optimization [See also [[49Q10|49Qxx]], [[93C20|93Cxx]], [[93C95|93Cxx]]]
* ''76D99'' None of the above, but in this section
!!![[76|76-XX]]Exx  Hydrodynamic stability {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Exx.html]]}{{moveright{< [[76Dxx |76Dxx]] | [[76-XX |76-XX]] | [[76Fxx |76Fxx]] >}}}
* ''76E05'' Parallel shear flows
* ''76E06'' Convection
* ''76E07'' Rotation
* ''76E09'' Stability and instability of nonparallel flows
* ''76E15'' Absolute and convective instability and stability
* ''76E17'' Interfacial stability and instability
* ''76E19'' Compressibility effects
* ''76E20'' Stability and instability of geophysical and astrophysical flows
* ''76E25'' Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
* ''76E30'' Nonlinear effects
* ''76E99'' None of the above, but in this section
!!![[76|76-XX]]Fxx  Turbulence [See also [[37-XX|37-XX]], [[60Gxx|60Gxx]], [[60Jxx|60Jxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Fxx.html]]}{{moveright{< [[76Exx |76Exx]] | [[76-XX |76-XX]] | [[76Gxx |76Gxx]] >}}}
* ''76F02'' Fundamentals
* ''76F05'' Isotropic turbulence; homogeneous turbulence
* ''76F06'' Transition to turbulence
* ''76F10'' Shear flows
* ''76F20'' Dynamical systems approach to turbulence [See also [[37-XX|37-XX]]]
* ''76F25'' Turbulent transport, mixing
* ''76F30'' Renormalization and other field-theoretical methods [See also [[81T99|81Txx]]]
* ''76F35'' Convective turbulence [See also [[76E15|76Exx]], [[76Rxx|76Rxx]]]
* ''76F40'' Turbulent boundary layers
* ''76F45'' Stratification effects
* ''76F50'' Compressibility effects
* ''76F55'' Statistical turbulence modeling [See also [[76M35|76Mxx]]]
* ''76F60'' $k$-$\varepsilon$ modeling
* ''76F65'' Direct numerical and large eddy simulation of turbulence
* ''76F70'' Control of turbulent flows
* ''76F99'' None of the above, but in this section
!!![[76|76-XX]]Gxx  General aerodynamics and subsonic flows {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Gxx.html]]}{{moveright{< [[76Fxx |76Fxx]] | [[76-XX |76-XX]] | [[76Hxx |76Hxx]] >}}}
* ''76G25'' General aerodynamics and subsonic flows
* ''76G99'' None of the above, but in this section
!!![[76|76-XX]]Hxx  Transonic flows {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Hxx.html]]}{{moveright{< [[76Gxx |76Gxx]] | [[76-XX |76-XX]] | [[76Jxx |76Jxx]] >}}}
* ''76H05'' Transonic flows
* ''76H99'' None of the above, but in this section
!!![[76|76-XX]]Jxx  Supersonic flows {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Jxx.html]]}{{moveright{< [[76Hxx |76Hxx]] | [[76-XX |76-XX]] | [[76Kxx |76Kxx]] >}}}
* ''76J20'' Supersonic flows
* ''76J99'' None of the above, but in this section
!!![[76|76-XX]]Kxx  Hypersonic flows {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Kxx.html]]}{{moveright{< [[76Jxx |76Jxx]] | [[76-XX |76-XX]] | [[76Lxx |76Lxx]] >}}}
* ''76K05'' Hypersonic flows
* ''76K99'' None of the above, but in this section
!!![[76|76-XX]]Lxx  Shock waves and blast waves [See also [[35L67|35Lxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Lxx.html]]}{{moveright{< [[76Kxx |76Kxx]] | [[76-XX |76-XX]] | [[76Mxx |76Mxx]] >}}}
* ''76L05'' Shock waves and blast waves [See also [[35L67|35Lxx]]]
* ''76L99'' None of the above, but in this section
!!![[76|76-XX]]Mxx  Basic methods in fluid mechanics [See also [[65-XX|65-XX]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Mxx.html]]}{{moveright{< [[76Lxx |76Lxx]] | [[76-XX |76-XX]] | [[76Nxx |76Nxx]] >}}}
* ''76M10'' Finite element methods
* ''76M12'' Finite volume methods
* ''76M15'' Boundary element methods
* ''76M20'' Finite difference methods
* ''76M22'' Spectral methods
* ''76M23'' Vortex methods
* ''76M25'' Other numerical methods
* ''76M27'' Visualization algorithms
* ''76M28'' Particle methods and lattice-gas methods
* ''76M30'' Variational methods
* ''76M35'' Stochastic analysis
* ''76M40'' Complex-variables methods
* ''76M45'' Asymptotic methods, singular perturbations
* ''76M50'' Homogenization
* ''76M55'' Dimensional analysis and similarity
* ''76M60'' Symmetry analysis, Lie group and algebra methods
* ''76M99'' None of the above, but in this section
!!![[76|76-XX]]Nxx  Compressible fluids and gas dynamics, general {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Nxx.html]]}{{moveright{< [[76Mxx |76Mxx]] | [[76-XX |76-XX]] | [[76Pxx |76Pxx]] >}}}
* ''76N10'' Existence, uniqueness, and regularity theory [See also [[35L60|35Lxx]], [[35L65|35Lxx]], [[35Q30|35Qxx]]]
* ''76N15'' Gas dynamics, general
* ''76N17'' Viscous-inviscid interaction
* ''76N20'' Boundary-layer theory
* ''76N25'' Flow control and optimization
* ''76N99'' None of the above, but in this section
!!![[76|76-XX]]Pxx  Rarefied gas flows, Boltzmann equation [See also [[82B40|82Bxx]], [[82C40|82Cxx]], [[82D05|82Dxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Pxx.html]]}{{moveright{< [[76Nxx |76Nxx]] | [[76-XX |76-XX]] | [[76Qxx |76Qxx]] >}}}
* ''76P05'' Rarefied gas flows, Boltzmann equation [See also [[82B40|82Bxx]], [[82C40|82Cxx]], [[82D05|82Dxx]]]
* ''76P99'' None of the above, but in this section
!!![[76|76-XX]]Qxx  Hydro- and aero-acoustics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Qxx.html]]}{{moveright{< [[76Pxx |76Pxx]] | [[76-XX |76-XX]] | [[76Rxx |76Rxx]] >}}}
* ''76Q05'' Hydro- and aero-acoustics
* ''76Q99'' None of the above, but in this section
!!![[76|76-XX]]Rxx  Diffusion and convection {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Rxx.html]]}{{moveright{< [[76Qxx |76Qxx]] | [[76-XX |76-XX]] | [[76Sxx |76Sxx]] >}}}
* ''76R05'' Forced convection
* ''76R10'' Free convection
* ''76R50'' Diffusion [See also [[60J60|60Jxx]]]
* ''76R99'' None of the above, but in this section
!!![[76|76-XX]]Sxx  Flows in porous media; filtration; seepage {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Sxx.html]]}{{moveright{< [[76Rxx |76Rxx]] | [[76-XX |76-XX]] | [[76Txx |76Txx]] >}}}
* ''76S05'' Flows in porous media; filtration; seepage
* ''76S99'' None of the above, but in this section
!!![[76|76-XX]]Txx  Two-phase and multiphase flows {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Txx.html]]}{{moveright{< [[76Sxx |76Sxx]] | [[76-XX |76-XX]] | [[76Uxx |76Uxx]] >}}}
* ''76T10'' Liquid-gas two-phase flows, bubbly flows
* ''76T15'' Dusty-gas two-phase flows
* ''76T20'' Suspensions
* ''76T25'' Granular flows [See also [[74C99|74Cxx]], [[74E20|74Exx]]]
* ''76T30'' Three or more component flows
* ''76T99'' None of the above, but in this section
!!![[76|76-XX]]Uxx  Rotating fluids {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Uxx.html]]}{{moveright{< [[76Txx |76Txx]] | [[76-XX |76-XX]] | [[76Vxx |76Vxx]] >}}}
* ''76U05'' Rotating fluids
* ''76U99'' None of the above, but in this section
!!![[76|76-XX]]Vxx  Reaction effects in flows [See also [[80A32|80Axx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Vxx.html]]}{{moveright{< [[76Uxx |76Uxx]] | [[76-XX |76-XX]] | [[76Wxx |76Wxx]] >}}}
* ''76V05'' Reaction effects in flows [See also [[80A32|80Axx]]]
* ''76V99'' None of the above, but in this section
!!![[76|76-XX]]Wxx  Magnetohydrodynamics and electrohydrodynamics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Wxx.html]]}{{moveright{< [[76Vxx |76Vxx]] | [[76-XX |76-XX]] | [[76Xxx |76Xxx]] >}}}
* ''76W05'' Magnetohydrodynamics and electrohydrodynamics
* ''76W99'' None of the above, but in this section
!!![[76|76-XX]]Xxx  Ionized gas flow in electromagnetic fields; plasmic flow [See also [[82D10|82Dxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Xxx.html]]}{{moveright{< [[76Wxx |76Wxx]] | [[76-XX |76-XX]] | [[76Yxx |76Yxx]] >}}}
* ''76X05'' Ionized gas flow in electromagnetic fields; plasmic flow [See also [[82D10|82Dxx]]]
* ''76X99'' None of the above, but in this section
!!![[76|76-XX]]Yxx  Quantum hydrodynamics and relativistic hydrodynamics [See also [[82D50|82Dxx]], [[83C55|83Cxx]], [[85A30|85Axx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Yxx.html]]}{{moveright{< [[76Xxx |76Xxx]] | [[76-XX |76-XX]] | [[76Zxx |76Zxx]] >}}}
* ''76Y05'' Quantum hydrodynamics and relativistic hydrodynamics [See also [[82D50|82Dxx]], [[83C55|83Cxx]], [[85A30|85Axx]]]
* ''76Y99'' None of the above, but in this section
!!!76-XX Fluid mechanics {For general continuum mechanics, see [[74Axx|74Axx]], or other parts of [[74-XX|74-XX]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76-XX.html]]}{{moveright{< [[74-XX |74-XX]] | [[MSC |MSC2010]] | [[76Axx |76Axx]] >}}}
* ''76-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''76-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''76-02'' Research exposition (monographs, survey articles)
* ''76-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''76-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''76-05'' Experimental work
* ''76-06'' Proceedings, conferences, collections, etc.
* ''[[76Axx|76Axx]]''  Foundations, constitutive equations, rheology
* ''[[76Bxx|76Bxx]]''  Incompressible inviscid fluids
* ''[[76Dxx|76Dxx]]''  Incompressible viscous fluids
* ''[[76Exx|76Exx]]''  Hydrodynamic stability
* ''[[76Fxx|76Fxx]]''  Turbulence [See also [[37-XX|37-XX]], [[60Gxx|60Gxx]], [[60Jxx|60Jxx]]]
* ''[[76Gxx|76Gxx]]''  General aerodynamics and subsonic flows
* ''[[76Hxx|76Hxx]]''  Transonic flows
* ''[[76Jxx|76Jxx]]''  Supersonic flows
* ''[[76Kxx|76Kxx]]''  Hypersonic flows
* ''[[76Lxx|76Lxx]]''  Shock waves and blast waves [See also [[35L67|35Lxx]]]
* ''[[76Mxx|76Mxx]]''  Basic methods in fluid mechanics [See also [[65-XX|65-XX]]]
* ''[[76Nxx|76Nxx]]''  Compressible fluids and gas dynamics, general
* ''[[76Pxx|76Pxx]]''  Rarefied gas flows, Boltzmann equation [See also [[82B40|82Bxx]], [[82C40|82Cxx]], [[82D05|82Dxx]]]
* ''[[76Qxx|76Qxx]]''  Hydro- and aero-acoustics
* ''[[76Rxx|76Rxx]]''  Diffusion and convection
* ''[[76Sxx|76Sxx]]''  Flows in porous media; filtration; seepage
* ''[[76Txx|76Txx]]''  Two-phase and multiphase flows
* ''[[76Uxx|76Uxx]]''  Rotating fluids
* ''[[76Vxx|76Vxx]]''  Reaction effects in flows [See also [[80A32|80Axx]]]
* ''[[76Wxx|76Wxx]]''  Magnetohydrodynamics and electrohydrodynamics
* ''[[76Xxx|76Xxx]]''  Ionized gas flow in electromagnetic fields; plasmic flow [See also [[82D10|82Dxx]]]
* ''[[76Yxx|76Yxx]]''  Quantum hydrodynamics and relativistic hydrodynamics [See also [[82D50|82Dxx]], [[83C55|83Cxx]], [[85A30|85Axx]]]
* ''[[76Zxx|76Zxx]]''  Biological fluid mechanics [See also [[74F10|74Fxx]], [[74L15|74Lxx]], [[92Cxx|92Cxx]]]
!!![[76|76-XX]]Zxx  Biological fluid mechanics [See also [[74F10|74Fxx]], [[74L15|74Lxx]], [[92Cxx|92Cxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/76Zxx.html]]}{{moveright{< [[76Yxx |76Yxx]] | [[76-XX |76-XX]] | [[78-XX |78-XX]] >}}}
* ''76Z05'' Physiological flows [See also [[92C35|92Cxx]]]
* ''76Z10'' Biopropulsion in water and in air
* ''76Z99'' None of the above, but in this section
!!![[78|78-XX]]Axx  General {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/78Axx.html]]}{{moveright{< [[76-XX |76-XX]] | [[78-XX |78-XX]] | [[78Mxx |78Mxx]] >}}}
* ''78A02'' Foundations
* ''78A05'' Geometric optics
* ''78A10'' Physical optics
* ''78A15'' Electron optics
* ''78A20'' Space charge waves
* ''78A25'' Electromagnetic theory, general
* ''78A30'' Electro- and magnetostatics
* ''78A35'' Motion of charged particles
* ''78A37'' Ion traps
* ''78A40'' Waves and radiation
* ''78A45'' Diffraction, scattering [See also [[34E20|34Exx]] for WKB methods]
* ''78A46'' Inverse scattering problems
* ''78A48'' Composite media; random media
* ''78A50'' Antennas, wave-guides
* ''78A55'' Technical applications
* ''78A57'' Electrochemistry
* ''78A60'' Lasers, masers, optical bistability, nonlinear optics [See also [[81V80|81Vxx]]]
* ''78A70'' Biological applications [See also [[91D30|91Dxx]], [[92C30|92Cxx]]]
* ''78A97'' Mathematically heuristic optics and electromagnetic theory (must also be assigned at least one other classification number in this section)
* ''78A99'' Miscellaneous topics
!!!78-XX Optics, electromagnetic theory {For quantum optics, see [[81V80|81Vxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/78-XX.html]]}{{moveright{< [[76-XX |76-XX]] | [[MSC |MSC2010]] | [[78Axx |78Axx]] >}}}
* ''78-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''78-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''78-02'' Research exposition (monographs, survey articles)
* ''78-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''78-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''78-05'' Experimental work
* ''78-06'' Proceedings, conferences, collections, etc.
* ''[[78Axx|78Axx]]''  General
* ''[[78Mxx|78Mxx]]''  Basic methods
!!![[78|78-XX]]Mxx  Basic methods {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/78Mxx.html]]}{{moveright{< [[78Axx |78Axx]] | [[78-XX |78-XX]] | [[80-XX |80-XX]] >}}}
* ''78M05'' Method of moments
* ''78M10'' Finite element methods
* ''78M12'' Finite volume methods, finite integration techniques
* ''78M15'' Boundary element methods
* ''78M16'' Multipole methods
* ''78M20'' Finite difference methods
* ''78M22'' Spectral methods
* ''78M25'' Other numerical methods
* ''78M30'' Variational methods
* ''78M31'' Monte Carlo methods
* ''78M32'' Neural and heuristic methods
* ''78M34'' Model reduction
* ''78M35'' Asymptotic analysis
* ''78M40'' Homogenization
* ''78M50'' Optimization
* ''78M99'' None of the above, but in this section
!!![[80|80-XX]]Axx  Thermodynamics and heat transfer {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/80Axx.html]]}{{moveright{< [[78-XX |78-XX]] | [[80-XX |80-XX]] | [[80Mxx |80Mxx]] >}}}
* ''80A05'' Foundations
* ''80A10'' Classical thermodynamics, including relativistic
* ''80A17'' Thermodynamics of continua [See also [[74A15|74Axx]]]
* ''80A20'' Heat and mass transfer, heat flow
* ''80A22'' Stefan problems, phase changes, etc. [See also [[74Nxx|74Nxx]]]
* ''80A23'' Inverse problems
* ''80A25'' Combustion
* ''80A30'' Chemical kinetics [See also [[76V05|76Vxx]], [[92C45|92Cxx]], [[92E20|92Exx]]]
* ''80A32'' Chemically reacting flows [See also [[92C45|92Cxx]], [[92E20|92Exx]]]
* ''80A50'' Chemistry (general) [See mainly [[92Exx|92Exx]]]
* ''80A99'' None of the above, but in this section
!!!80-XX Classical thermodynamics, heat transfer {For thermodynamics of solids, see [[74A15|74Axx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/80-XX.html]]}{{moveright{< [[78-XX |78-XX]] | [[MSC |MSC2010]] | [[80Axx |80Axx]] >}}}
* ''80-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''80-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''80-02'' Research exposition (monographs, survey articles)
* ''80-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''80-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''80-05'' Experimental work
* ''80-06'' Proceedings, conferences, collections, etc.
* ''[[80Axx|80Axx]]''  Thermodynamics and heat transfer
* ''[[80Mxx|80Mxx]]''  Basic methods
!!![[80|80-XX]]Mxx  Basic methods {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/80Mxx.html]]}{{moveright{< [[80Axx |80Axx]] | [[80-XX |80-XX]] | [[81-XX |81-XX]] >}}}
* ''80M10'' Finite element methods
* ''80M12'' Finite volume methods
* ''80M15'' Boundary element methods
* ''80M20'' Finite difference methods
* ''80M22'' Spectral methods
* ''80M25'' Other numerical methods
* ''80M30'' Variational methods
* ''80M31'' Monte Carlo methods
* ''80M35'' Asymptotic analysis
* ''80M40'' Homogenization
* ''80M50'' Optimization
* ''80M99'' None of the above, but in this section
!!![[81|81-XX]]Pxx  Axiomatics, foundations, philosophy {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/81Pxx.html]]}{{moveright{< [[80-XX |80-XX]] | [[81-XX |81-XX]] | [[81Qxx |81Qxx]] >}}}
* ''81P05'' General and philosophical
* ''81P10'' Logical foundations of quantum mechanics; quantum logic [See also [[03G12|03Gxx]], [[06C15|06Cxx]]]
* ''81P13'' Contextuality
* ''81P15'' Quantum measurement theory
* ''81P16'' Quantum state spaces, operational and probabilistic concepts
* ''81P20'' Stochastic mechanics (including stochastic electrodynamics)
* ''81P40'' Quantum coherence, entanglement, quantum correlations
* ''81P45'' Quantum information, communication, networks [See also [[94A15|94Axx]], [[94A17|94Axx]]]
* ''81P50'' Quantum state estimation, approximate cloning
* ''81P68'' Quantum computation [See also [[68Q05|68Qxx]], [[68Q12|68Qxx]]]
* ''81P70'' Quantum coding (general)
* ''81P94'' Quantum cryptography [See also [[94A60|94Axx]]]
* ''81P99'' None of the above, but in this section
!!![[81|81-XX]]Qxx  General mathematical topics and methods in quantum theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/81Qxx.html]]}{{moveright{< [[81Pxx |81Pxx]] | [[81-XX |81-XX]] | [[81Rxx |81Rxx]] >}}}
* ''81Q05'' Closed and approximate solutions to the Schrödinger, Dirac, ~Klein-Gordon and other equations of quantum mechanics
* ''81Q10'' Selfadjoint operator theory in quantum theory, including spectral analysis
* ''81Q12'' ~Non-selfadjoint operator theory in quantum theory
* ''81Q15'' Perturbation theories for operators and differential equations
* ''81Q20'' Semiclassical techniques, including WKB and Maslov methods
* ''81Q30'' Feynman integrals and graphs; applications of algebraic topology and algebraic geometry [See also [[14D05|14Dxx]], [[32S40|32Sxx]]]
* ''81Q35'' Quantum mechanics on special spaces: manifolds, fractals, graphs, etc.
* ''81Q37'' Quantum dots, waveguides, ratchets, etc.
* ''81Q40'' ~Bethe-Salpeter and other integral equations
* ''81Q50'' Quantum chaos [See also [[37Dxx|37Dxx]]]
* ''81Q60'' Supersymmetry and quantum mechanics
* ''81Q65'' Alternative quantum mechanics
* ''81Q70'' Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.
* ''81Q80'' Special quantum systems, such as solvable systems
* ''81Q93'' Quantum control
* ''81Q99'' None of the above, but in this section
!!![[81|81-XX]]Rxx  Groups and algebras in quantum theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/81Rxx.html]]}{{moveright{< [[81Qxx |81Qxx]] | [[81-XX |81-XX]] | [[81Sxx |81Sxx]] >}}}
* ''81R05'' Finite-dimensional groups and algebras motivated by physics and their representations [See also [[20C35|20Cxx]], [[22E70|22Exx]]]
* ''81R10'' Infinite-dimensional groups and algebras motivated by physics, including Virasoro, ~Kac-Moody, $W$-algebras and other current algebras and their representations [See also [[17B65|17Bxx]], [[17B67|17Bxx]], [[22E65|22Exx]], [[22E67|22Exx]], [[22E70|22Exx]]]
* ''81R12'' Relations with integrable systems [See also [[17Bxx|17Bxx]], [[37J35|37Jxx]]]
* ''81R15'' Operator algebra methods [See also [[46Lxx|46Lxx]], [[81T05|81Txx]]]
* ''81R20'' Covariant wave equations
* ''81R25'' Spinor and twistor methods [See also [[32L25|32Lxx]]]
* ''81R30'' Coherent states [See also [[22E45|22Exx]]]; squeezed states [See also [[81V80|81Vxx]]]
* ''81R40'' Symmetry breaking
* ''81R50'' Quantum groups and related algebraic methods [See also [[16T20|16Txx]], [[17B37|17Bxx]]]
* ''81R60'' Noncommutative geometry
* ''81R99'' None of the above, but in this section
!!![[81|81-XX]]Sxx  General quantum mechanics and problems of quantization {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/81Sxx.html]]}{{moveright{< [[81Rxx |81Rxx]] | [[81-XX |81-XX]] | [[81Txx |81Txx]] >}}}
* ''81S05'' Canonical quantization, commutation relations and statistics
* ''81S10'' Geometry and quantization, symplectic methods [See also [[53D50|53Dxx]]]
* ''81S20'' Stochastic quantization
* ''81S22'' Open systems, reduced dynamics, master equations, decoherence [See also [[82C31|82Cxx]]]
* ''81S25'' Quantum stochastic calculus
* ''81S30'' Phase-space methods including Wigner distributions, etc.
* ''81S40'' Path integrals [See also [[58D30|58Dxx]]]
* ''81S99'' None of the above, but in this section
!!![[81|81-XX]]Txx  Quantum field theory; related classical field theories [See also [[70Sxx|70Sxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/81Txx.html]]}{{moveright{< [[81Sxx |81Sxx]] | [[81-XX |81-XX]] | [[81Uxx |81Uxx]] >}}}
* ''81T05'' Axiomatic quantum field theory; operator algebras
* ''81T08'' Constructive quantum field theory
* ''81T10'' Model quantum field theories
* ''81T13'' ~Yang-Mills and other gauge theories [See also [[53C07|53Cxx]], [[58E15|58Exx]]]
* ''81T15'' Perturbative methods of renormalization
* ''81T16'' Nonperturbative methods of renormalization
* ''81T17'' Renormalization group methods
* ''81T18'' Feynman diagrams
* ''81T20'' Quantum field theory on curved space backgrounds
* ''81T25'' Quantum field theory on lattices
* ''81T27'' Continuum limits
* ''81T28'' Thermal quantum field theory [See also [[82B30|82Bxx]]]
* ''81T30'' String and superstring theories; other extended objects (e.g., branes) [See also [[83E30|83Exx]]]
* ''81T40'' Two-dimensional field theories, conformal field theories, etc.
* ''81T45'' Topological field theories [See also [[57R56|57Rxx]], [[58Dxx|58Dxx]]]
* ''81T50'' Anomalies
* ''81T55'' Casimir effect
* ''81T60'' Supersymmetric field theories
* ''81T70'' Quantization in field theory; cohomological methods [See also [[58D29|58Dxx]]]
* ''81T75'' Noncommutative geometry methods [See also [[46L85|46Lxx]], [[46L87|46Lxx]], [[58B34|58Bxx]]]
* ''81T80'' Simulation and numerical modeling
* ''81T99'' None of the above, but in this section
!!![[81|81-XX]]Uxx  Scattering theory [See also [[34A55|34Axx]], [[34L25|34Lxx]], [[34L40|34Lxx]], [[35P25|35Pxx]], [[47A40|47Axx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/81Uxx.html]]}{{moveright{< [[81Txx |81Txx]] | [[81-XX |81-XX]] | [[81Vxx |81Vxx]] >}}}
* ''81U05'' $2$-body potential scattering theory [See also [[34E20|34Exx]] for WKB methods]
* ''81U10'' $n$-body potential scattering theory
* ''81U15'' Exactly and quasi-solvable systems
* ''81U20'' $S$-matrix theory, etc.
* ''81U30'' Dispersion theory, dispersion relations
* ''81U35'' Inelastic and multichannel scattering
* ''81U40'' Inverse scattering problems
* ''81U99'' None of the above, but in this section
!!!81-XX Quantum theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/81-XX.html]]}{{moveright{< [[80-XX |80-XX]] | [[MSC |MSC2010]] | [[81Pxx |81Pxx]] >}}}
* ''81-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''81-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''81-02'' Research exposition (monographs, survey articles)
* ''81-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''81-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''81-05'' Experimental papers
* ''81-06'' Proceedings, conferences, collections, etc.
* ''81-08'' Computational methods
* ''[[81Pxx|81Pxx]]''  Axiomatics, foundations, philosophy
* ''[[81Qxx|81Qxx]]''  General mathematical topics and methods in quantum theory
* ''[[81Rxx|81Rxx]]''  Groups and algebras in quantum theory
* ''[[81Sxx|81Sxx]]''  General quantum mechanics and problems of quantization
* ''[[81Txx|81Txx]]''  Quantum field theory; related classical field theories [See also [[70Sxx|70Sxx]]]
* ''[[81Uxx|81Uxx]]''  Scattering theory [See also [[34A55|34Axx]], [[34L25|34Lxx]], [[34L40|34Lxx]], [[35P25|35Pxx]], [[47A40|47Axx]]]
* ''[[81Vxx|81Vxx]]''  Applications to specific physical systems
!!![[81|81-XX]]Vxx  Applications to specific physical systems {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/81Vxx.html]]}{{moveright{< [[81Uxx |81Uxx]] | [[81-XX |81-XX]] | [[82-XX |82-XX]] >}}}
* ''81V05'' Strong interaction, including quantum chromodynamics
* ''81V10'' Electromagnetic interaction; quantum electrodynamics
* ''81V15'' Weak interaction
* ''81V17'' Gravitational interaction [See also [[83Cxx|83Cxx]] and [[83Exx|83Exx]]]
* ''81V19'' Other fundamental interactions
* ''81V22'' Unified theories
* ''81V25'' Other elementary particle theory
* ''81V35'' Nuclear physics
* ''81V45'' Atomic physics
* ''81V55'' Molecular physics [See also [[92E10|92Exx]]]
* ''81V65'' Quantum dots [See also [[82D20|82Dxx]]]
* ''81V70'' Many-body theory; quantum Hall effect
* ''81V80'' Quantum optics
* ''81V99'' None of the above, but in this section
!!![[82|82-XX]]Bxx  Equilibrium statistical mechanics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/82Bxx.html]]}{{moveright{< [[81-XX |81-XX]] | [[82-XX |82-XX]] | [[82Cxx |82Cxx]] >}}}
* ''82B03'' Foundations
* ''82B05'' Classical equilibrium statistical mechanics (general)
* ''82B10'' Quantum equilibrium statistical mechanics (general)
* ''82B20'' Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
* ''82B21'' Continuum models (systems of particles, etc.)
* ''82B23'' Exactly solvable models; Bethe ansatz
* ''82B24'' Interface problems; diffusion-limited aggregation
* ''82B26'' Phase transitions (general)
* ''82B27'' Critical phenomena
* ''82B28'' Renormalization group methods [See also [[81T17|81Txx]]]
* ''82B30'' Statistical thermodynamics [See also [[80-XX|80-XX]]]
* ''82B31'' Stochastic methods
* ''82B35'' Irreversible thermodynamics, including ~Onsager-Machlup theory [See also [[92E20|92Exx]]]
* ''82B40'' Kinetic theory of gases
* ''82B41'' Random walks, random surfaces, lattice animals, etc. [See also [[60G50|60Gxx]], [[82C41|82Cxx]]]
* ''82B43'' Percolation [See also [[60K35|60Kxx]]]
* ''82B44'' Disordered systems (random Ising models, random Schrödinger operators, etc.)
* ''82B80'' Numerical methods (Monte Carlo, series resummation, etc.) [See also [[65-XX|65-XX]], [[81T80|81Txx]]]
* ''82B99'' None of the above, but in this section
!!![[82|82-XX]]Cxx  Time-dependent statistical mechanics (dynamic and nonequilibrium) {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/82Cxx.html]]}{{moveright{< [[82Bxx |82Bxx]] | [[82-XX |82-XX]] | [[82Dxx |82Dxx]] >}}}
* ''82C03'' Foundations
* ''82C05'' Classical dynamic and nonequilibrium statistical mechanics (general)
* ''82C10'' Quantum dynamics and nonequilibrium statistical mechanics (general)
* ''82C20'' Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs
* ''82C21'' Dynamic continuum models (systems of particles, etc.)
* ''82C22'' Interacting particle systems [See also [[60K35|60Kxx]]]
* ''82C23'' Exactly solvable dynamic models [See also [[37K60|37Kxx]]]
* ''82C24'' Interface problems; diffusion-limited aggregation
* ''82C26'' Dynamic and nonequilibrium phase transitions (general)
* ''82C27'' Dynamic critical phenomena
* ''82C28'' Dynamic renormalization group methods [See also [[81T17|81Txx]]]
* ''82C31'' Stochastic methods (~Fokker-Planck, Langevin, etc.) [See also [[60H10|60Hxx]]]
* ''82C32'' Neural nets [See also [[68T05|68Txx]], [[91E40|91Exx]], [[92B20|92Bxx]]]
* ''82C35'' Irreversible thermodynamics, including ~Onsager-Machlup theory
* ''82C40'' Kinetic theory of gases
* ''82C41'' Dynamics of random walks, random surfaces, lattice animals, etc. [See also [[60G50|60Gxx]]]
* ''82C43'' Time-dependent percolation [See also [[60K35|60Kxx]]]
* ''82C44'' Dynamics of disordered systems (random Ising systems, etc.)
* ''82C70'' Transport processes
* ''82C80'' Numerical methods (Monte Carlo, series resummation, etc.)
* ''82C99'' None of the above, but in this section
!!!82-XX Statistical mechanics, structure of matter {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/82-XX.html]]}{{moveright{< [[81-XX |81-XX]] | [[MSC |MSC2010]] | [[82Bxx |82Bxx]] >}}}
* ''82-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''82-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''82-02'' Research exposition (monographs, survey articles)
* ''82-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''82-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''82-05'' Experimental papers
* ''82-06'' Proceedings, conferences, collections, etc.
* ''82-08'' Computational methods
* ''[[82Bxx|82Bxx]]''  Equilibrium statistical mechanics
* ''[[82Cxx|82Cxx]]''  Time-dependent statistical mechanics (dynamic and nonequilibrium)
* ''[[82Dxx|82Dxx]]''  Applications to specific types of physical systems
!!![[82|82-XX]]Dxx  Applications to specific types of physical systems {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/82Dxx.html]]}{{moveright{< [[82Cxx |82Cxx]] | [[82-XX |82-XX]] | [[83-XX |83-XX]] >}}}
* ''82D05'' Gases
* ''82D10'' Plasmas
* ''82D15'' Liquids
* ''82D20'' Solids
* ''82D25'' Crystals {For crystallographic group theory, see [[20H15|20Hxx]]}
* ''82D30'' Random media, disordered materials (including liquid crystals and spin glasses)
* ''82D35'' Metals
* ''82D37'' Semiconductors
* ''82D40'' Magnetic materials
* ''82D45'' Ferroelectrics
* ''82D50'' Superfluids
* ''82D55'' Superconductors
* ''82D60'' Polymers
* ''82D75'' Nuclear reactor theory; neutron transport
* ''82D77'' Quantum wave guides, quantum wires [See also [[78A50|78Axx]]]
* ''82D80'' Nanostructures and nanoparticles
* ''82D99'' None of the above, but in this section
!!![[83|83-XX]]Axx  Special relativity {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/83Axx.html]]}{{moveright{< [[82-XX |82-XX]] | [[83-XX |83-XX]] | [[83Bxx |83Bxx]] >}}}
* ''83A05'' Special relativity
* ''83A99'' None of the above, but in this section
!!![[83|83-XX]]Bxx  Observational and experimental questions {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/83Bxx.html]]}{{moveright{< [[83Axx |83Axx]] | [[83-XX |83-XX]] | [[83Cxx |83Cxx]] >}}}
* ''83B05'' Observational and experimental questions
* ''83B99'' None of the above, but in this section
!!![[83|83-XX]]Cxx  General relativity {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/83Cxx.html]]}{{moveright{< [[83Bxx |83Bxx]] | [[83-XX |83-XX]] | [[83Dxx |83Dxx]] >}}}
* ''83C05'' Einstein's equations (general structure, canonical formalism, Cauchy problems)
* ''83C10'' Equations of motion
* ''83C15'' Exact solutions
* ''83C20'' Classes of solutions; algebraically special solutions, metrics with symmetries
* ''83C22'' ~Einstein-Maxwell equations
* ''83C25'' Approximation procedures, weak fields
* ''83C27'' Lattice gravity, Regge calculus and other discrete methods
* ''83C30'' Asymptotic procedures (radiation, news functions, $\scr H$-spaces, etc.)
* ''83C35'' Gravitational waves
* ''83C40'' Gravitational energy and conservation laws; groups of motions
* ''83C45'' Quantization of the gravitational field
* ''83C47'' Methods of quantum field theory [See also [[81T20|81Txx]]]
* ''83C50'' Electromagnetic fields
* ''83C55'' Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
* ''83C57'' Black holes
* ''83C60'' Spinor and twistor methods; ~Newman-Penrose formalism
* ''83C65'' Methods of noncommutative geometry [See also [[58B34|58Bxx]]]
* ''83C75'' Space-time singularities, cosmic censorship, etc.
* ''83C80'' Analogues in lower dimensions
* ''83C99'' None of the above, but in this section
!!![[83|83-XX]]Dxx  Relativistic gravitational theories other than Einstein's, including asymmetric field theories {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/83Dxx.html]]}{{moveright{< [[83Cxx |83Cxx]] | [[83-XX |83-XX]] | [[83Exx |83Exx]] >}}}
* ''83D05'' Relativistic gravitational theories other than Einstein's, including asymmetric field theories
* ''83D99'' None of the above, but in this section
!!![[83|83-XX]]Exx  Unified, higher-dimensional and super field theories {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/83Exx.html]]}{{moveright{< [[83Dxx |83Dxx]] | [[83-XX |83-XX]] | [[83Fxx |83Fxx]] >}}}
* ''83E05'' Geometrodynamics
* ''83E15'' ~Kaluza-Klein and other higher-dimensional theories
* ''83E30'' String and superstring theories [See also [[81T30|81Txx]]]
* ''83E50'' Supergravity
* ''83E99'' None of the above, but in this section
!!!83-XX Relativity and gravitational theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/83-XX.html]]}{{moveright{< [[82-XX |82-XX]] | [[MSC |MSC2010]] | [[83Axx |83Axx]] >}}}
* ''83-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''83-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''83-02'' Research exposition (monographs, survey articles)
* ''83-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''83-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''83-05'' Experimental work
* ''83-06'' Proceedings, conferences, collections, etc.
* ''83-08'' Computational methods
* ''[[83Axx|83Axx]]''  Special relativity
* ''[[83Bxx|83Bxx]]''  Observational and experimental questions
* ''[[83Cxx|83Cxx]]''  General relativity
* ''[[83Dxx|83Dxx]]''  Relativistic gravitational theories other than Einstein's, including asymmetric field theories
* ''[[83Exx|83Exx]]''  Unified, higher-dimensional and super field theories
* ''[[83Fxx|83Fxx]]''  Cosmology
!!![[83|83-XX]]Fxx  Cosmology {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/83Fxx.html]]}{{moveright{< [[83Exx |83Exx]] | [[83-XX |83-XX]] | [[85-XX |85-XX]] >}}}
* ''83F05'' Cosmology
* ''83F99'' None of the above, but in this section
!!!85-XX Astronomy and astrophysics {For celestial mechanics, see [[70F15|70Fxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/85-XX.html]]}{{moveright{< [[83-XX |83-XX]] | [[MSC |MSC2010]] | [[85Axx |85Axx]] >}}}
* ''85-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''85-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''85-02'' Research exposition (monographs, survey articles)
* ''85-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''85-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''85-05'' Experimental work
* ''85-06'' Proceedings, conferences, collections, etc.
* ''85-08'' Computational methods
* ''[[85Axx|85Axx]]''  Astronomy and astrophysics {For celestial mechanics, see [[70F15|70Fxx]]}
!!![[85|85-XX]]Axx  Astronomy and astrophysics {For celestial mechanics, see [[70F15|70Fxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/85Axx.html]]}{{moveright{< [[83-XX |83-XX]] | [[85-XX |85-XX]] | [[86-XX |86-XX]] >}}}
* ''85A04'' General
* ''85A05'' Galactic and stellar dynamics
* ''85A15'' Galactic and stellar structure
* ''85A20'' Planetary atmospheres
* ''85A25'' Radiative transfer
* ''85A30'' Hydrodynamic and hydromagnetic problems [See also [[76Y05|76Yxx]]]
* ''85A35'' Statistical astronomy
* ''85A40'' Cosmology {For relativistic cosmology, see [[83F05|83Fxx]]}
* ''85A99'' Miscellaneous topics
!!!86-XX Geophysics [See also [[76U05|76Uxx]], [[76V05|76Vxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/86-XX.html]]}{{moveright{< [[85-XX |85-XX]] | [[MSC |MSC2010]] | [[86Axx |86Axx]] >}}}
* ''86-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''86-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''86-02'' Research exposition (monographs, survey articles)
* ''86-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''86-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''86-05'' Experimental work
* ''86-06'' Proceedings, conferences, collections, etc.
* ''86-08'' Computational methods
* ''[[86Axx|86Axx]]''  Geophysics [See also [[76U05|76Uxx]], [[76V05|76Vxx]]]
!!![[86|86-XX]]Axx  Geophysics [See also [[76U05|76Uxx]], [[76V05|76Vxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/86Axx.html]]}{{moveright{< [[85-XX |85-XX]] | [[86-XX |86-XX]] | [[90-XX |90-XX]] >}}}
* ''86A04'' General
* ''86A05'' Hydrology, hydrography, oceanography [See also [[76Bxx|76Bxx]], [[76E20|76Exx]], [[76Q05|76Qxx]], [[76Rxx|76Rxx]], [[76U05|76Uxx]]]
* ''86A10'' Meteorology and atmospheric physics [See also [[76Bxx|76Bxx]], [[76E20|76Exx]], [[76N15|76Nxx]], [[76Q05|76Qxx]], [[76Rxx|76Rxx]], [[76U05|76Uxx]]]
* ''86A15'' Seismology
* ''86A17'' Global dynamics, earthquake problems
* ''86A20'' Potentials, prospecting
* ''86A22'' Inverse problems [See also [[35R30|35Rxx]]]
* ''86A25'' Geo-electricity and geomagnetism [See also [[76W05|76Wxx]], [[78A25|78Axx]]]
* ''86A30'' Geodesy, mapping problems
* ''86A32'' Geostatistics
* ''86A40'' Glaciology
* ''86A60'' Geological problems
* ''86A99'' Miscellaneous topics
!!![[90|90-XX]]Bxx  Operations research and management science {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/90Bxx.html]]}{{moveright{< [[86-XX |86-XX]] | [[90-XX |90-XX]] | [[90Cxx |90Cxx]] >}}}
* ''90B05'' Inventory, storage, reservoirs
* ''90B06'' Transportation, logistics
* ''90B10'' Network models, deterministic
* ''90B15'' Network models, stochastic
* ''90B18'' Communication networks [See also [[68M10|68Mxx]], [[94A05|94Axx]]]
* ''90B20'' Traffic problems
* ''90B22'' Queues and service [See also [[60K25|60Kxx]], [[68M20|68Mxx]]]
* ''90B25'' Reliability, availability, maintenance, inspection [See also [[60K10|60Kxx]], [[62N05|62Nxx]]]
* ''90B30'' Production models
* ''90B35'' Scheduling theory, deterministic [See also [[68M20|68Mxx]]]
* ''90B36'' Scheduling theory, stochastic [See also [[68M20|68Mxx]]]
* ''90B40'' Search theory
* ''90B50'' Management decision making, including multiple objectives [See also [[90C29|90Cxx]], [[90C31|90Cxx]], [[91A35|91Axx]], [[91B06|91Bxx]]]
* ''90B60'' Marketing, advertising [See also [[91B60|91Bxx]]]
* ''90B70'' Theory of organizations, manpower planning [See also [[91D35|91Dxx]]]
* ''90B80'' Discrete location and assignment [See also [[90C10|90Cxx]]]
* ''90B85'' Continuous location
* ''90B90'' Case-oriented studies
* ''90B99'' None of the above, but in this section
!!!90-XX Operations research, mathematical programming {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/90-XX.html]]}{{moveright{< [[86-XX |86-XX]] | [[MSC |MSC2010]] | [[90Bxx |90Bxx]] >}}}
* ''90-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''90-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''90-02'' Research exposition (monographs, survey articles)
* ''90-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''90-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''90-06'' Proceedings, conferences, collections, etc.
* ''90-08'' Computational methods
* ''[[90Bxx|90Bxx]]''  Operations research and management science
* ''[[90Cxx|90Cxx]]''  Mathematical programming [See also [[49Mxx|49Mxx]], [[65Kxx|65Kxx]]]
!!![[90|90-XX]]Cxx  Mathematical programming [See also [[49Mxx|49Mxx]], [[65Kxx|65Kxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/90Cxx.html]]}{{moveright{< [[90Bxx |90Bxx]] | [[90-XX |90-XX]] | [[91-XX |91-XX]] >}}}
* ''90C05'' Linear programming
* ''90C06'' Large-scale problems
* ''90C08'' Special problems of linear programming (transportation, multi-index, etc.)
* ''90C09'' Boolean programming
* ''90C10'' Integer programming
* ''90C11'' Mixed integer programming
* ''90C15'' Stochastic programming
* ''90C20'' Quadratic programming
* ''90C22'' Semidefinite programming
* ''90C25'' Convex programming
* ''90C26'' Nonconvex programming, global optimization
* ''90C27'' Combinatorial optimization
* ''90C29'' Multi-objective and goal programming
* ''90C30'' Nonlinear programming
* ''90C31'' Sensitivity, stability, parametric optimization
* ''90C32'' Fractional programming
* ''90C33'' Complementarity and equilibrium problems and variational inequalities (finite dimensions)
* ''90C34'' Semi-infinite programming
* ''90C35'' Programming involving graphs or networks [See also [[90C27|90Cxx]]]
* ''90C39'' Dynamic programming [See also [[49L20|49Lxx]]]
* ''90C40'' Markov and semi-Markov decision processes
* ''90C46'' Optimality conditions, duality [See also [[49N15|49Nxx]]]
* ''90C47'' Minimax problems [See also [[49K35|49Kxx]]]
* ''90C48'' Programming in abstract spaces
* ''90C49'' Extreme-point and pivoting methods
* ''90C51'' Interior-point methods
* ''90C52'' Methods of reduced gradient type
* ''90C53'' Methods of quasi-Newton type
* ''90C55'' Methods of successive quadratic programming type
* ''90C56'' Derivative-free methods and methods using generalized derivatives [See also [[49J52|49Jxx]]]
* ''90C57'' Polyhedral combinatorics, branch-and-bound, branch-and-cut
* ''90C59'' Approximation methods and heuristics
* ''90C60'' Abstract computational complexity for mathematical programming problems [See also [[68Q25|68Qxx]]]
* ''90C70'' Fuzzy programming
* ''90C90'' Applications of mathematical programming
* ''90C99'' None of the above, but in this section
!!![[91|91-XX]]Axx  Game theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/91Axx.html]]}{{moveright{< [[90-XX |90-XX]] | [[91-XX |91-XX]] | [[91Bxx |91Bxx]] >}}}
* ''91A05'' 2-person games
* ''91A06'' $n$-person games, $n>2$
* ''91A10'' Noncooperative games
* ''91A12'' Cooperative games
* ''91A13'' Games with infinitely many players
* ''91A15'' Stochastic games
* ''91A18'' Games in extensive form
* ''91A20'' Multistage and repeated games
* ''91A22'' Evolutionary games
* ''91A23'' Differential games [See also [[49N70|49Nxx]]]
* ''91A24'' Positional games (pursuit and evasion, etc.) [See also [[49N75|49Nxx]]]
* ''91A25'' Dynamic games
* ''91A26'' Rationality, learning
* ''91A28'' Signaling, communication
* ''91A30'' Utility theory for games [See also [[91B16|91Bxx]]]
* ''91A35'' Decision theory for games [See also [[62Cxx|62Cxx]], [[91B06|91Bxx]], [[90B50|90Bxx]]]
* ''91A40'' Game-theoretic models
* ''91A43'' Games involving graphs [See also [[05C57|05Cxx]]]
* ''91A44'' Games involving topology or set theory
* ''91A46'' Combinatorial games
* ''91A50'' Discrete-time games
* ''91A55'' Games of timing
* ''91A60'' Probabilistic games; gambling [See also [[60G40|60Gxx]]]
* ''91A65'' Hierarchical games
* ''91A70'' Spaces of games
* ''91A80'' Applications of game theory
* ''91A90'' Experimental studies
* ''91A99'' None of the above, but in this section
!!![[91|91-XX]]Bxx  Mathematical economics {For econometrics, see [[62P20|62Pxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/91Bxx.html]]}{{moveright{< [[91Axx |91Axx]] | [[91-XX |91-XX]] | [[91Cxx |91Cxx]] >}}}
* ''91B02'' Fundamental topics (basic mathematics, methodology; applicable to economics in general)
* ''91B06'' Decision theory [See also [[62Cxx|62Cxx]], [[90B50|90Bxx]], [[91A35|91Axx]]]
* ''91B08'' Individual preferences
* ''91B10'' Group preferences
* ''91B12'' Voting theory
* ''91B14'' Social choice
* ''91B15'' Welfare economics
* ''91B16'' Utility theory
* ''91B18'' Public goods
* ''91B24'' Price theory and market structure
* ''91B25'' Asset pricing models
* ''91B26'' Market models (auctions, bargaining, bidding, selling, etc.)
* ''91B30'' Risk theory, insurance
* ''91B32'' Resource and cost allocation
* ''91B38'' Production theory, theory of the firm
* ''91B40'' Labor market, contracts
* ''91B42'' Consumer behavior, demand theory
* ''91B44'' Informational economics
* ''91B50'' General equilibrium theory
* ''91B51'' Dynamic stochastic general equilibrium theory
* ''91B52'' Special types of equilibria
* ''91B54'' Special types of economies
* ''91B55'' Economic dynamics
* ''91B60'' Trade models
* ''91B62'' Growth models
* ''91B64'' Macro-economic models (monetary models, models of taxation)
* ''91B66'' Multisectoral models
* ''91B68'' Matching models
* ''91B69'' Heterogeneous agent models
* ''91B70'' Stochastic models
* ''91B72'' Spatial models
* ''91B74'' Models of real-world systems
* ''91B76'' Environmental economics (natural resource models, harvesting, pollution, etc.)
* ''91B80'' Applications of statistical and quantum mechanics to economics (econophysics)
* ''91B82'' Statistical methods; economic indices and measures
* ''91B84'' Economic time series analysis [See also [[62M10|62Mxx]]]
* ''91B99'' None of the above, but in this section
!!![[91|91-XX]]Cxx  Social and behavioral sciences: general topics {For statistics, see [[62-XX|62-XX]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/91Cxx.html]]}{{moveright{< [[91Bxx |91Bxx]] | [[91-XX |91-XX]] | [[91Dxx |91Dxx]] >}}}
* ''91C05'' Measurement theory
* ''91C15'' One- and multidimensional scaling
* ''91C20'' Clustering [See also [[62H30|62Hxx]]]
* ''91C99'' None of the above, but in this section
!!![[91|91-XX]]Dxx  Mathematical sociology (including anthropology) {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/91Dxx.html]]}{{moveright{< [[91Cxx |91Cxx]] | [[91-XX |91-XX]] | [[91Exx |91Exx]] >}}}
* ''91D10'' Models of societies, social and urban evolution
* ''91D20'' Mathematical geography and demography
* ''91D25'' Spatial models [See also [[91B72|91Bxx]]]
* ''91D30'' Social networks
* ''91D35'' Manpower systems [See also [[91B40|91Bxx]], [[90B70|90Bxx]]]
* ''91D99'' None of the above, but in this section
!!![[91|91-XX]]Exx  Mathematical psychology {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/91Exx.html]]}{{moveright{< [[91Dxx |91Dxx]] | [[91-XX |91-XX]] | [[91Fxx |91Fxx]] >}}}
* ''91E10'' Cognitive psychology
* ''91E30'' Psychophysics and psychophysiology; perception
* ''91E40'' Memory and learning [See also [[68T05|68Txx]]]
* ''91E45'' Measurement and performance
* ''91E99'' None of the above, but in this section
!!![[91|91-XX]]Fxx  Other social and behavioral sciences (mathematical treatment) {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/91Fxx.html]]}{{moveright{< [[91Exx |91Exx]] | [[91-XX |91-XX]] | [[91Gxx |91Gxx]] >}}}
* ''91F10'' History, political science
* ''91F20'' Linguistics [See also [[03B65|03Bxx]], [[68T50|68Txx]]]
* ''91F99'' None of the above, but in this section
!!!91-XX Game theory, economics, social and behavioral sciences {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/91-XX.html]]}{{moveright{< [[90-XX |90-XX]] | [[MSC |MSC2010]] | [[91Axx |91Axx]] >}}}
* ''91-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''91-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''91-02'' Research exposition (monographs, survey articles)
* ''91-03'' Historical (must also be assigned at least one classification number from section 01)
* ''91-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''91-06'' Proceedings, conferences, collections, etc.
* ''91-08'' Computational methods
* ''[[91Axx|91Axx]]''  Game theory
* ''[[91Bxx|91Bxx]]''  Mathematical economics {For econometrics, see [[62P20|62Pxx]]}
* ''[[91Cxx|91Cxx]]''  Social and behavioral sciences: general topics {For statistics, see [[62-XX|62-XX]]}
* ''[[91Dxx|91Dxx]]''  Mathematical sociology (including anthropology)
* ''[[91Exx|91Exx]]''  Mathematical psychology
* ''[[91Fxx|91Fxx]]''  Other social and behavioral sciences (mathematical treatment)
* ''[[91Gxx|91Gxx]]''  Mathematical finance
!!![[91|91-XX]]Gxx  Mathematical finance {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/91Gxx.html]]}{{moveright{< [[91Fxx |91Fxx]] | [[91-XX |91-XX]] | [[92-XX |92-XX]] >}}}
* ''91G10'' Portfolio theory
* ''91G20'' Derivative securities
* ''91G30'' Interest rates (stochastic models)
* ''91G40'' Credit risk
* ''91G50'' Corporate finance
* ''91G60'' Numerical methods (including Monte Carlo methods)
* ''91G70'' Statistical methods, econometrics
* ''91G80'' Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)
* ''91G99'' None of the above, but in this section
!!![[92|92-XX]]Bxx  Mathematical biology in general {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/92Bxx.html]]}{{moveright{< [[91-XX |91-XX]] | [[92-XX |92-XX]] | [[92Cxx |92Cxx]] >}}}
* ''92B05'' General biology and biomathematics
* ''92B10'' Taxonomy, cladistics, statistics
* ''92B15'' General biostatistics [See also [[62P10|62Pxx]]]
* ''92B20'' Neural networks, artificial life and related topics [See also [[68T05|68Txx]], [[82C32|82Cxx]], [[94Cxx|94Cxx]]]
* ''92B25'' Biological rhythms and synchronization
* ''92B99'' None of the above, but in this section
!!![[92|92-XX]]Cxx  Physiological, cellular and medical topics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/92Cxx.html]]}{{moveright{< [[92Bxx |92Bxx]] | [[92-XX |92-XX]] | [[92Dxx |92Dxx]] >}}}
* ''92C05'' Biophysics
* ''92C10'' Biomechanics [See also [[74L15|74Lxx]]]
* ''92C15'' Developmental biology, pattern formation
* ''92C17'' Cell movement (chemotaxis, etc.)
* ''92C20'' Neural biology
* ''92C30'' Physiology (general)
* ''92C35'' Physiological flow [See also [[76Z05|76Zxx]]]
* ''92C37'' Cell biology
* ''92C40'' Biochemistry, molecular biology
* ''92C42'' Systems biology, networks
* ''92C45'' Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) [See also [[80A30|80Axx]]]
* ''92C50'' Medical applications (general)
* ''92C55'' Biomedical imaging and signal processing [See also [[44A12|44Axx]], [[65R10|65Rxx]], [[94A08|94Axx]], [[94A12|94Axx]]]
* ''92C60'' Medical epidemiology
* ''92C80'' Plant biology
* ''92C99'' None of the above, but in this section
!!![[92|92-XX]]Dxx  Genetics and population dynamics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/92Dxx.html]]}{{moveright{< [[92Cxx |92Cxx]] | [[92-XX |92-XX]] | [[92Exx |92Exx]] >}}}
* ''92D10'' Genetics {For genetic algebras, see [[17D92|17Dxx]]}
* ''92D15'' Problems related to evolution
* ''92D20'' Protein sequences, DNA sequences
* ''92D25'' Population dynamics (general)
* ''92D30'' Epidemiology
* ''92D40'' Ecology
* ''92D50'' Animal behavior
* ''92D99'' None of the above, but in this section
!!![[92|92-XX]]Exx  Chemistry {For biochemistry, see [[92C40|92Cxx]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/92Exx.html]]}{{moveright{< [[92Dxx |92Dxx]] | [[92-XX |92-XX]] | [[92Fxx |92Fxx]] >}}}
* ''92E10'' Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
* ''92E20'' Classical flows, reactions, etc. [See also [[80A30|80Axx]], [[80A32|80Axx]]]
* ''92E99'' None of the above, but in this section
!!!92-XX Biology and other natural sciences {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/92-XX.html]]}{{moveright{< [[91-XX |91-XX]] | [[MSC |MSC2010]] | [[92Bxx |92Bxx]] >}}}
* ''92-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''92-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''92-02'' Research exposition (monographs, survey articles)
* ''92-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''92-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''92-06'' Proceedings, conferences, collections, etc.
* ''92-08'' Computational methods
* ''[[92Bxx|92Bxx]]''  Mathematical biology in general
* ''[[92Cxx|92Cxx]]''  Physiological, cellular and medical topics
* ''[[92Dxx|92Dxx]]''  Genetics and population dynamics
* ''[[92Exx|92Exx]]''  Chemistry {For biochemistry, see [[92C40|92Cxx]]}
* ''[[92Fxx|92Fxx]]''  Other natural sciences (should also be assigned at least one other classification number in this section)
!!![[92|92-XX]]Fxx  Other natural sciences (should also be assigned at least one other classification number in this section) {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/92Fxx.html]]}{{moveright{< [[92Exx |92Exx]] | [[92-XX |92-XX]] | [[93-XX |93-XX]] >}}}
* ''92F05'' Other natural sciences (should also be assigned at least one other classification number in section 92)
* ''92F99'' None of the above, but in this section
!!![[93|93-XX]]Axx  General {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/93Axx.html]]}{{moveright{< [[92-XX |92-XX]] | [[93-XX |93-XX]] | [[93Bxx |93Bxx]] >}}}
* ''93A05'' Axiomatic system theory
* ''93A10'' General systems
* ''93A13'' Hierarchical systems
* ''93A14'' Decentralized systems
* ''93A15'' Large scale systems
* ''93A30'' Mathematical modeling (models of systems, model-matching, etc.)
* ''93A99'' None of the above, but in this section
!!![[93|93-XX]]Bxx  Controllability, observability, and system structure {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/93Bxx.html]]}{{moveright{< [[93Axx |93Axx]] | [[93-XX |93-XX]] | [[93Cxx |93Cxx]] >}}}
* ''93B03'' Attainable sets
* ''93B05'' Controllability
* ''93B07'' Observability
* ''93B10'' Canonical structure
* ''93B11'' System structure simplification
* ''93B12'' Variable structure systems
* ''93B15'' Realizations from input-output data
* ''93B17'' Transformations
* ''93B18'' Linearizations
* ''93B20'' Minimal systems representations
* ''93B25'' Algebraic methods
* ''93B27'' Geometric methods
* ''93B28'' Operator-theoretic methods [See also [[47A48|47Axx]], [[47A57|47Axx]], [[47B35|47Bxx]], [[47N70|47Nxx]]]
* ''93B30'' System identification
* ''93B35'' Sensitivity (robustness)
* ''93B36'' $H^\infty$-control
* ''93B40'' Computational methods
* ''93B50'' Synthesis problems
* ''93B51'' Design techniques (robust design, computer-aided design, etc.)
* ''93B52'' Feedback control
* ''93B55'' Pole and zero placement problems
* ''93B60'' Eigenvalue problems
* ''93B99'' None of the above, but in this section
!!![[93|93-XX]]Cxx  Control systems {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/93Cxx.html]]}{{moveright{< [[93Bxx |93Bxx]] | [[93-XX |93-XX]] | [[93Dxx |93Dxx]] >}}}
* ''93C05'' Linear systems
* ''93C10'' Nonlinear systems
* ''93C15'' Systems governed by ordinary differential equations [See also [[34H05|34Hxx]]]
* ''93C20'' Systems governed by partial differential equations
* ''93C23'' Systems governed by functional-differential equations [See also [[34K35|34Kxx]]]
* ''93C25'' Systems in abstract spaces
* ''93C30'' Systems governed by functional relations other than differential equations (such as hybrid and switching systems)
* ''93C35'' Multivariable systems
* ''93C40'' Adaptive control
* ''93C41'' Problems with incomplete information
* ''93C42'' Fuzzy control systems
* ''93C55'' Discrete-time systems
* ''93C57'' Sampled-data systems
* ''93C62'' Digital systems
* ''93C65'' Discrete event systems
* ''93C70'' Time-scale analysis and singular perturbations
* ''93C73'' Perturbations
* ''93C80'' Frequency-response methods
* ''93C83'' Control problems involving computers (process control, etc.)
* ''93C85'' Automated systems (robots, etc.) [See also [[68T40|68Txx]], [[70B15|70Bxx]], [[70Q05|70Qxx]]]
* ''93C95'' Applications
* ''93C99'' None of the above, but in this section
!!![[93|93-XX]]Dxx  Stability {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/93Dxx.html]]}{{moveright{< [[93Cxx |93Cxx]] | [[93-XX |93-XX]] | [[93Exx |93Exx]] >}}}
* ''93D05'' Lyapunov and other classical stabilities (Lagrange, Poisson, $L^p, l^p$, etc.)
* ''93D09'' Robust stability
* ''93D10'' Popov-type stability of feedback systems
* ''93D15'' Stabilization of systems by feedback
* ''93D20'' Asymptotic stability
* ''93D21'' Adaptive or robust stabilization
* ''93D25'' Input-output approaches
* ''93D30'' Scalar and vector Lyapunov functions
* ''93D99'' None of the above, but in this section
!!!93-XX Systems theory; control {For optimal control, see [[49-XX|49-XX]]} {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/93-XX.html]]}{{moveright{< [[92-XX |92-XX]] | [[MSC |MSC2010]] | [[93Axx |93Axx]] >}}}
* ''93-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''93-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''93-02'' Research exposition (monographs, survey articles)
* ''93-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''93-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''93-06'' Proceedings, conferences, collections, etc.
* ''[[93Axx|93Axx]]''  General
* ''[[93Bxx|93Bxx]]''  Controllability, observability, and system structure
* ''[[93Cxx|93Cxx]]''  Control systems
* ''[[93Dxx|93Dxx]]''  Stability
* ''[[93Exx|93Exx]]''  Stochastic systems and control
!!![[93|93-XX]]Exx  Stochastic systems and control {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/93Exx.html]]}{{moveright{< [[93Dxx |93Dxx]] | [[93-XX |93-XX]] | [[94-XX |94-XX]] >}}}
* ''93E03'' Stochastic systems, general
* ''93E10'' Estimation and detection [See also [[60G35|60Gxx]]]
* ''93E11'' Filtering [See also [[60G35|60Gxx]]]
* ''93E12'' System identification
* ''93E14'' Data smoothing
* ''93E15'' Stochastic stability
* ''93E20'' Optimal stochastic control
* ''93E24'' Least squares and related methods
* ''93E25'' Other computational methods
* ''93E35'' Stochastic learning and adaptive control
* ''93E99'' None of the above, but in this section
!!![[94|94-XX]]Axx  Communication, information {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/94Axx.html]]}{{moveright{< [[93-XX |93-XX]] | [[94-XX |94-XX]] | [[94Bxx |94Bxx]] >}}}
* ''94A05'' Communication theory [See also [[60G35|60Gxx]], [[90B18|90Bxx]]]
* ''94A08'' Image processing (compression, reconstruction, etc.) [See also [[68U10|68Uxx]]]
* ''94A11'' Application of orthogonal and other special functions
* ''94A12'' Signal theory (characterization, reconstruction, filtering, etc.)
* ''94A13'' Detection theory
* ''94A14'' Modulation and demodulation
* ''94A15'' Information theory, general [See also [[62B10|62Bxx]], [[81P45|81Pxx]]]
* ''94A17'' Measures of information, entropy
* ''94A20'' Sampling theory
* ''94A24'' Coding theorems (Shannon theory)
* ''94A29'' Source coding [See also [[68P30|68Pxx]]]
* ''94A34'' Rate-distortion theory
* ''94A40'' Channel models (including quantum)
* ''94A45'' Prefix, length-variable, comma-free codes [See also [[20M35|20Mxx]], [[68Q45|68Qxx]]]
* ''94A50'' Theory of questionnaires
* ''94A55'' Shift register sequences and sequences over finite alphabets
* ''94A60'' Cryptography [See also [[11T71|11Txx]], [[14G50|14Gxx]], [[68P25|68Pxx]], [[81P94|81Pxx]]]
* ''94A62'' Authentication and secret sharing [See also [[81P94|81Pxx]]]
* ''94A99'' None of the above, but in this section
!!![[94|94-XX]]Bxx  Theory of error-correcting codes and error-detecting codes {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/94Bxx.html]]}{{moveright{< [[94Axx |94Axx]] | [[94-XX |94-XX]] | [[94Cxx |94Cxx]] >}}}
* ''94B05'' Linear codes, general
* ''94B10'' Convolutional codes
* ''94B12'' Combined modulation schemes (including trellis codes)
* ''94B15'' Cyclic codes
* ''94B20'' Burst-correcting codes
* ''94B25'' Combinatorial codes
* ''94B27'' Geometric methods (including applications of algebraic geometry) [See also [[11T71|11Txx]], [[14G50|14Gxx]]]
* ''94B30'' Majority codes
* ''94B35'' Decoding
* ''94B40'' Arithmetic codes [See also [[11T71|11Txx]], [[14G50|14Gxx]]]
* ''94B50'' Synchronization error-correcting codes
* ''94B60'' Other types of codes
* ''94B65'' Bounds on codes
* ''94B70'' Error probability
* ''94B75'' Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) [See also [[11H31|11Hxx]], [[11H71|11Hxx]]]
* ''94B99'' None of the above, but in this section
!!![[94|94-XX]]Cxx  Circuits, networks {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/94Cxx.html]]}{{moveright{< [[94Bxx |94Bxx]] | [[94-XX |94-XX]] | [[94Dxx |94Dxx]] >}}}
* ''94C05'' Analytic circuit theory
* ''94C10'' Switching theory, application of Boolean algebra; Boolean functions [See also [[06E30|06Exx]]]
* ''94C12'' Fault detection; testing
* ''94C15'' Applications of graph theory [See also [[05Cxx|05Cxx]], [[68R10|68Rxx]]]
* ''94C30'' Applications of design theory [See also [[05Bxx|05Bxx]]]
* ''94C99'' None of the above, but in this section
!!!94-XX Information and communication, circuits {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/94-XX.html]]}{{moveright{< [[93-XX |93-XX]] | [[MSC |MSC2010]] | [[94Axx |94Axx]] >}}}
* ''94-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''94-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''94-02'' Research exposition (monographs, survey articles)
* ''94-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''94-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''94-06'' Proceedings, conferences, collections, etc.
* ''[[94Axx|94Axx]]''  Communication, information
* ''[[94Bxx|94Bxx]]''  Theory of error-correcting codes and error-detecting codes
* ''[[94Cxx|94Cxx]]''  Circuits, networks
* ''[[94Dxx|94Dxx]]''  Fuzzy sets and logic (in connection with questions of Section 94) [See also [[03B52|03Bxx]], [[03E72|03Exx]], [[28E10|28Exx]]]
!!![[94|94-XX]]Dxx  Fuzzy sets and logic (in connection with questions of Section 94) [See also [[03B52|03Bxx]], [[03E72|03Exx]], [[28E10|28Exx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/94Dxx.html]]}{{moveright{< [[94Cxx |94Cxx]] | [[94-XX |94-XX]] | [[97-XX |97-XX]] >}}}
* ''94D05'' Fuzzy sets and logic (in connection with questions of Section 94) [See also [[03B52|03Bxx]], [[03E72|03Exx]], [[28E10|28Exx]]]
* ''94D99'' None of the above, but in this section
!!![[97|97-XX]]Axx  General, mathematics and education {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/97Axx.html]]}{{moveright{< [[94-XX |94-XX]] | [[97-XX |97-XX]] | [[97Bxx |97Bxx]] >}}}
* ''97A10'' Comprehensive works, reference books
* ''97A20'' Recreational mathematics, games [See also [[00A08|00Axx]]]
* ''97A30'' History of mathematics and mathematics education [See also [[01-XX|01-XX]]]
* ''97A40'' Mathematics and society
* ''97A50'' Bibliographies [See also [[01-00|01-XX]]]
* ''97A70'' Theses and postdoctoral theses
* ''97A80'' Popularization of mathematics
* ''97A99'' None of the above, but in this section
!!![[97|97-XX]]Bxx  Educational policy and systems {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/97Bxx.html]]}{{moveright{< [[97Axx |97Axx]] | [[97-XX |97-XX]] | [[97Cxx |97Cxx]] >}}}
* ''97B10'' Educational research and planning
* ''97B20'' General education
* ''97B30'' Vocational education
* ''97B40'' Higher education
* ''97B50'' Teacher education {For research aspects, see [[97C70|97Cxx]]}
* ''97B60'' Adult and further education
* ''97B70'' Syllabuses, educational standards
* ''97B99'' None of the above, but in this section
!!![[97|97-XX]]Cxx  Psychology of mathematics education, research in mathematics education {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/97Cxx.html]]}{{moveright{< [[97Bxx |97Bxx]] | [[97-XX |97-XX]] | [[97Dxx |97Dxx]] >}}}
* ''97C10'' Comprehensive works
* ''97C20'' Affective behavior
* ''97C30'' Cognitive processes, learning theories
* ''97C40'' Intelligence and aptitudes
* ''97C50'' Language and verbal communities
* ''97C60'' Sociological aspects of learning
* ''97C70'' Teaching-learning processes
* ''97C99'' None of the above, but in this section
!!![[97|97-XX]]Dxx  Education and instruction in mathematics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/97Dxx.html]]}{{moveright{< [[97Cxx |97Cxx]] | [[97-XX |97-XX]] | [[97Exx |97Exx]] >}}}
* ''97D10'' Comprehensive works, comparative studies
* ''97D20'' Philosophical and theoretical contributions (maths didactics)
* ''97D30'' Objectives and goals
* ''97D40'' Teaching methods and classroom techniques
* ''97D50'' Teaching problem solving and heuristic strategies {For research aspects, see [[97Cxx|97Cxx]]}
* ''97D60'' Student assessment, achievement control and rating
* ''97D70'' Learning difficulties and student errors
* ''97D80'' Teaching units and draft lessons
* ''97D99'' None of the above, but in this section
!!![[97|97-XX]]Exx  Foundations of mathematics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/97Exx.html]]}{{moveright{< [[97Dxx |97Dxx]] | [[97-XX |97-XX]] | [[97Fxx |97Fxx]] >}}}
* ''97E10'' Comprehensive works
* ''97E20'' Philosophy and mathematics
* ''97E30'' Logic
* ''97E40'' Language of mathematics
* ''97E50'' Reasoning and proving in the mathematics classroom
* ''97E60'' Sets, relations, set theory
* ''97E99'' None of the above, but in this section
!!![[97|97-XX]]Fxx  Arithmetic, number theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/97Fxx.html]]}{{moveright{< [[97Exx |97Exx]] | [[97-XX |97-XX]] | [[97Gxx |97Gxx]] >}}}
* ''97F10'' Comprehensive works
* ''97F20'' Pre-numerical stage, concept of numbers
* ''97F30'' Natural numbers
* ''97F40'' Integers, rational numbers
* ''97F50'' Real numbers, complex numbers
* ''97F60'' Number theory
* ''97F70'' Measures and units
* ''97F80'' Ratio and proportion, percentages
* ''97F90'' Real life mathematics, practical arithmetic
* ''97F99'' None of the above, but in this section
!!![[97|97-XX]]Gxx  Geometry {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/97Gxx.html]]}{{moveright{< [[97Fxx |97Fxx]] | [[97-XX |97-XX]] | [[97Hxx |97Hxx]] >}}}
* ''97G10'' Comprehensive works
* ''97G20'' Informal geometry
* ''97G30'' Areas and volumes
* ''97G40'' Plane and solid geometry
* ''97G50'' Transformation geometry
* ''97G60'' Plane and spherical trigonometry
* ''97G70'' Analytic geometry. Vector algebra
* ''97G80'' Descriptive geometry
* ''97G99'' None of the above, but in this section
!!![[97|97-XX]]Hxx  Algebra {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/97Hxx.html]]}{{moveright{< [[97Gxx |97Gxx]] | [[97-XX |97-XX]] | [[97Ixx |97Ixx]] >}}}
* ''97H10'' Comprehensive works
* ''97H20'' Elementary algebra
* ''97H30'' Equations and inequalities
* ''97H40'' Groups, rings, fields
* ''97H50'' Ordered algebraic structures
* ''97H60'' Linear algebra
* ''97H99'' None of the above, but in this section
!!![[97|97-XX]]Ixx  Analysis {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/97Ixx.html]]}{{moveright{< [[97Hxx |97Hxx]] | [[97-XX |97-XX]] | [[97Kxx |97Kxx]] >}}}
* ''97I10'' Comprehensive works
* ''97I20'' Mappings and functions
* ''97I30'' Sequences and series
* ''97I40'' Differential calculus
* ''97I50'' Integral calculus
* ''97I60'' Functions of several variables
* ''97I70'' Functional equations
* ''97I80'' Complex analysis
* ''97I99'' None of the above, but in this section
!!![[97|97-XX]]Kxx  Combinatorics, graph theory, probability theory, statistics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/97Kxx.html]]}{{moveright{< [[97Ixx |97Ixx]] | [[97-XX |97-XX]] | [[97Mxx |97Mxx]] >}}}
* ''97K10'' Comprehensive works
* ''97K20'' Combinatorics
* ''97K30'' Graph theory
* ''97K40'' Descriptive statistics
* ''97K50'' Probability theory
* ''97K60'' Distributions and stochastic processes
* ''97K70'' Foundations and methodology of statistics
* ''97K80'' Applied statistics
* ''97K99'' None of the above, but in this section
!!![[97|97-XX]]Mxx  Mathematical modeling, applications of mathematics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/97Mxx.html]]}{{moveright{< [[97Kxx |97Kxx]] | [[97-XX |97-XX]] | [[97Nxx |97Nxx]] >}}}
* ''97M10'' Modeling and interdisciplinarity
* ''97M20'' Mathematics in vocational training and career education
* ''97M30'' Financial and insurance mathematics
* ''97M40'' Operations research, economics
* ''97M50'' Physics, astronomy, technology, engineering
* ''97M60'' Biology, chemistry, medicine
* ''97M70'' Behavioral and social sciences
* ''97M80'' Arts, music, language, architecture
* ''97M99'' None of the above, but in this section
!!![[97|97-XX]]Nxx  Numerical mathematics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/97Nxx.html]]}{{moveright{< [[97Mxx |97Mxx]] | [[97-XX |97-XX]] | [[97Pxx |97Pxx]] >}}}
* ''97N10'' Comprehensive works
* ''97N20'' Rounding, estimation, theory of errors
* ''97N30'' Numerical algebra
* ''97N40'' Numerical analysis
* ''97N50'' Interpolation and approximation
* ''97N60'' Mathematical programming
* ''97N70'' Discrete mathematics
* ''97N80'' Mathematical software, computer programs
* ''97N99'' None of the above, but in this section
!!![[97|97-XX]]Pxx  Computer science {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/97Pxx.html]]}{{moveright{< [[97Nxx |97Nxx]] | [[97-XX |97-XX]] | [[97Qxx |97Qxx]] >}}}
* ''97P10'' Comprehensive works
* ''97P20'' Theory of computer science
* ''97P30'' System software
* ''97P40'' Programming languages
* ''97P50'' Programming techniques
* ''97P60'' Hardware
* ''97P70'' Computer science and society
* ''97P99'' None of the above, but in this section
!!![[97|97-XX]]Qxx  Computer science education {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/97Qxx.html]]}{{moveright{< [[97Pxx |97Pxx]] | [[97-XX |97-XX]] | [[97Rxx |97Rxx]] >}}}
* ''97Q10'' Comprehensive works
* ''97Q20'' Affective aspects in teaching computer science
* ''97Q30'' Cognitive processes
* ''97Q40'' Sociological aspects
* ''97Q50'' Objectives
* ''97Q60'' Teaching methods and classroom techniques
* ''97Q70'' Student assessment
* ''97Q80'' Teaching units
* ''97Q99'' None of the above, but in this section
!!![[97|97-XX]]Rxx  Computer science applications {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/97Rxx.html]]}{{moveright{< [[97Qxx |97Qxx]] | [[97-XX |97-XX]] | [[97Uxx |97Uxx]] >}}}
* ''97R10'' Comprehensive works, collections of programs
* ''97R20'' Applications in mathematics
* ''97R30'' Applications in sciences
* ''97R40'' Artificial intelligence
* ''97R50'' Data bases, information systems
* ''97R60'' Computer graphics
* ''97R70'' User programs, administrative applications
* ''97R80'' Recreational computing
* ''97R99'' None of the above, but in this section
!!![[97|97-XX]]Uxx  Educational material and media, educational technology {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/97Uxx.html]]}{{moveright{< [[97Rxx |97Rxx]] | [[97-XX |97-XX]] | [[MSC |MSC2010]] >}}}
* ''97U10'' Comprehensive works
* ''97U20'' Textbooks. Textbook research
* ''97U30'' Teachers' manuals and planning aids
* ''97U40'' Problem books. Competitions. Examinations
* ''97U50'' Computer assisted instruction; e-learning
* ''97U60'' Manipulative materials
* ''97U70'' Technological tools, calculators
* ''97U80'' Audiovisual media
* ''97U99'' None of the above, but in this section
!!!97-XX Mathematics education {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/97-XX.html]]}{{moveright{< [[94-XX |94-XX]] | [[MSC |MSC2010]] | [[97Axx |97Axx]] >}}}
* ''97-00'' General reference works (handbooks, dictionaries, bibliographies, etc.)
* ''97-01'' Instructional exposition (textbooks, tutorial papers, etc.)
* ''97-02'' Research exposition (monographs, survey articles)
* ''97-03'' Historical (must also be assigned at least one classification number from Section 01)
* ''97-04'' Explicit machine computation and programs (not the theory of computation or programming)
* ''97-06'' Proceedings, conferences, collections, etc.
* ''[[97Axx|97Axx]]''  General, mathematics and education
* ''[[97Bxx|97Bxx]]''  Educational policy and systems
* ''[[97Cxx|97Cxx]]''  Psychology of mathematics education, research in mathematics education
* ''[[97Dxx|97Dxx]]''  Education and instruction in mathematics
* ''[[97Exx|97Exx]]''  Foundations of mathematics
* ''[[97Fxx|97Fxx]]''  Arithmetic, number theory
* ''[[97Gxx|97Gxx]]''  Geometry
* ''[[97Hxx|97Hxx]]''  Algebra
* ''[[97Ixx|97Ixx]]''  Analysis
* ''[[97Kxx|97Kxx]]''  Combinatorics, graph theory, probability theory, statistics
* ''[[97Mxx|97Mxx]]''  Mathematical modeling, applications of mathematics
* ''[[97Nxx|97Nxx]]''  Numerical mathematics
* ''[[97Pxx|97Pxx]]''  Computer science
* ''[[97Qxx|97Qxx]]''  Computer science education
* ''[[97Rxx|97Rxx]]''  Computer science applications
* ''[[97Uxx|97Uxx]]''  Educational material and media, educational technology
!!!----
<<miniBrowser http://www.ams.org/>>
<<miniBrowser http://www.acm.org/class/>>
! The main elements of a Tiddler
[img[http://www.giffmex.org/images/tiddler.GIF]]

! The Tiddler's hidden buttons
[img[http://www.giffmex.org/images/buttonseng.GIF]]

! A tiddler in 'edit' mode
When you double-click on a Tiddler or click the edit button, the Tiddler opens up into edit mode. Here is what it looks like:

[img[http://www.giffmex.org/images/editmode.GIF]]

When you are done editing the Tiddler, here are the options.
[img[http://www.giffmex.org/images/donecanceldelete.GIF]]
This tiddler was created was taken from the [[TiddlyWiki for the rest of us website|http://www.giffmex.org/twfortherestofus.html]].
<<miniBrowser http://front.math.ucdavis.edu/categories/math>>
[[00|00-XX]] [[01|01-XX]] [[03|03-XX]] [[05|05-XX]] [[06|06-XX]] [[08|08-XX]]
[[11|11-XX]] [[12|12-XX]] [[13|13-XX]] [[14|14-XX]] [[15|15-XX]]
[[16|16-XX]] [[17|17-XX]] [[18|18-XX]] [[19|19-XX]]
[[20|20-XX]] [[22|22-XX]] [[26|26-XX]] [[28|28-XX]]
[[30|30-XX]] [[31|31-XX]] [[32|32-XX]] [[33|33-XX]] [[34|34-XX]]
[[35|35-XX]] [[37|37-XX]] [[39|39-XX]]
[[40|40-XX]] [[41|41-XX]] [[42|42-XX]] [[43|43-XX]] [[44|44-XX]]
[[45|45-XX]] [[46|46-XX]] [[47|47-XX]] [[49|49-XX]]
[[51|51-XX]] [[52|52-XX]] [[53|53-XX]] [[54|54-XX]]
[[55|55-XX]] [[57|57-XX]] [[58|58-XX]]
[[60|60-XX]] [[62|62-XX]] [[65|65-XX]] [[68|68-XX]]
[[70|70-XX]] [[74|74-XX]] [[76|76-XX]] [[78|78-XX]]
[[80|80-XX]] [[81|81-XX]] [[82|82-XX]] [[83|83-XX]] [[85|85-XX]] [[86|86-XX]]
[[90|90-XX]] [[91|91-XX]] [[92|92-XX]] [[93|93-XX]] [[94|94-XX]] [[97|97-XX]]
[[Special note for users of Internet Explorer]]
[[Tips for making Mozilla Firefox run faster]]
This tiddler was  taken from the [[TiddlyWiki for the rest of us website|http://www.giffmex.org/twfortherestofus.html]], an excellent information page written by Dave Gifford about ~TiddlyWikis .
<<showUpdates>>
This is a version of the Mathematics Subject Classification (MSC) scheme prepared in the form of an enhanced ~TiddlyWiki.  This one allows browsing by hyperlinks of the structure of the MSC, searching for keywords in the text of classification descriptions, and, in the personal form one can download, the adding of personalized notes to each of the nearly 500 subsections of the MSC.  Having 63 major sections and about 500 subsections, the MSC can be viewed as a three-level planar tree with 63 first-level nodes, 500 or so second-level nodes and about 5000 leaves.  Thus navigational aids are useful.

The revision of the MSC is done by the editors of 
[[Mathematical Reviews|http://www.ams.org/mr-database]] (MR), in Ann Arbor, 
Michigan USA, and  
[[Zentralblatt MATH|http://www.zblmath.fiz-karlsruhe.de/MATH/home]] 
(Zbl), in Berlin, Germany, with consultation of the mathematical community. 
The previous large-scale revision was done for the year 2000 and the result 
was the ~MSC2000 presently in use.  This revision has been carried out using 
the collaborative environment of an [[MSCwiki|http://msc2020.org/MSCwiki]], 
a jointly editable wiki employing ~MediaWiki software (version 1.6.3) and 
hosted at [[MSC2010.org|http://MSC2010.org]]. 
 
In 2006 the Executive Editor of MR, Kevin Clancey, and the Chief Editor of Zbl, 
Bernd Wegner, issued the 
[[call for comments|http://www.zblmath.fiz-karlsruhe.de/msc/en/msc2010/]] 
leading to the present revision.  At MR the coordinating editors are Dean 
Carlson and Patrick Ion; they act as webmasters for the 
[[msc2010.org|http://msc2010.org]] Web site, where public comments are 
gathered, and Ion is responsible for what programming is needed.  At Zbl the 
lead editor for the MSC revision is Wolfram Sperber.  The 2009 launch of 
the Public version was presided over by the new Executive Editor of MR, 
Graeme Fairweather, and the Chief Editor of Zbl, Bernd Wegner.

The pages of the ~MSCwiki were initially filled from a [[TeX|http:///www.tug.org]] file in the format previously used by both MR and Zbl to produce printed and online versions of ~MSC2000.  The ~MSCwiki system runs on a ~MediaWiki platform, which employs [[PHP scripting|http://www.php.net]] and the [[MySQL|http://ww.mysql.com]] database, taking up in our case about 13.5 MB on Linux and Macintosh machines.  
After revisions are made by the editors on the ~MSCwiki, the pages of the revised MSC there are extracted using a [[Python|http://www.python.org]] script, of about 680 lines (ca. 24 kB) which depends on the special package [[BeautifulSoup|http://www.crummy.com/software/BeautifulSoup/]]; the data is converted into the previously mentioned ~TeX form.  The resulting ~TeX file of about 6200 lines (ca. 445~kB) is compiled with ~TeX to produce [[various PDF versions|http://www.msc2010.org/mscwiki/index.php?title=MSC-PDF]], for instance a single-column format of about 160 pages of the MSC (ca. 650~kB) by use of further custom ~TeX macro packages.

To produce the ~TiddlyWiki form of the MSC a [[Perl|http://www.perl.org]] script of about 1,200 lines (ca. 51 kB), is run over the ~TeX source of the MSC combining it with a template version of the ~TiddlyWiki with the functionality we want.  That functionality involves a number of special plug-ins added to the generous capacities provided by Jeremy Ruston's original [[TiddlyWiki|http://tiddlywiki.com]], which in the version 2.2.6 we use as a base, already runs to about 9,000 lines as an  [[XHTML|http://www.w3.org/MarkUp/]] page (ca. 280~kB) with a great deal of included ~JavaScript.  The release for July 2009 has been accompanied by an upgrade of the ~TiddlyWiki base to version 2.5.2 (now about 12,7000 lines of about 580 kB).  The extra information for the MSC2010 itself added amounts to about 8,500 lines of about 607kB, but with ancillary materials the final msc-2010-server.html amounts to about 30,000 lines and 1.8MB. The plug-ins we use include several by Eric Shulman from his [[TiddlyTools site|http://www.tiddlytools.com/]].  Several resources offered by the active ~TiddlyWiki community, that can be located through [[http://www.tiddlywiki.org|http://www.tiddlywiki.org]], have been 
very helpful, in particular plug-ins from [[Udo Borkowski|http://www.abego-software.com]], [[Paulo Soares|http://www.math.ist.utl.pt/~psoares/addons.html]] and [[Eric Shulman|http://www.tiddlytools.com]], and explanations from [[Dave Gifford|http://www.giffmex.org]].

The mathematical formulas in the MSC were given with [[MathML|http://www.w3.org/Math/] markup styled using [[CSS|http://www.w3.org/Style/CSS/]].  George Chavchanidze was generously helpful in ensuring this came out correctly.  For more on this see the [[W3C|http://www.w3.org]] Working Draft [[MathML for CSS|http://www.w3.org/TR/mathml-for-css/]].  We went back to the use of the LaTeXMathML plug-in and simple TeX coding for the formulas so that the formula strings can now be searched for, and the coding is consistent with that allowed within Note fields.
Name: MR-colors
Background: #fff
Foreground: #000
PrimaryPale: #8cf
PrimaryLight: #e8793e
PrimaryMid: #ff4500
PrimaryDark: #014
SecondaryPale: #ffc
SecondaryLight: #fe8
SecondaryMid: #db4
SecondaryDark: #841
TertiaryPale: #eee
TertiaryLight: #ccc
TertiaryMid: #999
TertiaryDark: #666
Error: #f88
!!!
Date of MSC TiddlyWiki creation: 20091203164006
Disclaimer
MSC2010
ToggleScrollingSidebars
/***
|Name|DisableWikiLinksPlugin|
|Source|http://www.TiddlyTools.com/#DisableWikiLinksPlugin|
|Version|1.5.0|
|Author|Eric Shulman - ELS Design Studios|
|License|http://www.TiddlyTools.com/#LegalStatements <<br>>and [[Creative Commons Attribution-ShareAlike 2.5 License|http://creativecommons.org/licenses/by-sa/2.5/]]|
|~CoreVersion|2.1|
|Type|plugin|
|Requires||
|Overrides|Tiddler.prototype.autoLinkWikiWords, 'wikiLink' formatter|
|Description|selectively disable ~TiddlyWiki's automatic ~WikiWord linking behavior|

This plugin allows you to disable ~TiddlyWiki's automatic ~WikiWord linking behavior, so that WikiWords embedded in tiddler content will be rendered as regular text, instead of being automatically converted to tiddler links.  To create a tiddler link when automatic linking is disabled, you must enclose the link text within {{{[[...]]}}}.

You can block automatic WikiWord linking behavior for any specific tiddler by ''tagging it with<<tag excludeWikiWords>>'' (see configuration below) or, check a plugin option to disable automatic WikiWord links to non-existing tiddler titles, while still linking WikiWords that correspond to existing tiddlers titles or shadow tiddler titles.  You can also block specific selected WikiWords from being automatically linked by listing them in [[DisableWikiLinksList]] (see configuration below), separated by whitespace.  This tiddler is optional and, when present, causes the listed words to always be excluded, even if automatic linking of other WikiWords is being permitted.  

Note: WikiWords contained in default ''shadow'' tiddlers will be automatically linked unless you select an additional checkbox option lets you disable these automatic links as well, though this is not recommended, since it can make it more difficult to access some ~TiddlyWiki standard default content (such as AdvancedOptions or SideBarTabs)

!!!!!Configuration
<<<
Self-contained control panel:
<<option chkDisableWikiLinks>> Disable ALL automatic WikiWord tiddler links
<<option chkAllowLinksFromShadowTiddlers>> ... except for WikiWords //contained in// shadow tiddlers
<<option chkDisableNonExistingWikiLinks>> Disable automatic WikiWord links for non-existing tiddlers
Disable automatic WikiWord links for words listed in: <<option txtDisableWikiLinksList>>
Disable automatic WikiWord links for tiddlers tagged with: <<option txtDisableWikiLinksTag>>
<<<
!!!!!Installation
<<<
import (or copy/paste) the following tiddlers into your document:
''DisableWikiLinksPlugin'' (tagged with <<tag systemConfig>>)
<<<
!!!!!Revision History
<<<
''2006.06.09 [1.5.0]'' added configurable txtDisableWikiLinksTag (default value: "excludeWikiWords") to allows selective disabling of automatic WikiWord links for any tiddler tagged with that value.
''2006.12.31 [1.4.0]'' in formatter, test for chkDisableNonExistingWikiLinks
''2006.12.09 [1.3.0]'' in formatter, test for excluded wiki words specified in DisableWikiLinksList
''2006.12.09 [1.2.2]'' fix logic in autoLinkWikiWords() (was allowing links TO shadow tiddlers, even when chkDisableWikiLinks is TRUE).  
''2006.12.09 [1.2.1]'' revised logic for handling links in shadow content
''2006.12.08 [1.2.0]'' added hijack of Tiddler.prototype.autoLinkWikiWords so regular (non-bracketed) WikiWords won't be added to the missing list
''2006.05.24 [1.1.0]'' added option to NOT bypass automatic wikiword links when displaying default shadow content (default is to auto-link shadow content)
''2006.02.05 [1.0.1]'' wrapped wikifier hijack in init function to eliminate globals and avoid FireFox 1.5.0.1 crash bug when referencing globals
''2005.12.09 [1.0.0]'' initial release
<<<
!!!!!Credits
<<<
This feature was developed by EricShulman from [[ELS Design Studios|http:/www.elsdesign.com]]
<<<
!!!!!Code
***/
//{{{
version.extensions.disableWikiLinks= {major: 1, minor: 5, revision: 0, date: new Date(2007,6,9)};

if (config.options.chkDisableNonExistingWikiLinks==undefined) config.options.chkDisableNonExistingWikiLinks= false;
if (config.options.chkDisableWikiLinks==undefined) config.options.chkDisableWikiLinks=false;
if (config.options.txtDisableWikiLinksList==undefined) config.options.txtDisableWikiLinksList="DisableWikiLinksList";
if (config.options.chkAllowLinksFromShadowTiddlers==undefined) config.options.chkAllowLinksFromShadowTiddlers=true;
if (config.options.txtDisableWikiLinksTag==undefined) config.options.txtDisableWikiLinksTag="excludeWikiWords";

// find the formatter for wikiLink and replace handler with 'pass-thru' rendering
initDisableWikiLinksFormatter();
function initDisableWikiLinksFormatter() {
	for (var i=0; i<config.formatters.length && config.formatters[i].name!="wikiLink"; i++);
	config.formatters[i].coreHandler=config.formatters[i].handler;
	config.formatters[i].handler=function(w) {
		// supress any leading "~" (if present)
		var skip=(w.matchText.substr(0,1)==config.textPrimitives.unWikiLink)?1:0;
		var title=w.matchText.substr(skip);
		var exists=store.tiddlerExists(title);
		var inShadow=w.tiddler && store.isShadowTiddler(w.tiddler.title);

		// check for excluded Tiddler
		if (w.tiddler && w.tiddler.isTagged(config.options.txtDisableWikiLinksTag))
			{ w.outputText(w.output,w.matchStart+skip,w.nextMatch); return; }
		
		// check for specific excluded wiki words
		var t=store.getTiddlerText(config.options.txtDisableWikiLinksList)
		if (t && t.length && t.indexOf(w.matchText)!=-1)
			{ w.outputText(w.output,w.matchStart+skip,w.nextMatch); return; }

		// if not disabling links from shadows (default setting)
		if (config.options.chkAllowLinksFromShadowTiddlers && inShadow)
			return this.coreHandler(w);

		// check for non-existing non-shadow tiddler
		if (config.options.chkDisableNonExistingWikiLinks && !exists)
			{ w.outputText(w.output,w.matchStart+skip,w.nextMatch); return; }

		// if not enabled, just do standard WikiWord link formatting
		if (!config.options.chkDisableWikiLinks)
			return this.coreHandler(w);

		// just return text without linking
		w.outputText(w.output,w.matchStart+skip,w.nextMatch)
	}
}

Tiddler.prototype.coreAutoLinkWikiWords = Tiddler.prototype.autoLinkWikiWords;
Tiddler.prototype.autoLinkWikiWords = function()
{
	// DEBUG alert("processing: "+this.title);
	// if all automatic links are not disabled, just return results from core function
	if (!config.options.chkDisableWikiLinks)
		return this.coreAutoLinkWikiWords.apply(this,arguments);
	return false;
}
//}}}
!!!<script>
if (Array.every)
document.write('You are using Firefox 1.5 or better.  You will be able to view the MSC nicely.  For further browser information see the FAQ on the left.')
else
document.write('You are not using Firefox 1.5 or better.   You can view the MSC but it may not look as nice. For further browser information see the FAQ on the left.')
</script>
!!This is a webserver copy, NOT for a local machine. For a local personal copy please click on Download a personal copy at the left.
This Mathematics Subject Classification is the Final Public Version of ~MSC2010 produced jointly by the editorial staffs of Mathematical Reviews (MR) and Zentralblatt für Mathematik (Zbl) in consultation with the mathematical community.   The goals of this revision were set out in the [[announcement and call for comments|http://msc2010.org/msc2010-announce.html]] by the Executive Editor of MR and Chief Editor of Zbl.
Publication of this Final Version implies  an endorsement by MR and Zbl. The MSC2010 will be used by them in their work from July 2009. Any updates of the MSC2010 are expected to be minor over the next decade, although corrections will  presumably have to be made.
The editors of MR and Zbl preparing this revision can still consider  feedback and suggestions to help in removing errors in this work, which should be given at the Web site http://www.msc2010.org (which is preferred) or through e-mail to feedback@msc2010.org.
!! Copyright 2006-2010: the Editors of Mathematical Reviews (MR) and Zentralblatt MATH (Zbl).
This document is made available under the Creative Commons ~Attribution-Noncommercial-Share Alike License: http://creativecommons.org/licenses/by-nc-sa/3.0/  Additional terms may apply.
To close this disclaimer click on the word ''close'' in the upper right corner menu.   For further help in using this form of the MSC please click on  the FAQ item in the main menu at the left.
<<miniBrowser http://www.euro-math-soc.eu/>>
/***
|Name|EditTiddlerPlugin|
|Source|http://www.TiddlyTools.com/#EditTiddlerPlugin|
|Version|1.2.0|
|Author|Eric Shulman - ELS Design Studios|
|License|http://www.TiddlyTools.com/#LegalStatements <br>and [[Creative Commons Attribution-ShareAlike 2.5 License|http://creativecommons.org/licenses/by-sa/2.5/]]|
|~CoreVersion|2.1|
|Type|plugin|
|Requires||
|Overrides||
|Description|embed an 'edit' link in tiddler content to invoke edit on any specified tiddler title|

!!!!!Usage:
<<<
{{{<<editTiddler TiddlerName linktext>>}}}
If no tiddler title is specified (or the special keyword "here" is used), the tiddler containing the rendered macro is assumed.  You can also specify optional alternative "link text" to be displayed. The default link text is "edit".
<<<
!!!!!Revisions:
<<<
2007.03.22 1.2.0 added support for 'here' keyword and optional 2nd param to specify label text
2007.03.15 1.1.1 fixed 'get tiddler ID' logic so it actually works! D'oh! 
2007.03.11 1.1.0 changed 'get tiddler ID' logic so that macro can be used outside a tiddler (i.e., in mainMenu) by specifying the ID
2006.10.04 1.0.1 invoke findContainingTiddler() as fallback when 'tiddler' param is null
2006.04.28 1.0.0 Initial release
<<<
!!!Code:
***/
//{{{
config.macros.editTiddler={
	handler: function(place,macroName,params,wikifier,paramString,tiddler) {
		var tid=params.shift(); // use specified tiddler ID (or "here")
		if (!tid || tid=="here") {
			if (tiddler)
				tid=tiddler.title; // use current tiddler, fallback to find tiddler if none provided
			else { 
				var here=story.findContainingTiddler(place);
				if (!here) return; // not in a tiddler, do nothing
				tid=here.getAttribute('tiddler'); // get ID from tiddler element
			}
		}
		var label="edit"; if (params[0]) label=params.shift();
		createTiddlyButton(place,label,'edit tiddler: '+tid,this.onclick).setAttribute('which',tid);
	},
	onclick: function(e) {
		story.displayTiddler(null,this.getAttribute('which'),DEFAULT_EDIT_TEMPLATE);
	}
}
//}}}
/***
|Name|ExternalTiddlersPlugin|
|Source|http://www.TiddlyTools.com/#ExternalTiddlersPlugin|
|Documentation|http://www.TiddlyTools.com/#ExternalTiddlersPluginInfo|
|Version|1.3.0|
|Author|Eric Shulman - ELS Design Studios|
|License|http://www.TiddlyTools.com/#LegalStatements <br>and [[Creative Commons Attribution-ShareAlike 2.5 License|http://creativecommons.org/licenses/by-sa/2.5/]]|
|~CoreVersion|2.1|
|Type|plugin|
|Requires|TemporaryTiddlersPlugin (optional, recommended)|
|Overrides|config.macros.tiddler.handler|
|Options|##Configuration|
|Description|retrieve and wikify content from external files or remote URLs|
This plugin extends the {{{<<tiddler>>}}} macro syntax so you can retrieve and wikify content directly from external files or remote URLs.  You can also define alternative "fallback" sources to provide basic "import on demand" handling by automatically creating/importing tiddler content from external sources when the specified ~TiddlerName does not already exist in your document.
!!!!!Documentation
>see [[ExternalTiddlersPluginInfo]]
!!!!!Configuration
<<<
<<option chkExternalTiddlersImport>> automatically create/import tiddlers when using external fallback references
{{{usage: <<option chkExternalTiddlersImport>>}}}
<<option chkExternalTiddlersQuiet>> don't display messages when adding tiddlers ("quiet mode")
{{{usage: <<option chkExternalTiddlersQuiet>>}}}
<<option chkExternalTiddlersTemporary>> tag retrieved tiddlers as 'temporary'(requires [[TemporaryTiddlersPlugin]])
{{{usage: <<option chkExternalTiddlersTemporary>>}}}
tag retrieved tiddlers with: <<option txtExternalTiddlersTags>>
{{{usage: <<option txtExternalTiddlersTags>>}}}

__password-protected server settings //(optional, if needed)//:__
>username: <<option txtRemoteUsername>> password: <<option txtRemotePassword>>
>{{{usage: <<option txtRemoteUsername>> <<option txtRemotePassword>>}}}
>''note: these settings are also used by [[LoadTiddlersPlugin]] and [[ImportTiddlersPlugin]]''
<<<
!!!!!Revisions
<<<
2008.01.08 [*.*.*] plugin size reduction: documentation moved to ExternalTiddlersPluginInfo
2008.01.03 [1.3.0] use lower-level doHttp() instead loadRemoteFile() so that optional username/password values can be used in XMLHttpRequest
2007.12.22 [1.2.2] in handler(), when reading from local file with relative path fixup, use decodeURIComponent() instead of decodeURI 
2007.11.30 [1.2.1] lots of code/docmentation cleanup.  renamed option cookies.  changed auto tag value to "external".
2007.11.27 [1.2.0] added support for automatically importing external tiddlers
2007.11.26 [1.1.1] improved XMLHttpRequest() error reporting for cross-domain security issues
2007.11.26 [1.1.0] added support for multiple alternative fallback references
2007.11.25 [1.0.0] initial release - moved from CoreTweaks
<<<
!!!!!Code
***/
//{{{
version.extensions.ExternalTiddlersPlugin= {major: 1, minor: 3, revision: 0, date: new Date(2008,1,3)};

// optional automatic import/create for missing tiddlers
if (config.options.chkExternalTiddlersImport==undefined) config.options.chkExternalTiddlersImport=true;
if (config.options.chkExternalTiddlersTemporary==undefined) config.options.chkExternalTiddlersTemporary=true;
if (config.options.chkExternalTiddlersQuiet==undefined) config.options.chkExternalTiddlersQuiet=false;
if (config.options.txtExternalTiddlersTags==undefined) config.options.txtExternalTiddlersTags="external";
if (config.options.txtRemoteUsername==undefined) config.options.txtRemoteUsername="";
if (config.options.txtRemotePassword==undefined) config.options.txtRemotePassword="";

config.macros.tiddler.externalTiddlers_handler = config.macros.tiddler.handler;
config.macros.tiddler.handler = function(place,macroName,params,wikifier,paramString,tiddler)
{
	params = paramString.parseParams("name",null,true,false,true);
	var names = params[0]["name"];
	var list = names[0];
	var items = list.split("|"); 
	var className = names[1] ? names[1] : null;
	var args = params[0]["with"];

	// UTILITY FUNCTIONS
	function extract(text,tids) { // get tiddler source content from plain text or TW doc
		if (!text || !tids || !tids.length) return text; // no text or no tiddler list... return text as-is
		var remoteStore=new TiddlyWiki();
		if (!remoteStore.importTiddlyWiki(text)) return text; // not a TW document... return text as-is
		var out=[]; for (var t=0;t<tids.length;t++)
			{ var txt=remoteStore.getTiddlerText(tids[t]); if (txt) out.push(txt); }
		return out.join("\n");
	}
	function substitute(text,args) { // replace "substitution markers" ($1-$9) with macro param values (if any)
		if (!text || !args || !args.length) return text;
		var n=args.length; if (n>9) n=9;
		for(var i=0; i<n; i++) { var re=new RegExp("\\$" + (i + 1),"mg"); text=text.replace(re,args[i]); }
		return text;
	}
	function addTiddler(src,text,tids) { // extract tiddler(s) from text and create local copy
		if (!config.options.chkExternalTiddlersImport) return; // not enabled... do nothing
		if (!text || !tids || !tids.length) return; // no text or no tiddler list... do nothing
		var remoteStore=new TiddlyWiki();
		if (!remoteStore.importTiddlyWiki(text)) // not a TW document... create a single tiddler from text
			makeTiddler(src,text,tids[0]);
		else // TW document with "permaview-like" suffix... copy tiddler(s) from remote store
			for (var t=0;t<tids.length;t++)
				insertTiddler(src,remoteStore.getTiddler(tids[t]));
		return;
	}
	function makeTiddler(src,text,title) { // create a new tiddler object from text
		var who=config.options.txtUserName; var when=new Date();
		var msg="/%\n\nThis tiddler was automatically created using ExternalTiddlersPlugin\n";
		msg+="by %0 on %1\nsource: %2\n\n%/";
		var tags=config.options.txtExternalTiddlersTags.readBracketedList();
		if (config.options.chkExternalTiddlersTemporary) tags.pushUnique(config.options.txtTemporaryTag); 
		store.saveTiddler(null,title,msg.format([who,when,src])+text,who,when,tags,{});
		if (!config.options.chkExternalTiddlersQuiet) displayMessage("Created new tiddler '"+title+"' from text file "+src);
	}
	function insertTiddler(src,t) { // import a single tiddler object into the current document store
		if (!t) return;
		var who=config.options.txtUserName; var when=new Date();
		var msg="/%\n\nThis tiddler was automatically imported using ExternalTiddlersPlugin\n";
		msg+="by %0 on %1\nsource: %2\n\n%/";
		var newtags=Array.concat(t.tags,config.options.txtExternalTiddlersTags.readBracketedList());
		if (config.options.chkExternalTiddlersTemporary) newtags.push(config.options.txtTemporaryTag);
		store.saveTiddler(null,t.title,msg.format([who,when,src])+t.text,t.modifier,t.modified,newtags,t.fields);
		if (!config.options.chkExternalTiddlersQuiet) displayMessage("Imported tiddler '"+t.title+"' from "+src);
	}
	function getGUID()  // create a Globally Unique ID (for async reference to DOM elements)
		 { return new Date().getTime()+Math.random().toString(); }

	// loop through "|"-separated list of alternative tiddler/file/URL references until successful
	var fallback="";
	for (var i=0; i<items.length; i++) { var src=items[i];
		// if tiddler (or shadow) exists, replace reference list with current source name and apply core handler
		if (store.getTiddlerText(src)) {
			arguments[2][0]=src; // params[] array
			var p=arguments[4].split(list); arguments[4]=p[0]+src+p[1]; // paramString
			this.externalTiddlers_handler.apply(this,arguments);
			break; // stop processing alternatives
		}
		// tiddler doesn't exist, and not an external file/URL reference... skip it
		if (!config.formatterHelpers.isExternalLink(src)) {
			if (!fallback.length) fallback=src; // title to use when importing external tiddler
			continue;
		}
		// separate 'permaview' list of tiddlers (if any) from file/URL (i.e., '#name name name..." suffix)
		var p=src.split("#"); src=p[0]; var tids=p[1]?p[1].readBracketedList(false):[];
		// if reference is to a remotely hosted document or the current document is remotely hosted...
		if (src.substr(0,4)=="http" || document.location.protocol.substr(0,4)=="http") {
			if (src.substr(0,4)!="http") // fixup URL for relative remote references
				{ var h=document.location.href; src=h.substr(0,h.lastIndexOf("/")+1)+src; }
			var wrapper = createTiddlyElement(place,"span",getGUID(),className); // create placeholder for async rendering
			var callback=function(success,params,text,src,xhr) { // ASYNC CALLBACK
				if (!success) { displayMessage(xhr.status); return; } // couldn't read remote file... report the error 
				if (params.fallback.length)
					addTiddler(params.url,text,params.tids.length?params.tids:[params.fallback]); // import tiddler
				var wrapper=document.getElementById(params.id); if (!wrapper) return; 
				wikify(substitute(extract(text,params.tids),params.args),wrapper); // ASYNC RENDER
			};
			var callbackparams={ url:src, id:wrapper.id, args:args, tids:tids, fallback:fallback }  // ASYNC PARAMS
			var name=config.options.txtRemoteUsername; // optional value
			var pass=config.options.txtRemotePassword; // optional value
			var x=doHttp("GET",src,null,null,name,pass,callback,callbackparams,null)
			if (typeof(x)=="string") // couldn't start XMLHttpRequest... report error
				{ displayMessage("error: cannot access "+src); displayMessage(x); }
			break; // can't tell if async read will succeed.... stop processing alternatives anyway.
		}
		else { // read file from local filesystem
			var text=loadFile(getLocalPath(src));
			if (!text) { // couldn't load file... fixup path for relative reference and retry...
				var h=document.location.href;
				var text=loadFile(getLocalPath(decodeURIComponent(h.substr(0,h.lastIndexOf("/")+1)))+src);
			}
			if (text) { // test it again... if file was loaded OK, render it in a class wrapper
				if (fallback.length) // create new tiddler using primary source name (if any)
					addTiddler(src,text,tids.length?tids:[fallback]);
				var wrapper=createTiddlyElement(place,"span",null,className);
				wikify(substitute(extract(text,tids),args),wrapper); // render
				break; // stop processing alternatives
			}
		}
	}
};
//}}}
|Name|ExternalTiddlersPluginInfo|
|Source|http://www.TiddlyTools.com/#ExternalTiddlersPlugin|
|Documentation|http://www.TiddlyTools.com/#ExternalTiddlersPluginInfo|
|Version|1.3.0|
|Author|Eric Shulman - ELS Design Studios|
|License|http://www.TiddlyTools.com/#LegalStatements <br>and [[Creative Commons Attribution-ShareAlike 2.5 License|http://creativecommons.org/licenses/by-sa/2.5/]]|
|~CoreVersion|2.1|
|Type|documentation|
|Requires||
|Overrides||
|Description|documentation for ExternalTiddlersPlugin|
This plugin extends the {{{<<tiddler>>}}} macro syntax so you can retrieve and wikify content directly from external files or remote URLs.  You can also define alternative "fallback" sources to provide basic "import on demand" handling by automatically creating/importing tiddler content from external sources when the specified ~TiddlerName does not already exist in your document.
!!!!!Configuration
>see ExternalTiddlersPlugin
!!!!!Usage
<<<
The standard ~TiddlyWiki core syntax for the {{{<<tiddler>>}}} macro is:
>{{{<<tiddler TiddlerName with: param param param ...>>}}}
where the optional {{{with: param param param...}}} values are used to replace any corresponding "substitution markers" ($1 to $9) that may be embedded in the referenced tiddler content.

This plugin allows the {{{<<tiddler>>}}} macro to ''use external file/URL references in place of the usual ~TiddlerName parameter'', so that you can render wiki-formatted source content retrieved from an external file/URL reference (as determined by the core's isExternalLink() test function), ''//as if// it had come from a tiddler in the current document''.  The external file/URL can be either ''a relative or absolute reference'' and can contain ''"plain text" or a full TiddlyWiki document''.  When using a TiddlyWiki document, you must specify which tiddlers should be included in the output by appending a permaview-like suffix to the file or URL reference, e.g.:
>{{{<<tiddler "myfile.txt" with: param param param...>>}}}
>or
>{{{<<tiddler "myfile.html#TiddlerName TiddlerName..." with: param param param...>>}}}
>or
>{{{<<tiddler "http://www.TiddlyWiki.com/index.html#HelloThere" with: param param param...>>}}}
If the plugin-enhanced {{{<<tiddler>>}}} macro is unable to retrieve the external content --  perhaps because the file doesn't exist or doesn't contain the requested tiddler(s), or cross-domain security blocked file access, or the network/server "timed out", etc., -- then it produces no output (i.e., just as when the standard {{{<<tiddler>>}}} macro is given a ~TiddlerName does not exist in the current document.)
<<<
!!!!!Using alternative "fallback" references
<<<
In addition to using external file/URL references in place of the usual ~TiddlerName, the plugin also allows you to use a ''fallback list'' consisting of a combination of alternative sources: tiddlers, local files, and/or URL references, each separated by "|".  The first reference in a fallback list is the "primary source"; the remaining references are "fallback sources".  The plugin will attempt to retrieve content from each fallback source until one is successfully retrieved or all alternatives have been tried.

For example, if you create a tiddler called [[HelloThere]], as well as a remotely-hosted TW document containing a published tiddler, also called [[HelloThere]], then you can write:
>{{{<<tiddler [[HelloThere|http://www.TiddlyWiki.com/#HelloThere]]>>}}}
When [[HelloThere]] is present in the local document, it is processed in the normal manner.  However, if you delete the  local [[HelloThere]] tiddler, the plugin will attempt to retrieve the [[HelloThere]] tiddler from the indicated remote URL.

Please note: although you can list any number of alternative sources, in whatever order you prefer, retrieval from a remote URL occurs asynchronously via XMLHttpRequest() processing.  As a consequence, there can be ''no more than one remote URL reference in the fallback list'', and any alternatives that follow a remote URL reference will not be processed.
<<<
!!!!!Automatically import/create missing tiddlers
<<<
When content is retrieved from an external fallback source, the plugin can automatically import/create tiddler(s) containing that content into your document, allowing you to display, modify, save and/or search for text in that tiddler from within your own document, without needing to retrieve it again from the external source.

If no local ~TiddlerName(s) are specified in the fallback list (i.e., only direct file/URL references are present), then a tiddler will NOT be created, so that each time you render the tiddler display the external source will be re-read in order to render the most recently saved external file content.  To illustrate using the example from above:
>&nbsp;&nbsp;&nbsp;{{{<<tiddler [[HelloThere|http://www.TiddlyWiki.com/#HelloThere]]>>}}}
will automatically create a locally-stored [[HelloThere]] tiddler, so that the external source is only accessed the first time the content is rendered, while:
>&nbsp;&nbsp;&nbsp;{{{<<tiddler [[http://www.TiddlyWiki.com/#HelloThere]]>>}}}
will re-load the content from the external source each time the display is rendered.

For easy identification, any tiddlers that are automatically created/imported are tagged with <<tag external>> (or other custom-defined tag values).  These tiddlers can also be automatically tagged with <<tag temporary>> for use with [[TemporaryTiddlersPlugin]], which will skip over those tiddlers when saving changes to your document so that when you reload the document, the temporary tiddlers will no longer be present and will be retrieved anew from the external source, on demand, when (or if) they are needed.  Important reminder: ''If you modify a temporary tiddler and want to retain it in your local document, be sure to remove the <<tag temporary>> tag from the tiddler before saving.''
<<<
!!!!!~XMLHttpRequest: performance and security issues
<<<
This plugin uses asynchronous XMLHttpRequest() processing to access external content directly from URLs hosted on remote web servers.  This often creates delays ranging from mere moments to many minutes while waiting for the remote web server to transfer the requested file.  This performance can vary greatly depending upon the size of the remote file, how the remote server responds to repeated requests for the same URL (e.g, with a //"304 - no change"// response code), as well as how your ''browser's cache mechanism'' has been configured (to avoid repeated downloads).

In addition to server-originated delays, ''cross-domain access from one remote domain to another using XMLHttpRequest() processing is generally restricted for security reasons''.  As a result, if you publish your document to a remote web server, then external file/URL references contained in that document will not work if they are not located on the same server as the hosted document.

Fortunately, this security restriction does NOT usually apply when accessing remote URLs rendered into a locally-viewed document, since blocking such access would interfere with normal browser functions!  As a "rule of thumb", in order to ensure that external content included in server-hosted documents will be displayed as intended, you should ''always use either a relative path/file reference or an http: reference located on the same domain as the published document.'' for any document you intend to publish.

Note: Some hosting providers, such as http://www.TiddlySpot.com/ offer ''"proxy" services that may allow you to bypass the security restrictions'' for certain designated remote web sites.  Consult your hosting service for information regarding their proxy arrangments (if any).
<<<
!What is this?  
This is the  ~MSC2010 in ~TiddlyWiki form created and prepared  by Dean Carlson and Patrick Ion at MR/AMS.   It is designed to be used locally as a searchable tree-structured version of the MSC which can be privately annotated.  When the ~MSC2010 is finalized, a new version of this file will be made available.

!What is a ~TiddlyWiki?
A free ~MicroContent ~WikiWikiWeb created by ~JeremyRuston.  For further information go to the [[TiddlyWiki website|http://www.tiddlywiki.com]].

!Why a ~TiddlyWiki?  
The ~TiddlyWiki format allows us to create a ''downloadable''  file that you can use locally (without internet access) and in which you can add personal notes, and enhance through any number of ways using available plugins and macros developed by a large community of developers.

!How do I get a personal copy?  
First navigate to the official ~MSC2010 website at http://msc2010.org/MSC-2010-server.html. On the left side of the page click on  ''Download your personal copy''.  You now have a personal copy of the ~MSC2010 (''draft'') which you use by loading into your web browser. 

!How do I keep my personal copy up to date?
On the ''~MainMenu'' (the left side panel) click on ''Toggle More Help''.  Now click on ''~UpDateMSC''.  Any changes made to ~MSC-2010 that have been implemented since your last update will be automatically updated.  Please note that if a lot of changes have been made, this operation may take some time.  Upon completion of this task a tiddler called [[ImportedTiddlers]] opens with a list of your updates.
 
!Are there any browser specific issues?  
The ~MSC2010 ~TiddlyWiki can be viewed in any browser.  However to  add notes (see below) and to save your changes the best browser is Mozilla Firefox.  Go to [[Browser-specific issues]].

!How do I use a ~TiddlyWiki?  
Navigating the ~MSC2010 ~TiddlyWiki is easy.  For a quick start guide go to the [[Navigating the MSC2010 as a TiddlyWiki]].  For a more detailed tutorial go  [[TiddlyWiki for the rest of us site|http://www.giffmex.org/twfortherestofus.html]].  For more comprehensive information see the  help pages at [[Tiddlyspot.com|http://tiddlyspot.com/twhelp/]] as well as mediawiki at [[TiddlyWiki.org|http://www.tiddlywiki.org/wiki/Main_Page]]

!What does ''~ToggleSidebar'' do?  
Be adventurous!  Click on it to see a new sidebar on the right.  Here are a number of options.  In particular is the search window which allows you to search through your the contents of this file.  Also there are some other options as well which allow you to change the color scheme, save changes, etc.
 
!What is the ''Notes'' feature?  
This allows you to add personal notes to any ''tiddler'' (what the individual components of a ~TiddlyWiki are called).  Each tiddler has an embedded ''Notes'' window.  Simply click on the ''edit notes'' tab on the right side.  Then you can type in anything you like.  For a ~CheatSheet on ~TiddlyWiki markup see [[CheatSheet|TiddlyWiki Markup CheatSheet]].  Be sure to save the file when you are done by clicking on the ''save notes'' tab.  Finally before you close the file save it all by ''toggling'' the sidebar and clicking on ''save changes''.  Also, regarding the notes feature, there is the capability of using ~LaTeX syntax via the ~LaTeXMathML plugin.  For further information see [[Inputting LaTeX|LaTeX Help]]

!How do I hide the ''Disclaimer''?  
First close it by clicking on the word ''close'' in the upper right corner menu.  Then toggle the sidebar (click on ''~ToggleSidebar'' on the top left).  Finally, click on ''permaview'' and then ''save changes''.   Save page as a bookmark.  The next time you use your copy of the MSC2010 use the bookmarked page.  Note to read the disclaimer again just click on [[DISCLAIMER|Disclaimer]] on the left.  

<<miniBrowser http://gams.nist.gov/serve.cgi>>

/***
|Name|InlineJavascriptPlugin|
|Source|http://www.TiddlyTools.com/#InlineJavascriptPlugin|
|Documentation|http://www.TiddlyTools.com/#InlineJavascriptPluginInfo|
|Version|1.8.0|
|Author|Eric Shulman - ELS Design Studios|
|License|http://www.TiddlyTools.com/#LegalStatements <br>and [[Creative Commons Attribution-ShareAlike 2.5 License|http://creativecommons.org/licenses/by-sa/2.5/]]|
|~CoreVersion|2.1|
|Type|plugin|
|Requires||
|Overrides||
|Description|Insert Javascript executable code directly into your tiddler content.|
''Call directly into TW core utility routines, define new functions, calculate values, add dynamically-generated TiddlyWiki-formatted output'' into tiddler content, or perform any other programmatic actions each time the tiddler is rendered.
!!!!!Documentation
>see [[InlineJavascriptPluginInfo]]
!!!!!Revision History
<<<
''2008.01.08 [*.*.*]'' plugin size reduction: documentation moved to ...Info and ...History tiddlers
''2007.12.28 [1.8.0]'' added support for key="X" syntax to specify custom access key definitions
|please see [[InlineJavascriptPluginHistory]] for additional revision details|
''2005.11.08 [1.0.0]'' initial release
<<<
!!!!!Code
***/
//{{{
version.extensions.inlineJavascript= {major: 1, minor: 8, revision: 0, date: new Date(2007,12,28)};

config.formatters.push( {
	name: "inlineJavascript",
	match: "\\<script",
	lookahead: "\\<script(?: src=\\\"((?:.|\\n)*?)\\\")?(?: label=\\\"((?:.|\\n)*?)\\\")?(?: title=\\\"((?:.|\\n)*?)\\\")?(?: key=\\\"((?:.|\\n)*?)\\\")?( show)?\\>((?:.|\\n)*?)\\</script\\>",

	handler: function(w) {
		var lookaheadRegExp = new RegExp(this.lookahead,"mg");
		lookaheadRegExp.lastIndex = w.matchStart;
		var lookaheadMatch = lookaheadRegExp.exec(w.source)
		if(lookaheadMatch && lookaheadMatch.index == w.matchStart) {
			var src=lookaheadMatch[1];
			var label=lookaheadMatch[2];
			var tip=lookaheadMatch[3];
			var key=lookaheadMatch[4];
			var show=lookaheadMatch[5];
			var code=lookaheadMatch[6];
			if (src) { // load a script library
				// make script tag, set src, add to body to execute, then remove for cleanup
				var script = document.createElement("script"); script.src = src;
				document.body.appendChild(script); document.body.removeChild(script);
			}
			if (code) { // there is script code
				if (show) // show inline script code in tiddler output
					wikify("{{{\n"+lookaheadMatch[0]+"\n}}}\n",w.output);
				if (label) { // create a link to an 'onclick' script
					// add a link, define click handler, save code in link (pass 'place'), set link attributes
					var link=createTiddlyElement(w.output,"a",null,"tiddlyLinkExisting",wikifyPlainText(label));
					link.onclick=function(){try{return(eval(this.code))}catch(e){alert(e.description||e.toString())}}
					var fixup=code.replace(/document.write\s*\(/gi,'place.innerHTML+=(');
					link.code="function _out(place){"+fixup+"\n};_out(this);"
					link.setAttribute("title",tip||"");
					var URIcode='javascript:void(eval(decodeURIComponent(%22(function(){try{';
					URIcode+=encodeURIComponent(encodeURIComponent(code.replace(/\n/g,' ')));
					URIcode+='}catch(e){alert(e.description||e.toString())}})()%22)))';
					link.setAttribute("href",URIcode);
					link.style.cursor="pointer";
					if (key) link.accessKey=key.substr(0,1); // single character only
				}
				else { // run inline script code
					var fixup=code.replace(/document.write\s*\(/gi,'place.innerHTML+=(');
					var code="function _out(place){"+fixup+"\n};_out(w.output);"
					try { var out=eval(code); } catch(e) { out=e.description?e.description:e.toString(); }
					if (out && out.length) wikify(out,w.output,w.highlightRegExp,w.tiddler);
				}
			}
			w.nextMatch = lookaheadMatch.index + lookaheadMatch[0].length;
		}
	}
} )
//}}}
/***
|Name|InlineJavascriptPluginInfo|
|Source|http://www.TiddlyTools.com/#InlineJavascriptPlugin|
|Documentation|http://www.TiddlyTools.com/#InlineJavascriptPluginInfo|
|Version|1.8.0|
|Author|Eric Shulman - ELS Design Studios|
|License|http://www.TiddlyTools.com/#LegalStatements <br>and [[Creative Commons Attribution-ShareAlike 2.5 License|http://creativecommons.org/licenses/by-sa/2.5/]]|
|~CoreVersion|2.1|
|Type|documentation|
|Requires||
|Overrides||
|Description|Documentation for InlineJavascriptPlugin|
''Call directly into TW core utility routines, define new functions, calculate values, add dynamically-generated TiddlyWiki-formatted output'' into tiddler content, or perform any other programmatic actions each time the tiddler is rendered.
!!!!!Usage
<<<
When installed, this plugin adds new wiki syntax for surrounding tiddler content with {{{<script>}}} and {{{</script>}}} markers, so that it can be treated as embedded javascript and executed each time the tiddler is rendered.

''Deferred execution from an 'onClick' link''
By including a {{{label="..."}}} parameter in the initial {{{<script>}}} marker, the plugin will create a link to an 'onclick' script that will only be executed when that specific link is clicked, rather than running the script each time the tiddler is rendered.  You may also include a {{{title="..."}}} parameter to specify the 'tooltip' text that will appear whenever the mouse is moved over the onClick link text, and a {{{key="X"}}} parameter to specify an //access key// (which must be a //single// letter or numeric digit only)

''External script source files:''
You can also load javascript from an external source URL, by including a src="..." parameter in the initial {{{<script>}}} marker (e.g., {{{<script src="demo.js"></script>}}}).  This is particularly useful when incorporating third-party javascript libraries for use in custom extensions and plugins.  The 'foreign' javascript code remains isolated in a separate file that can be easily replaced whenever an updated library file becomes available.

''Display script source in tiddler output''
By including the keyword parameter "show", in the initial {{{<script>}}} marker, the plugin will include the script source code in the output that it displays in the tiddler.

''Defining javascript functions and libraries:''
Although the external javascript file is loaded while the tiddler content is being rendered, any functions it defines will not be available for use until //after// the rendering has been completed.  Thus, you cannot load a library and //immediately// use it's functions within the same tiddler.  However, once that tiddler has been loaded, the library functions can be freely used in any tiddler (even the one in which it was initially loaded).

To ensure that your javascript functions are always available when needed, you should load the libraries from a tiddler that will be rendered as soon as your TiddlyWiki document is opened.  For example, you could put your {{{<script src="..."></script>}}} syntax into a tiddler called LoadScripts, and then add {{{<<tiddler LoadScripts>>}}} in your MainMenu tiddler.

Since the MainMenu is always rendered immediately upon opening your document, the library will always be loaded before any other tiddlers that rely upon the functions it defines.  Loading an external javascript library does not produce any direct output in the tiddler, so these definitions should have no impact on the appearance of your MainMenu.

''Creating dynamic tiddler content''
An important difference between this implementation of embedded scripting and conventional embedded javascript techniques for web pages is the method used to produce output that is dynamically inserted into the document:
* In a typical web document, you use the document.write() function to output text sequences (often containing HTML tags) that are then rendered when the entire document is first loaded into the browser window.
* However, in a ~TiddlyWiki document, tiddlers (and other DOM elements) are created, deleted, and rendered "on-the-fly", so writing directly to the global 'document' object does not produce the results you want (i.e., replacing the embedded script within the tiddler content), and completely replaces the entire ~TiddlyWiki document in your browser window.
* To allow these scripts to work unmodified, the plugin automatically converts all occurences of document.write() so that the output is inserted into the tiddler content instead of replacing the entire ~TiddlyWiki document.

If your script does not use document.write() to create dynamically embedded content within a tiddler, your javascript can, as an alternative, explicitly return a text value that the plugin can then pass through the wikify() rendering engine to insert into the tiddler display.  For example, using {{{return "thistext"}}} will produce the same output as {{{document.write("thistext")}}}.

//Note: your script code is automatically 'wrapped' inside a function, {{{_out()}}}, so that any return value you provide can be correctly handled by the plugin and inserted into the tiddler.  To avoid unpredictable results (and possibly fatal execution errors), this function should never be redefined or called from ''within'' your script code.//

''Accessing the ~TiddlyWiki DOM''
The plugin provides one pre-defined variable, 'place', that is passed in to your javascript code so that it can have direct access to the containing DOM element into which the tiddler output is currently being rendered.

Access to this DOM element allows you to create scripts that can:
* vary their actions based upon the specific location in which they are embedded
* access 'tiddler-relative' information (use findContainingTiddler(place))
* perform direct DOM manipulations (when returning wikified text is not enough)
<<<
!!!!!Examples
<<<
an "alert" message box:
><script show>
	alert('InlineJavascriptPlugin: this is a demonstration message');
</script>
dynamic output:
><script show>
	return (new Date()).toString();
</script>
wikified dynamic output:
><script show>
	return "link to current user: [["+config.options.txtUserName+"]]";
</script>
dynamic output using 'place' to get size information for current tiddler:
><script show>
	if (!window.story) window.story=window;
	var title=story.findContainingTiddler(place).id.substr(7);
	return title+" is using "+store.getTiddlerText(title).length+" bytes";
</script>
creating an 'onclick' button/link that runs a script:
><script label="click here" title="clicking this link will show an 'alert' box" key="H" show>
	if (!window.story) window.story=window;
	alert("Hello World!\nlinktext='"+place.firstChild.data+"'\ntiddler='"+story.findContainingTiddler(place).id.substr(7)+"'");
	return false;
</script>
loading a script from a source url:
>http://www.TiddlyTools.com/demo.js contains:
>>{{{function demo() { alert('this output is from demo(), defined in demo.js') } }}}
>>{{{alert('InlineJavascriptPlugin: demo.js has been loaded'); }}}
><script src="demo.js" show>
	return "loading demo.js..."
</script>
><script label="click to execute demo() function" key="D" show>
	demo();
	return false;
</script>
<<<
<<miniBrowser http://www.elsevier.com/authored_subject_sections/S04/misc/subject_cat.htm>>
Your personal copy of the ~MSC2010 includes the ~LaTeXMathML plugin which allows you to input some ~LaTeX commands.  To do so you will need to load the appropriate fonts.  To learn how to load the appropriate fonts please see  [[MathML fonts | http://www.mozilla.org/projects/mathml/fonts/]]For information on this feature please see the help docs  on the [[LatexMathML-plugin|LaTeXMathMLPluginDoc]].  For some simple example see the notes section below.
In this note you can input ~LaTeX either inline or displayed.  Instead of using {{{\[ \]}}} for displayed math, use {{{$$...$$}}} instead.

For example one can have $\frac{1}{2}\sqrt{1+x^2}$ inline or 
$$\frac{1}{2}\sqrt{1+x^2}\qquad\qquad \mbox{as displayed}$$
$$
\dot{x}(t)=f(t,x(t))
$$
For displayed environments like \begin{eqnarray} \end{eqnarray} it is necessary to begin and end with {{{$$...$$}}}.  If you don't it will look like this
\begin{eqnarray}
\dot{x}(t)&=&f(x(t),y(t))\\
\dot{y}(t)&=&g(x(t),y(t))
\end{eqnarray}
rather than
$$
\begin{eqnarray}
\dot{x}(t)&=&f(x(t),y(t))\\
\dot{y}(t)&=&g(x(t),y(t))
\end{eqnarray}
$$
$$
\left\{\begin{array}{ll}
\dot{x}(t)=f(t,x(t)) & \mbox{for }t\in [0,1]\\
\displaystyle{x(\frac12)=\int_0^1g(s,x(s)) ds} &\\
x(0)=x_0&x(1)=x_1
\right.
\end{array}
$$

Some other examples of LaTeX markup

$\vec{x},\overrightarrow{x},\overleftarrow{x}$
$\acute{\mbox{x}},\grave{\mbox{x}},\breve{\mbox{x}},\check{\mbox{x}}$
$\hat{x},\widehat{x},\tilde{x},\widetilde{x}$
$\dot{x},\ddot{x},\mathring{x}$
$\bar{x},\overline{x},\underline{x}$

The available fonts:
$$\begin{eqnarray}
\mbox{\mathrm}&\mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\mbox{\mathbf}&\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\mbox{\mathit}&\mathit{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\mbox{\mathtt}&\mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\mbox{\mathsf}&\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\mbox{\mathbb}&\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\mbox{\mathcal}&\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\mbox{\mathfrak}&\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}
\end{eqnarray}$$

To see what was actually typed to obtain the above display click on "edit notes" in the tab above.
/***
|''Name:''|LaTeXMathMLPlugin|
|''Description:''|~LaTeX plugin with ~MathML output based on [[LaTeXMathML|http://www.maths.nottingham.ac.uk/personal/drw/lm.html]]|
|''Version:''|1.1|
|''Date:''|Oct 06, 2007|
|''Source:''|http://www.math.ist.utl.pt/~psoares/addons.html|
|''Documentation:''|[[LaTeXMathMLPlugin Documentation|LaTeXMathMLPluginDoc]]|
|''Author:''|Paulo Soares|
|''License:''|[[Creative Commons Attribution-Share Alike 3.0 License|http://creativecommons.org/licenses/by-sa/3.0/]]|
|''~CoreVersion:''|2.1.0|
***/
//{{{
config.macros.LaTeXMathMLPlugin = {
	AMnames: [],
	isIE: document.createElementNS==null,
	AMmathml: "http://www.w3.org/1998/Math/MathML",
	AMcal: [0xEF35,0x212C,0xEF36,0xEF37,0x2130,0x2131,0xEF38,0x210B,0x2110,0xEF39,0xEF3A,0x2112,0x2133,0xEF3B,0xEF3C,0xEF3D,0xEF3E,0x211B,0xEF3F,0xEF40,0xEF41,0xEF42,0xEF43,0xEF44,0xEF45,0xEF46],
	AMfrk: [0xEF5D,0xEF5E,0x212D,0xEF5F,0xEF60,0xEF61,0xEF62,0x210C,0x2111,0xEF63,0xEF64,0xEF65,0xEF66,0xEF67,0xEF68,0xEF69,0xEF6A,0x211C,0xEF6B,0xEF6C,0xEF6D,0xEF6E,0xEF6F,0xEF70,0xEF71,0x2128],
	AMbbb: [0xEF8C,0xEF8D,0x2102,0xEF8E,0xEF8F,0xEF90,0xEF91,0x210D,0xEF92,0xEF93,0xEF94,0xEF95,0xEF96,0x2115,0xEF97,0x2119,0x211A,0x211D,0xEF98,0xEF99,0xEF9A,0xEF9B,0xEF9C,0xEF9D,0xEF9E,0x2124],
	CONST: 0, UNARY: 1, BINARY: 2, INFIX: 3, LEFTBRACKET: 4, RIGHTBRACKET: 5, SPACE: 6, UNDEROVER: 7, DEFINITION: 8, TEXT: 9, BIG: 10, LONG: 11, STRETCHY: 12, MATRIX: 13,
	AMsymbols: [
	//Greek letters
		{input:"\\alpha", tag:"mi", output:"\u03B1", ttype:0},
		{input:"\\beta", tag:"mi", output:"\u03B2", ttype:0},
		{input:"\\gamma", tag:"mi", output:"\u03B3", ttype:0},
		{input:"\\delta", tag:"mi", output:"\u03B4", ttype:0},
		{input:"\\epsilon", tag:"mi", output:"\u03B5", ttype:0},
		{input:"\\varepsilon", tag:"mi", output:"\u025B", ttype:0},
		{input:"\\zeta", tag:"mi", output:"\u03B6", ttype:0},
		{input:"\\eta", tag:"mi", output:"\u03B7", ttype:0},
		{input:"\\theta", tag:"mi", output:"\u03B8", ttype:0},
		{input:"\\vartheta", tag:"mi", output:"\u03D1", ttype:0},
		{input:"\\iota", tag:"mi", output:"\u03B9", ttype:0},
		{input:"\\kappa", tag:"mi", output:"\u03BA", ttype:0},
		{input:"\\lambda", tag:"mi", output:"\u03BB", ttype:0},
		{input:"\\mu", tag:"mi", output:"\u03BC", ttype:0},
		{input:"\\nu", tag:"mi", output:"\u03BD", ttype:0},
		{input:"\\xi", tag:"mi", output:"\u03BE", ttype:0},
		{input:"\\pi", tag:"mi", output:"\u03C0", ttype:0},
		{input:"\\varpi", tag:"mi", output:"\u03D6", ttype:0},
		{input:"\\rho", tag:"mi", output:"\u03C1", ttype:0},
		{input:"\\varrho", tag:"mi", output:"\u03F1", ttype:0},
		{input:"\\varsigma", tag:"mi", output:"\u03C2", ttype:0},
		{input:"\\sigma", tag:"mi", output:"\u03C3", ttype:0},
		{input:"\\tau", tag:"mi", output:"\u03C4", ttype:0},
		{input:"\\upsilon", tag:"mi", output:"\u03C5", ttype:0},
		{input:"\\phi", tag:"mi", output:"\u03C6", ttype:0},
		{input:"\\varphi", tag:"mi", output:"\u03D5", ttype:0},
		{input:"\\chi", tag:"mi", output:"\u03C7", ttype:0},
		{input:"\\psi", tag:"mi", output:"\u03C8", ttype:0},
		{input:"\\omega", tag:"mi", output:"\u03C9", ttype:0},
		{input:"\\Gamma", tag:"mo", output:"\u0393", ttype:0},
		{input:"\\Delta", tag:"mo", output:"\u0394", ttype:0},
		{input:"\\Theta", tag:"mo", output:"\u0398", ttype:0},
		{input:"\\Lambda", tag:"mo", output:"\u039B", ttype:0},
		{input:"\\Xi", tag:"mo", output:"\u039E", ttype:0},
		{input:"\\Pi", tag:"mo", output:"\u03A0", ttype:0},
		{input:"\\Sigma", tag:"mo", output:"\u03A3", ttype:0},
		{input:"\\Upsilon", tag:"mo", output:"\u03A5", ttype:0},
		{input:"\\Phi", tag:"mo", output:"\u03A6", ttype:0},
		{input:"\\Psi", tag:"mo", output:"\u03A8", ttype:0},
		{input:"\\Omega", tag:"mo", output:"\u03A9", ttype:0},
	//fractions
		{input:"\\frac12", tag:"mo", output:"\u00BD", ttype:0},
		{input:"\\frac14", tag:"mo", output:"\u00BC", ttype:0},
		{input:"\\frac34", tag:"mo", output:"\u00BE", ttype:0},
		{input:"\\frac13", tag:"mo", output:"\u2153", ttype:0},
		{input:"\\frac23", tag:"mo", output:"\u2154", ttype:0},
		{input:"\\frac15", tag:"mo", output:"\u2155", ttype:0},
		{input:"\\frac25", tag:"mo", output:"\u2156", ttype:0},
		{input:"\\frac35", tag:"mo", output:"\u2157", ttype:0},
		{input:"\\frac45", tag:"mo", output:"\u2158", ttype:0},
		{input:"\\frac16", tag:"mo", output:"\u2159", ttype:0},
		{input:"\\frac56", tag:"mo", output:"\u215A", ttype:0},
		{input:"\\frac18", tag:"mo", output:"\u215B", ttype:0},
		{input:"\\frac38", tag:"mo", output:"\u215C", ttype:0},
		{input:"\\frac58", tag:"mo", output:"\u215D", ttype:0},
		{input:"\\frac78", tag:"mo", output:"\u215E", ttype:0},
	//binary operation symbols
		{input:"\\pm", tag:"mo", output:"\u00B1", ttype:0},
		{input:"\\mp", tag:"mo", output:"\u2213", ttype:0},
		{input:"\\triangleleft",tag:"mo", output:"\u22B2", ttype:0},
		{input:"\\triangleright",tag:"mo",output:"\u22B3", ttype:0},
		{input:"\\cdot", tag:"mo", output:"\u22C5", ttype:0},
		{input:"\\star", tag:"mo", output:"\u22C6", ttype:0},
		{input:"\\ast", tag:"mo", output:"\u002A", ttype:0},
		{input:"\\times", tag:"mo", output:"\u00D7", ttype:0},
		{input:"\\div", tag:"mo", output:"\u00F7", ttype:0},
		{input:"\\circ", tag:"mo", output:"\u2218", ttype:0},
		{input:"\\bullet", tag:"mo", output:"\u2022", ttype:0},
		{input:"\\oplus", tag:"mo", output:"\u2295", ttype:0},
		{input:"\\ominus", tag:"mo", output:"\u2296", ttype:0},
		{input:"\\otimes", tag:"mo", output:"\u2297", ttype:0},
		{input:"\\bigcirc", tag:"mo", output:"\u25CB", ttype:0},
		{input:"\\oslash", tag:"mo", output:"\u2298", ttype:0},
		{input:"\\odot", tag:"mo", output:"\u2299", ttype:0},
		{input:"\\land", tag:"mo", output:"\u2227", ttype:0},
		{input:"\\wedge", tag:"mo", output:"\u2227", ttype:0},
		{input:"\\lor", tag:"mo", output:"\u2228", ttype:0},
		{input:"\\vee", tag:"mo", output:"\u2228", ttype:0},
		{input:"\\cap", tag:"mo", output:"\u2229", ttype:0},
		{input:"\\cup", tag:"mo", output:"\u222A", ttype:0},
		{input:"\\sqcap", tag:"mo", output:"\u2293", ttype:0},
		{input:"\\sqcup", tag:"mo", output:"\u2294", ttype:0},
		{input:"\\uplus", tag:"mo", output:"\u228E", ttype:0},
		{input:"\\amalg", tag:"mo", output:"\u2210", ttype:0},
		{input:"\\bigtriangleup",tag:"mo",output:"\u25B3", ttype:0},
		{input:"\\bigtriangledown",tag:"mo",output:"\u25BD", ttype:0},
		{input:"\\dag", tag:"mo", output:"\u2020", ttype:0},
		{input:"\\dagger", tag:"mo", output:"\u2020", ttype:0},
		{input:"\\ddag", tag:"mo", output:"\u2021", ttype:0},
		{input:"\\ddagger", tag:"mo", output:"\u2021", ttype:0},
		{input:"\\lhd", tag:"mo", output:"\u22B2", ttype:0},
		{input:"\\rhd", tag:"mo", output:"\u22B3", ttype:0},
		{input:"\\unlhd", tag:"mo", output:"\u22B4", ttype:0},
		{input:"\\unrhd", tag:"mo", output:"\u22B5", ttype:0},
	//Big Operators
		{input:"\\sum", tag:"mo", output:"\u2211", ttype:7},
		{input:"\\prod", tag:"mo", output:"\u220F", ttype:7},
		{input:"\\bigcap", tag:"mo", output:"\u22C2", ttype:7},
		{input:"\\bigcup", tag:"mo", output:"\u22C3", ttype:7},
		{input:"\\bigwedge", tag:"mo", output:"\u22C0", ttype:7},
		{input:"\\bigvee", tag:"mo", output:"\u22C1", ttype:7},
		{input:"\\bigsqcap", tag:"mo", output:"\u2A05", ttype:7},
		{input:"\\bigsqcup", tag:"mo", output:"\u2A06", ttype:7},
		{input:"\\coprod", tag:"mo", output:"\u2210", ttype:7},
		{input:"\\bigoplus", tag:"mo", output:"\u2A01", ttype:7},
		{input:"\\bigotimes", tag:"mo", output:"\u2A02", ttype:7},
		{input:"\\bigodot", tag:"mo", output:"\u2A00", ttype:7},
		{input:"\\biguplus", tag:"mo", output:"\u2A04", ttype:7},
		{input:"\\int", tag:"mo", output:"\u222B", ttype:0},
		{input:"\\oint", tag:"mo", output:"\u222E", ttype:0},
	//binary relation symbols
		{input:":=", tag:"mo", output:":=", ttype:0},
		{input:"\\lt", tag:"mo", output:"<", ttype:0},
		{input:"\\gt", tag:"mo", output:">", ttype:0},
		{input:"\\ne", tag:"mo", output:"\u2260", ttype:0},
		{input:"\\neq", tag:"mo", output:"\u2260", ttype:0},
		{input:"\\le", tag:"mo", output:"\u2264", ttype:0},
		{input:"\\leq", tag:"mo", output:"\u2264", ttype:0},
		{input:"\\leqslant", tag:"mo", output:"\u2264", ttype:0},
		{input:"\\ge", tag:"mo", output:"\u2265", ttype:0},
		{input:"\\geq", tag:"mo", output:"\u2265", ttype:0},
		{input:"\\geqslant", tag:"mo", output:"\u2265", ttype:0},
		{input:"\\equiv", tag:"mo", output:"\u2261", ttype:0},
		{input:"\\ll", tag:"mo", output:"\u226A", ttype:0},
		{input:"\\gg", tag:"mo", output:"\u226B", ttype:0},
		{input:"\\doteq", tag:"mo", output:"\u2250", ttype:0},
		{input:"\\prec", tag:"mo", output:"\u227A", ttype:0},
		{input:"\\succ", tag:"mo", output:"\u227B", ttype:0},
		{input:"\\preceq", tag:"mo", output:"\u227C", ttype:0},
		{input:"\\succeq", tag:"mo", output:"\u227D", ttype:0},
		{input:"\\subset", tag:"mo", output:"\u2282", ttype:0},
		{input:"\\supset", tag:"mo", output:"\u2283", ttype:0},
		{input:"\\subseteq", tag:"mo", output:"\u2286", ttype:0},
		{input:"\\supseteq", tag:"mo", output:"\u2287", ttype:0},
		{input:"\\sqsubset", tag:"mo", output:"\u228F", ttype:0},
		{input:"\\sqsupset", tag:"mo", output:"\u2290", ttype:0},
		{input:"\\sqsubseteq", tag:"mo", output:"\u2291", ttype:0},
		{input:"\\sqsupseteq", tag:"mo", output:"\u2292", ttype:0},
		{input:"\\sim", tag:"mo", output:"\u223C", ttype:0},
		{input:"\\simeq", tag:"mo", output:"\u2243", ttype:0},
		{input:"\\approx", tag:"mo", output:"\u2248", ttype:0},
		{input:"\\cong", tag:"mo", output:"\u2245", ttype:0},
		{input:"\\Join", tag:"mo", output:"\u22C8", ttype:0},
		{input:"\\bowtie", tag:"mo", output:"\u22C8", ttype:0},
		{input:"\\in", tag:"mo", output:"\u2208", ttype:0},
		{input:"\\ni", tag:"mo", output:"\u220B", ttype:0},
		{input:"\\owns", tag:"mo", output:"\u220B", ttype:0},
		{input:"\\propto", tag:"mo", output:"\u221D", ttype:0},
		{input:"\\vdash", tag:"mo", output:"\u22A2", ttype:0},
		{input:"\\dashv", tag:"mo", output:"\u22A3", ttype:0},
		{input:"\\models", tag:"mo", output:"\u22A8", ttype:0},
		{input:"\\perp", tag:"mo", output:"\u22A5", ttype:0},
		{input:"\\smile", tag:"mo", output:"\u2323", ttype:0},
		{input:"\\frown", tag:"mo", output:"\u2322", ttype:0},
		{input:"\\asymp", tag:"mo", output:"\u224D", ttype:0},
		{input:"\\notin", tag:"mo", output:"\u2209", ttype:0},
	//matrices
		{input:"\\begin{eqnarray}", output:"X", ttype:13, invisible:true},
		{input:"\\begin{array}", output:"X", ttype:13, invisible:true},
		{input:"\\\\", output:"}&{", ttype:8},
		{input:"\\end{eqnarray}", output:"}}", ttype:8},
		{input:"\\end{array}", output:"}}", ttype:8},
	//grouping and literal brackets -- ieval is for IE
		{input:"\\big", tag:"mo", output:"X", atval:"1.2", ieval:"2.2", ttype:10},
		{input:"\\Big", tag:"mo", output:"X", atval:"1.6", ieval:"2.6", ttype:10},
		{input:"\\bigg", tag:"mo", output:"X", atval:"2.2", ieval:"3.2", ttype:10},
		{input:"\\Bigg", tag:"mo", output:"X", atval:"2.9", ieval:"3.9", ttype:10},
		{input:"\\left", tag:"mo", output:"X", ttype:4},
		{input:"\\right", tag:"mo", output:"X", ttype:5},
		{input:"{", output:"{", ttype:4, invisible:true},
		{input:"}", output:"}", ttype:5, invisible:true},
		{input:"(", tag:"mo", output:"(", atval:"1", ttype:12},
		{input:"[", tag:"mo", output:"[", atval:"1", ttype:12},
		{input:"\\lbrack", tag:"mo", output:"[", atval:"1", ttype:12},
		{input:"\\{", tag:"mo", output:"{", atval:"1", ttype:12},
		{input:"\\lbrace", tag:"mo", output:"{", atval:"1", ttype:12},
		{input:"\\langle", tag:"mo", output:"\u2329", atval:"1", ttype:12},
		{input:"\\lfloor", tag:"mo", output:"\u230A", atval:"1", ttype:12},
		{input:"\\lceil", tag:"mo", output:"\u2308", atval:"1", ttype:12},
	// rtag:"mi" causes space to be inserted before a following sin, cos, etc.
	// (see function AMparseExpr() )
		{input:")", tag:"mo",output:")", rtag:"mi",atval:"1",ttype:12},
		{input:"]", tag:"mo",output:"]", rtag:"mi",atval:"1",ttype:12},
		{input:"\\rbrack",tag:"mo",output:"]", rtag:"mi",atval:"1",ttype:12},
		{input:"\\}", tag:"mo",output:"}", rtag:"mi",atval:"1",ttype:12},
		{input:"\\rbrace",tag:"mo",output:"}", rtag:"mi",atval:"1",ttype:12},
		{input:"\\rangle",tag:"mo",output:"\u232A", rtag:"mi",atval:"1",ttype:12},
		{input:"\\rfloor",tag:"mo",output:"\u230B", rtag:"mi",atval:"1",ttype:12},
		{input:"\\rceil", tag:"mo",output:"\u2309", rtag:"mi",atval:"1",ttype:12},
	// "|", "\\|", "\\vert" and "\\Vert" modified later: lspace = rspace = 0em
		{input:"|", tag:"mo", output:"\u2223", atval:"1", ttype:12},
		{input:"\\|", tag:"mo", output:"\u2225", atval:"1", ttype:12},
		{input:"\\vert", tag:"mo", output:"\u2223", atval:"1", ttype:12},
		{input:"\\Vert", tag:"mo", output:"\u2225", atval:"1", ttype:12},
		{input:"\\mid", tag:"mo", output:"\u2223", atval:"1", ttype:12},
		{input:"\\parallel", tag:"mo", output:"\u2225", atval:"1", ttype:12},
		{input:"/", tag:"mo", output:"/", atval:"1.01", ttype:12},
		{input:"\\backslash", tag:"mo", output:"\u2216", atval:"1", ttype:12},
		{input:"\\setminus", tag:"mo", output:"\\", ttype:0},
	//miscellaneous symbols
		{input:"\\!", tag:"mspace", atname:"width", atval:"-0.167em", ttype:6},
		{input:"\\,", tag:"mspace", atname:"width", atval:"0.167em", ttype:6},
		{input:"\\>", tag:"mspace", atname:"width", atval:"0.222em", ttype:6},
		{input:"\\:", tag:"mspace", atname:"width", atval:"0.222em", ttype:6},
		{input:"\\;", tag:"mspace", atname:"width", atval:"0.278em", ttype:6},
		{input:"~", tag:"mspace", atname:"width", atval:"0.333em", ttype:6},
		{input:"\\quad", tag:"mspace", atname:"width", atval:"1em", ttype:6},
		{input:"\\qquad", tag:"mspace", atname:"width", atval:"2em", ttype:6},
		{input:"\\prime", tag:"mo", output:"\u2032", ttype:0},
		{input:"'", tag:"mo", output:"\u02B9", ttype:0},
		{input:"''", tag:"mo", output:"\u02BA", ttype:0},
		{input:"'''", tag:"mo", output:"\u2034", ttype:0},
		{input:"''''", tag:"mo", output:"\u2057", ttype:0},
		{input:"\\ldots", tag:"mo", output:"\u2026", ttype:0},
		{input:"\\cdots", tag:"mo", output:"\u22EF", ttype:0},
		{input:"\\vdots", tag:"mo", output:"\u22EE", ttype:0},
		{input:"\\ddots", tag:"mo", output:"\u22F1", ttype:0},
		{input:"\\forall", tag:"mo", output:"\u2200", ttype:0},
		{input:"\\exists", tag:"mo", output:"\u2203", ttype:0},
		{input:"\\Re", tag:"mo", output:"\u211C", ttype:0},
		{input:"\\Im", tag:"mo", output:"\u2111", ttype:0},
		{input:"\\aleph", tag:"mo", output:"\u2135", ttype:0},
		{input:"\\hbar", tag:"mo", output:"\u210F", ttype:0},
		{input:"\\ell", tag:"mo", output:"\u2113", ttype:0},
		{input:"\\wp", tag:"mo", output:"\u2118", ttype:0},
		{input:"\\emptyset", tag:"mo", output:"\u2205", ttype:0},
		{input:"\\infty", tag:"mo", output:"\u221E", ttype:0},
		{input:"\\surd", tag:"mo", output:"\\sqrt{}", ttype:8},
		{input:"\\partial", tag:"mo", output:"\u2202", ttype:0},
		{input:"\\nabla", tag:"mo", output:"\u2207", ttype:0},
		{input:"\\triangle", tag:"mo", output:"\u25B3", ttype:0},
		{input:"\\therefore", tag:"mo", output:"\u2234", ttype:0},
		{input:"\\angle", tag:"mo", output:"\u2220", ttype:0},
		{input:"\\diamond", tag:"mo", output:"\u22C4", ttype:0},
		{input:"\\Diamond", tag:"mo", output:"\u25C7", ttype:0},
		{input:"\\neg", tag:"mo", output:"\u00AC", ttype:0},
		{input:"\\lnot", tag:"mo", output:"\u00AC", ttype:0},
		{input:"\\bot", tag:"mo", output:"\u22A5", ttype:0},
		{input:"\\top", tag:"mo", output:"\u22A4", ttype:0},
		{input:"\\square", tag:"mo", output:"\u25AB", ttype:0},
		{input:"\\Box", tag:"mo", output:"\u25A1", ttype:0},
		{input:"\\wr", tag:"mo", output:"\u2240", ttype:0},
	//standard functions
	//Note DEFINITION *must* have tag:"mo" to work properly
		{input:"\\arccos", tag:"mi", output:"arccos", ttype:1, func:true},
		{input:"\\arcsin", tag:"mi", output:"arcsin", ttype:1, func:true},
		{input:"\\arctan", tag:"mi", output:"arctan", ttype:1, func:true},
		{input:"\\arg", tag:"mi", output:"arg", ttype:1, func:true},
		{input:"\\cos", tag:"mi", output:"cos", ttype:1, func:true},
		{input:"\\cosh", tag:"mi", output:"cosh", ttype:1, func:true},
		{input:"\\cot", tag:"mi", output:"cot", ttype:1, func:true},
		{input:"\\coth", tag:"mi", output:"coth", ttype:1, func:true},
		{input:"\\csc", tag:"mi", output:"csc", ttype:1, func:true},
		{input:"\\deg", tag:"mi", output:"deg", ttype:1, func:true},
		{input:"\\det", tag:"mi", output:"det", ttype:1, func:true},
		{input:"\\dim", tag:"mi", output:"dim", ttype:1, func:true}, //0?
		{input:"\\exp", tag:"mi", output:"exp", ttype:1, func:true},
		{input:"\\gcd", tag:"mi", output:"gcd", ttype:1, func:true}, //0?
		{input:"\\hom", tag:"mi", output:"hom", ttype:1, func:true},
		{input:"\\inf", tag:"mo", output:"inf", ttype:7},
		{input:"\\ker", tag:"mi", output:"ker", ttype:1, func:true},
		{input:"\\lg", tag:"mi", output:"lg", ttype:1, func:true},
		{input:"\\lim", tag:"mo", output:"lim", ttype:7},
		{input:"\\liminf", tag:"mo", output:"liminf", ttype:7},
		{input:"\\limsup", tag:"mo", output:"limsup", ttype:7},
		{input:"\\ln", tag:"mi", output:"ln", ttype:1, func:true},
		{input:"\\log", tag:"mi", output:"log", ttype:1, func:true},
		{input:"\\max", tag:"mo", output:"max", ttype:7},
		{input:"\\min", tag:"mo", output:"min", ttype:7},
		{input:"\\Pr", tag:"mi", output:"Pr", ttype:1, func:true},
		{input:"\\sec", tag:"mi", output:"sec", ttype:1, func:true},
		{input:"\\sin", tag:"mi", output:"sin", ttype:1, func:true},
		{input:"\\sinh", tag:"mi", output:"sinh", ttype:1, func:true},
		{input:"\\sup", tag:"mo", output:"sup", ttype:7},
		{input:"\\tan", tag:"mi", output:"tan", ttype:1, func:true},
		{input:"\\tanh", tag:"mi", output:"tanh", ttype:1, func:true},
	//arrows
		{input:"\\gets", tag:"mo", output:"\u2190", ttype:0},
		{input:"\\leftarrow", tag:"mo", output:"\u2190", ttype:0},
		{input:"\\to", tag:"mo", output:"\u2192", ttype:0},
		{input:"\\rightarrow", tag:"mo", output:"\u2192", ttype:0},
		{input:"\\leftrightarrow", tag:"mo", output:"\u2194", ttype:0},
		{input:"\\uparrow", tag:"mo", output:"\u2191", ttype:0},
		{input:"\\downarrow", tag:"mo", output:"\u2193", ttype:0},
		{input:"\\updownarrow", tag:"mo", output:"\u2195", ttype:0},
		{input:"\\Leftarrow", tag:"mo", output:"\u21D0", ttype:0},
		{input:"\\Rightarrow", tag:"mo", output:"\u21D2", ttype:0},
		{input:"\\Leftrightarrow", tag:"mo", output:"\u21D4", ttype:0},
		{input:"\\iff", tag:"mo", output:"~\\Longleftrightarrow~", ttype:8},
		{input:"\\Uparrow", tag:"mo", output:"\u21D1", ttype:0},
		{input:"\\Downarrow", tag:"mo", output:"\u21D3", ttype:0},
		{input:"\\Updownarrow", tag:"mo", output:"\u21D5", ttype:0},
		{input:"\\mapsto", tag:"mo", output:"\u21A6", ttype:0},
		{input:"\\longleftarrow", tag:"mo", output:"\u2190", ttype:11},
		{input:"\\longrightarrow", tag:"mo", output:"\u2192", ttype:11},
		{input:"\\longleftrightarrow", tag:"mo", output:"\u2194", ttype:11},
		{input:"\\Longleftarrow", tag:"mo", output:"\u21D0", ttype:11},
		{input:"\\Longrightarrow", tag:"mo", output:"\u21D2", ttype:11},
		{input:"\\Longleftrightarrow", tag:"mo", output:"\u21D4", ttype:11},
		{input:"\\longmapsto", tag:"mo", output:"\u21A6", ttype:0}, // disaster if LONG
	//commands with argument
		{input:"\\sqrt", tag:"msqrt", output:"sqrt", ttype:1},
		{input:"\\root", tag:"mroot", output:"root", ttype:2},
		{input:"\\frac", tag:"mfrac", output:"/", ttype:2},
		{input:"\\stackrel", tag:"mover", output:"stackrel", ttype:2},
		{input:"\\atop", tag:"mfrac", output:"", ttype:3},
		{input:"\\choose", tag:"mfrac", output:"", ttype:3},
		{input:"_", tag:"msub", output:"_", ttype:3},
		{input:"^", tag:"msup", output:"^", ttype:3},
		{input:"\\mathrm", tag:"mtext", output:"text", ttype:9},
		{input:"\\mbox", tag:"mtext", output:"mbox", ttype:9},
	//diacritical marks
		{input:"\\acute", tag:"mover", output:"\u00B4", ttype:1, acc:true},
		{input:"\\grave", tag:"mover", output:"\u0060", ttype:1, acc:true},
		{input:"\\breve", tag:"mover", output:"\u02D8", ttype:1, acc:true},
		{input:"\\check", tag:"mover", output:"\u02C7", ttype:1, acc:true},
		{input:"\\dot", tag:"mover", output:".", ttype:1, acc:true},
		{input:"\\ddot", tag:"mover", output:"..", ttype:1, acc:true},
		{input:"\\mathring", tag:"mover", output:"\u00B0", ttype:1, acc:true},
		{input:"\\vec", tag:"mover", output:"\u20D7", ttype:1, acc:true},
		{input:"\\overrightarrow",tag:"mover",output:"\u20D7", ttype:1, acc:true},
		{input:"\\overleftarrow",tag:"mover", output:"\u20D6", ttype:1, acc:true},
		{input:"\\hat", tag:"mover", output:"\u005E", ttype:1, acc:true},
		{input:"\\widehat", tag:"mover", output:"\u0302", ttype:1, acc:true},
		{input:"\\tilde", tag:"mover", output:"~", ttype:1, acc:true},
		{input:"\\widetilde", tag:"mover", output:"\u02DC", ttype:1, acc:true},
		{input:"\\bar", tag:"mover", output:"\u203E", ttype:1, acc:true},
		{input:"\\overbrace", tag:"mover", output:"\u23B4", ttype:1, acc:true},
		{input:"\\overline", tag:"mover", output:"\u00AF", ttype:1, acc:true},
		{input:"\\underbrace", tag:"munder", output:"\u23B5", ttype:1, acc:true},
		{input:"\\underline", tag:"munder", output:"\u00AF", ttype:1, acc:true},
	//typestyles and fonts
                {input:"\\bf", tag:"mstyle", atname:"mathvariant", atval:"bold", ttype:1},
                {input:"\\boldkey", tag:"mstyle", atname:"mathvariant", atval:"bold", ttype:1},
                {input:"\\bold", tag:"mstyle", atname:"mathvariant", atval:"bold", ttype:1},
		{input:"\\displaystyle",tag:"mstyle",atname:"displaystyle",atval:"true", ttype:1},
		{input:"\\textstyle",tag:"mstyle",atname:"displaystyle",atval:"false", ttype:1},
		{input:"\\scriptstyle",tag:"mstyle",atname:"scriptlevel",atval:"1", ttype:1},
		{input:"\\scriptscriptstyle",tag:"mstyle",atname:"scriptlevel",atval:"2", ttype:1},
		{input:"\\textrm", tag:"mstyle", output:"\\mathrm", ttype: 8},
		{input:"\\mathbf", tag:"mstyle", atname:"mathvariant", atval:"bold", ttype:1},
		{input:"\\textbf", tag:"mstyle", atname:"mathvariant", atval:"bold", ttype:1},
		{input:"\\mathit", tag:"mstyle", atname:"mathvariant", atval:"italic", ttype:1},
		{input:"\\textit", tag:"mstyle", atname:"mathvariant", atval:"italic", ttype:1},
		{input:"\\mathtt", tag:"mstyle", atname:"mathvariant", atval:"monospace", ttype:1},
		{input:"\\texttt", tag:"mstyle", atname:"mathvariant", atval:"monospace", ttype:1},
		{input:"\\mathsf", tag:"mstyle", atname:"mathvariant", atval:"sans-serif", ttype:1},
		{input:"\\mathbb", tag:"mstyle", atname:"mathvariant", atval:"double-struck", ttype:1, codes:AMbbb},
                {input:"\\Bbb", tag:"mstyle", atname:"mathvariant", atval:"double-struck", ttype:1, codes:AMbbb},
		{input:"\\mathcal",tag:"mstyle", atname:"mathvariant", atval:"script", ttype:1, codes:AMcal},
                {input:"\\scr",tag:"mstyle", atname:"mathvariant", atval:"script", ttype:1, codes:AMcal},
		{input:"\\mathfrak",tag:"mstyle",atname:"mathvariant", atval:"fraktur",ttype:1, codes:AMfrk}
	],
	AMcompareNames: function(s1,s2) {
			if (s1.input > s2.input) return 1
			else return -1;
	},
	init: function() {
		this.AMsymbols.sort(this.AMcompareNames);
		for (var i=0; i<this.AMsymbols.length; i++) this.AMnames[i] = this.AMsymbols[i].input;
	},
	AMcreateElementMathML: function(t) {
		if (this.isIE) return document.createElement("m:"+t);
		else return document.createElementNS(this.AMmathml,t);
	},
	AMcreateMmlNode: function(t,frag) {
		if (this.isIE) var node = document.createElement("m:"+t);
		else var node = document.createElementNS(this.AMmathml,t);
		node.appendChild(frag);
		return node;
	},
	newCommand: function(oldstr,newstr) {
		this.AMsymbols = this.AMsymbols.concat([{input:oldstr, tag:"mo", output:newstr, ttype:this.DEFINITION}]);
	},
	AMremoveCharsAndBlanks: function(str,n) {
		//remove n characters and any following blanks
		var st;
		st = str.slice(n);
		for (var i=0; i<st.length && st.charCodeAt(i)<=32; i=i+1);
		return st.slice(i);
	},
	AMposition: function(arr, str, n) {
		// return position >=n where str appears or would be inserted
		// assumes arr is sorted
		if (n==0) {
			var h,m;
			n = -1;
			h = arr.length;
			while (n+1<h) {
				m = (n+h) >> 1;
				if (arr[m]<str) n = m; else h = m;
			}
			return h;
		} else
			for (var i=n; i<arr.length && arr[i]<str; i++);
				return i; // i=arr.length || arr[i]>=str
	},
	AMgetSymbol: function(str) {
		//return maximal initial substring of str that appears in AMnames
		//return null if there is none
		var k = 0; //new pos
		var j = 0; //old pos
		var mk; //match pos
		var st;
		var tagst;
		var match = "";
		var more = true;
		for (var i=1; i<=str.length && more; i++) {
			st = str.slice(0,i); //initial substring of length i
			j = k;
			k = this.AMposition(this.AMnames, st, j);
			if (k<this.AMnames.length && str.slice(0,this.AMnames[k].length)==this.AMnames[k]){
				match = this.AMnames[k];
				mk = k;
				i = match.length;
			}
			more = k<this.AMnames.length && str.slice(0,this.AMnames[k].length)>=this.AMnames[k];
		}
		this.AMpreviousSymbol=this.AMcurrentSymbol;
		if (match!=""){
			this.AMcurrentSymbol=this.AMsymbols[mk].ttype;
			return this.AMsymbols[mk];
		}
		this.AMcurrentSymbol=this.CONST;
		k = 1;
		st = str.slice(0,1); //take 1 character
		if ("0"<=st && st<="9") tagst = "mn";
		else tagst = (("A">st || st>"Z") && ("a">st || st>"z")?"mo":"mi");
		return {input:st, tag:tagst, output:st, ttype:this.CONST};
	},
	AMpreviousSymbol: null,
	AMcurrentSymbol: null,
	AMparseSexpr: function(str) { //parses str and returns [node,tailstr,(node)tag]
		var symbol, node, result, result2, i, st,// rightvert = false,
		newFrag = document.createDocumentFragment();
		str = this.AMremoveCharsAndBlanks(str,0);
		symbol = this.AMgetSymbol(str); //either a token or a bracket or empty
		if (symbol == null || symbol.ttype == this.RIGHTBRACKET)
			return [null,str,null];
		if (symbol.ttype == this.DEFINITION) {
			str = symbol.output+this.AMremoveCharsAndBlanks(str,symbol.input.length);
			symbol = this.AMgetSymbol(str);
			if (symbol == null || symbol.ttype == this.RIGHTBRACKET)
				return [null,str,null];
		}
		str = this.AMremoveCharsAndBlanks(str,symbol.input.length);
		switch (symbol.ttype) {
		case this.SPACE:
			node = this.AMcreateElementMathML(symbol.tag);
			node.setAttribute(symbol.atname,symbol.atval);
			return [node,str,symbol.tag];
		case this.UNDEROVER:
			if (this.isIE) {
				if (symbol.input.substr(0,4) == "\\big") { // botch for missing symbols
					str = "\\"+symbol.input.substr(4)+str; // make \bigcup = \cup etc.
					symbol = this.AMgetSymbol(str);
					symbol.ttype = this.UNDEROVER;
					str = this.AMremoveCharsAndBlanks(str,symbol.input.length);
				}
			}
			return [this.AMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output)),str,symbol.tag];
		case this.CONST:
			var output = symbol.output;
			if (this.isIE) {
				if (symbol.input == "'")
					output = "\u2032";
				else if (symbol.input == "''")
					output = "\u2033";
				else if (symbol.input == "'''")
					output = "\u2033\u2032";
				else if (symbol.input == "''''")
					output = "\u2033\u2033";
				else if (symbol.input == "\\square")
					output = "\u25A1"; // same as \Box
				else if (symbol.input.substr(0,5) == "\\frac") {
					// botch for missing fractions
					var denom = symbol.input.substr(6,1);
					if (denom == "5" || denom == "6") {
						str = symbol.input.replace(/\\frac/,"\\frac ")+str;
						return [node,str,symbol.tag];
					}
				}
			}
			node = this.AMcreateMmlNode(symbol.tag,document.createTextNode(output));
			return[node,str,symbol.tag];
		case this.LONG: // added by DRW
			node = this.AMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output));
			node.setAttribute("minsize","1.5");
			node.setAttribute("maxsize","1.5");
			node = this.AMcreateMmlNode("mover",node);
			node.appendChild(this.AMcreateElementMathML("mspace"));
			return [node,str,symbol.tag];
		case this.STRETCHY: // added by DRW
			if (this.isIE && symbol.input == "\\backslash")
				symbol.output = "\\"; // doesn't expand, but then nor does "\u2216"
			node = this.AMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output));
			if (symbol.input == "|" || symbol.input == "\\vert" || symbol.input == "\\|" || symbol.input == "\\Vert") {
				node.setAttribute("lspace","0em");
				node.setAttribute("rspace","0em");
			}
			node.setAttribute("maxsize",symbol.atval); // don't allow to stretch here
			if (symbol.rtag != null)
				return [node,str,symbol.rtag];
			else
				return [node,str,symbol.tag];
		case this.BIG: // added by DRW
			var atval = symbol.atval;
			if (this.isIE)
				atval = symbol.ieval;
			symbol = this.AMgetSymbol(str);
			if (symbol == null)
				return [null,str,null];
			str = this.AMremoveCharsAndBlanks(str,symbol.input.length);
			node = this.AMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output));
			if (this.isIE) { // to get brackets to expand
				var space = this.AMcreateElementMathML("mspace");
				space.setAttribute("height",atval+"ex");
				node = this.AMcreateMmlNode("mrow",node);
				node.appendChild(space);
			} else { // ignored in IE
				node.setAttribute("minsize",atval);
				node.setAttribute("maxsize",atval);
			}
			return [node,str,symbol.tag];
		case this.LEFTBRACKET: //read (expr+)
			if (symbol.input == "\\left") { // left what?
				symbol = this.AMgetSymbol(str);
				if (symbol != null) {
					if (symbol.input == ".")
						symbol.invisible = true;
					str = this.AMremoveCharsAndBlanks(str,symbol.input.length);
				}
			}
			result = this.AMparseExpr(str,true,false);
			if (symbol==null || (typeof symbol.invisible == "boolean" && symbol.invisible))
				node = this.AMcreateMmlNode("mrow",result[0]);
			else {
				node = this.AMcreateMmlNode("mo",document.createTextNode(symbol.output));
				node = this.AMcreateMmlNode("mrow",node);
				node.appendChild(result[0]);
			}
			return [node,result[1],result[2]];
		case this.MATRIX: //read (expr+)
			if (symbol.input == "\\begin{array}") {
				var mask = "";
				symbol = this.AMgetSymbol(str);
				str = this.AMremoveCharsAndBlanks(str,0);
				if (symbol == null)
					mask = "l";
				else {
					str = this.AMremoveCharsAndBlanks(str,symbol.input.length);
					if (symbol.input != "{")
						mask = "l";
					else do {
						symbol = this.AMgetSymbol(str);
						if (symbol != null) {
							str = this.AMremoveCharsAndBlanks(str,symbol.input.length);
							if (symbol.input != "}")
								mask = mask+symbol.input;
						}
					} while (symbol != null && symbol.input != "" && symbol.input != "}");
				}
				result = this.AMparseExpr("{"+str,true,true);
				node = this.AMcreateMmlNode("mtable",result[0]);
				mask = mask.replace(/l/g,"left ");
				mask = mask.replace(/r/g,"right ");
				mask = mask.replace(/c/g,"center ");
				node.setAttribute("columnalign",mask);
				node.setAttribute("displaystyle","false");
				if (this.isIE)
					return [node,result[1],null];
				// trying to get a *little* bit of space around the array
				// (IE already includes it)
				var lspace = this.AMcreateElementMathML("mspace");
				lspace.setAttribute("width","0.167em");
				var rspace = this.AMcreateElementMathML("mspace");
				rspace.setAttribute("width","0.167em");
				var node1 = this.AMcreateMmlNode("mrow",lspace);
				node1.appendChild(node);
				node1.appendChild(rspace);
				return [node1,result[1],null];
			} else { // eqnarray
				result = this.AMparseExpr("{"+str,true,true);
				node = this.AMcreateMmlNode("mtable",result[0]);
				if (this.isIE)
					node.setAttribute("columnspacing","0.25em"); // best in practice?
				else
					node.setAttribute("columnspacing","0.167em"); // correct (but ignored?)
				node.setAttribute("columnalign","right center left");
				node.setAttribute("displaystyle","true");
				node = this.AMcreateMmlNode("mrow",node);
				return [node,result[1],null];
			}
		case this.TEXT:
			if (str.charAt(0)=="{") i=str.indexOf("}");
			else i = 0;
			if (i==-1) i = str.length;
			st = str.slice(1,i);
			if (st.charAt(0) == " ") {
				node = this.AMcreateElementMathML("mspace");
				node.setAttribute("width","0.33em"); // was 1ex
				newFrag.appendChild(node);
			}
			newFrag.appendChild(this.AMcreateMmlNode(symbol.tag,document.createTextNode(st)));
			if (st.charAt(st.length-1) == " ") {
				node = this.AMcreateElementMathML("mspace");
				node.setAttribute("width","0.33em"); // was 1ex
				newFrag.appendChild(node);
			}
			str = this.AMremoveCharsAndBlanks(str,i+1);
			return [this.AMcreateMmlNode("mrow",newFrag),str,null];
		case this.UNARY:
			result = this.AMparseSexpr(str);
			if (result[0]==null) return [this.AMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output)),str];
			if (typeof symbol.func == "boolean" && symbol.func) { // functions hack
				st = str.charAt(0);
				if (st=="^" || st=="_" || st==",") {
					return [this.AMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output)),str,symbol.tag];
				} else {
					node = this.AMcreateMmlNode("mrow",this.AMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output)));
					if (this.isIE) {
						var space = this.AMcreateElementMathML("mspace");
						space.setAttribute("width","0.167em");
						node.appendChild(space);
					}
					node.appendChild(result[0]);
					return [node,result[1],symbol.tag];
				}
			}
			if (symbol.input == "\\sqrt") { // sqrt
				if (this.isIE) { // set minsize, for \surd
					var space = this.AMcreateElementMathML("mspace");
					space.setAttribute("height","1.2ex");
					space.setAttribute("width","0em"); // probably no effect
					node = this.AMcreateMmlNode(symbol.tag,result[0])
					node.appendChild(space);
					return [node,result[1],symbol.tag];
				} else
					return [this.AMcreateMmlNode(symbol.tag,result[0]),result[1],symbol.tag];
			} else if (typeof symbol.acc == "boolean" && symbol.acc) { // accent
				node = this.AMcreateMmlNode(symbol.tag,result[0]);
				var output = symbol.output;
				if (this.isIE) {
					if (symbol.input == "\\hat")
						output = "\u0302";
					else if (symbol.input == "\\widehat")
						output = "\u005E";
					else if (symbol.input == "\\bar")
						output = "\u00AF";
					else if (symbol.input == "\\grave")
						output = "\u0300";
					else if (symbol.input == "\\tilde")
						output = "\u0303";
				}
				var node1 = this.AMcreateMmlNode("mo",document.createTextNode(output));
				if (symbol.input == "\\vec" || symbol.input == "\\check") // don't allow to stretch
					node1.setAttribute("maxsize","1.2"); // why doesn't "1" work? \vec nearly disappears in firefox
				if (this.isIE && symbol.input == "\\bar")
					node1.setAttribute("maxsize","0.5");
				if (symbol.input == "\\underbrace" || symbol.input == "\\underline")
					node1.setAttribute("accentunder","true");
				else
					node1.setAttribute("accent","true");
				node.appendChild(node1);
				if (symbol.input == "\\overbrace" || symbol.input == "\\underbrace")
					node.ttype = UNDEROVER;
				return [node,result[1],symbol.tag];
			} else { // font change or displaystyle command
				if (!this.isIE && typeof symbol.codes != "undefined") {
					for (i=0; i<result[0].childNodes.length; i++)
						if (result[0].childNodes[i].nodeName=="mi" || result[0].nodeName=="mi") {
							st = (result[0].nodeName=="mi"?result[0].firstChild.nodeValue:result[0].childNodes[i].firstChild.nodeValue);
						var newst = [];
						for (var j=0; j<st.length; j++)
							if (st.charCodeAt(j)>64 && st.charCodeAt(j)<91) newst = newst + String.fromCharCode(symbol.codes[st.charCodeAt(j)-65]);
							else newst = newst + st.charAt(j);
						if (result[0].nodeName=="mi")
							result[0]=this.AMcreateElementMathML("mo").appendChild(document.createTextNode(newst));
						else result[0].replaceChild(this.AMcreateElementMathML("mo").appendChild(document.createTextNode(newst)),result[0].childNodes[i]);
					}
				}
				node = this.AMcreateMmlNode(symbol.tag,result[0]);
				node.setAttribute(symbol.atname,symbol.atval);
				if (symbol.input == "\\scriptstyle" || symbol.input == "\\scriptscriptstyle")
					node.setAttribute("displaystyle","false");
				return [node,result[1],symbol.tag];
			}
		case this.BINARY:
			result = this.AMparseSexpr(str);
			if (result[0]==null) return [this.AMcreateMmlNode("mo",document.createTextNode(symbol.input)),str,null];
			result2 = this.AMparseSexpr(result[1]);
			if (result2[0]==null) return [this.AMcreateMmlNode("mo",document.createTextNode(symbol.input)),str,null];
			if (symbol.input=="\\root" || symbol.input=="\\stackrel")
				newFrag.appendChild(result2[0]);
			newFrag.appendChild(result[0]);
			if (symbol.input=="\\frac") newFrag.appendChild(result2[0]);
			return [this.AMcreateMmlNode(symbol.tag,newFrag),result2[1],symbol.tag];
		case this.INFIX:
			str = this.AMremoveCharsAndBlanks(str,symbol.input.length);
			return [this.AMcreateMmlNode("mo",document.createTextNode(symbol.output)),str,symbol.tag];
		default:
			return [this.AMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output)),str,symbol.tag];
		}
 	},
	AMparseIexpr: function(str) {
		var symbol, sym1, sym2, node, result, tag, underover;
		str = this.AMremoveCharsAndBlanks(str,0);
		sym1 = this.AMgetSymbol(str);
		result = this.AMparseSexpr(str);
		node = result[0];
		str = result[1];
		tag = result[2];
		symbol = this.AMgetSymbol(str);
		if (symbol.ttype == this.INFIX) {
			str = this.AMremoveCharsAndBlanks(str,symbol.input.length);
			result = this.AMparseSexpr(str);
			if (result[0] == null) // show box in place of missing argument
				result[0] = this.AMcreateMmlNode("mo",document.createTextNode("\u25A1"));
			str = result[1];
			tag = result[2];
			if (symbol.input == "_" || symbol.input == "^") {
				sym2 = this.AMgetSymbol(str);
				tag = null; // no space between x^2 and a following sin, cos, etc.
				// This is for \underbrace and \overbrace
				underover = ((sym1.ttype == this.UNDEROVER) || (node.ttype == this.UNDEROVER));
				if (symbol.input == "_" && sym2.input == "^") {
					str = this.AMremoveCharsAndBlanks(str,sym2.input.length);
					var res2 = this.AMparseSexpr(str);
					str = res2[1];
					tag = res2[2]; // leave space between x_1^2 and a following sin etc.
					node = this.AMcreateMmlNode((underover?"munderover":"msubsup"),node);
					node.appendChild(result[0]);
					node.appendChild(res2[0]);
				} else if (symbol.input == "_") {
					node = this.AMcreateMmlNode((underover?"munder":"msub"),node);
					node.appendChild(result[0]);
				} else {
					node = this.AMcreateMmlNode((underover?"mover":"msup"),node);
					node.appendChild(result[0]);
				}
				node = this.AMcreateMmlNode("mrow",node); // so sum does not stretch
			} else {
				node = this.AMcreateMmlNode(symbol.tag,node);
				if (symbol.input == "\\atop" || symbol.input == "\\choose")
					node.setAttribute("linethickness","0ex");
				node.appendChild(result[0]);
				if (symbol.input == "\\choose")
					node = this.AMcreateMmlNode("mfenced",node);
			}
		}
		 return [node,str,tag];
	},
	AMparseExpr: function(str,rightbracket,matrix) {
 		var symbol, node, result, i, tag,
		newFrag = document.createDocumentFragment();
		do {
			str = this.AMremoveCharsAndBlanks(str,0);
			result = this.AMparseIexpr(str);
			node = result[0];
			str = result[1];
			tag = result[2];
			symbol = this.AMgetSymbol(str);
			if (node!=undefined) {
				if ((tag == "mn" || tag == "mi") && symbol!=null && typeof symbol.func == "boolean" && symbol.func) {
					// Add space before \sin in 2\sin x or x\sin x
					var space = this.AMcreateElementMathML("mspace");
					space.setAttribute("width","0.167em");
					node = this.AMcreateMmlNode("mrow",node);
					node.appendChild(space);
				}
				newFrag.appendChild(node);
			}
		} while ((symbol.ttype != this.RIGHTBRACKET) && symbol!=null && symbol.output!="");
		tag = null;
		if (symbol.ttype == this.RIGHTBRACKET) {
			if (symbol.input == "\\right") { // right what?
				str = this.AMremoveCharsAndBlanks(str,symbol.input.length);
				symbol = this.AMgetSymbol(str);
				if (symbol != null && symbol.input == ".")
					symbol.invisible = true;
				if (symbol != null)
					tag = symbol.rtag;
			}
			if (symbol!=null)
				str = this.AMremoveCharsAndBlanks(str,symbol.input.length); // ready to return
			var len = newFrag.childNodes.length;
			if (matrix && len>0 && newFrag.childNodes[len-1].nodeName == "mrow" && len>1 && newFrag.childNodes[len-2].nodeName == "mo" && newFrag.childNodes[len-2].firstChild.nodeValue == "&") { //matrix
				var pos = []; // positions of ampersands
				var m = newFrag.childNodes.length;
				for (i=0; matrix && i<m; i=i+2) {
					pos[i] = [];
					node = newFrag.childNodes[i];
					for (var j=0; j<node.childNodes.length; j++)
						if (node.childNodes[j].firstChild.nodeValue=="&") pos[i][pos[i].length]=j;
				}
				var row, frag, n, k, table = document.createDocumentFragment();
				for (i=0; i<m; i=i+2) {
					row = document.createDocumentFragment();
					frag = document.createDocumentFragment();
					node = newFrag.firstChild; // <mrow> -&-&...&-&- </mrow>
					n = node.childNodes.length;
					k = 0;
					for (j=0; j<n; j++) {
						if (typeof pos[i][k] != "undefined" && j==pos[i][k]){
							node.removeChild(node.firstChild); //remove &
							row.appendChild(this.AMcreateMmlNode("mtd",frag));
							k++;
						} else frag.appendChild(node.firstChild);
					}
					row.appendChild(this.AMcreateMmlNode("mtd",frag));
					if (newFrag.childNodes.length>2) {
						newFrag.removeChild(newFrag.firstChild); //remove <mrow> </mrow>
						newFrag.removeChild(newFrag.firstChild); //remove <mo>&</mo>
					}
					table.appendChild(this.AMcreateMmlNode("mtr",row));
				}
				return [table,str];
			}
			if (typeof symbol.invisible != "boolean" || !symbol.invisible) {
				node = this.AMcreateMmlNode("mo",document.createTextNode(symbol.output));
				newFrag.appendChild(node);
			}
		}
		return [newFrag,str,tag];
	},
	AMparseMath: function(str) {
		var result, node = this.AMcreateElementMathML("mstyle");
		node.appendChild(this.AMparseExpr(str.replace(/^\s+/g,""),false,false)[0]);
		node = this.AMcreateMmlNode("math",node);
		return node;
	},
	AMstrarr2docFrag: function(arr) {
		var newFrag=document.createDocumentFragment();
		newFrag.appendChild(this.AMparseMath(arr));
		return newFrag;
	}
};

config.macros.LaTeXMathMLPlugin.init();

config.formatters.push({
	name: "eqmath0",
	match: "\\$\\$",
	lookaheadRegExp: /\$\$((?:.|\n)*?)\$\$/mg,
	handler: function(w){
		this.lookaheadRegExp.lastIndex = w.matchStart;
		var lookaheadMatch = this.lookaheadRegExp.exec(w.source);
		if(lookaheadMatch){
			var eq = createTiddlyElement(w.output,"div");
			eq.style.textAlign='center';
			eq.appendChild(config.macros.LaTeXMathMLPlugin.AMstrarr2docFrag("\\displaystyle\{"+lookaheadMatch[1]+"\}"));
			w.nextMatch = lookaheadMatch.index + lookaheadMatch[0].length;
		}
	}
});

config.formatters.push({
	name: "eqmath1",
	match: "\\$",
	lookaheadRegExp: /\$((?:.|\n)*?)\$/mg,
	handler: function(w){
		this.lookaheadRegExp.lastIndex = w.matchStart;
		var lookaheadMatch = this.lookaheadRegExp.exec(w.source);
		if(lookaheadMatch){
			var eq = createTiddlyElement(w.output,"span");
			eq.appendChild(config.macros.LaTeXMathMLPlugin.AMstrarr2docFrag(lookaheadMatch[1]));
			w.nextMatch = lookaheadMatch.index + lookaheadMatch[0].length;
		}
	}
});

config.shadowTiddlers.LaTeXMathMLPluginDoc="The documentation is available [[here.|http://www.math.ist.utl.pt/~psoares/addons.html#LaTeXMathMLPluginDoc]]";
//}}}
//{{{
with(config.macros.LaTeXMathMLPlugin){
	newCommand("\\nle","\u2270");
	newCommand("\\R","\u211D");
        newCommand("\\tag","\\qquad\\qquad\\qquad\\qquad\\qquad\(");
        newCommand("\\cases","\\left\\{ \\begin{array}{ll}");
        newCommand("\\endcases","\\right.\\end{array}");
        newCommand("\\gather","\\left.\\begin{array}{c}");
        newCommand("\\endgather","\\right.\\end{array}");
        newCommand("\\text", "\\mbox");
        newCommand("\\ ","\u2009\u200A");
        newCommand("\\align","\\left.\\begin{eqnarray}");
        newCommand("\\endalign", "\\right.\\end{eqnarray}");
        newCommand("\\multline","\\begin{eqnarray}");
        newCommand("\\endmultline", "\\end{eqnarray}");
        newCommand("\\coloneq", ":=");
        newCommand("\\dots","\u2026\\,");
        newCommand("\\sbs","\\setminus");
        newCommand("\\limits_","_");
        newCommand("\\rm","\\mathrm\{");
        newCommand("\&gt;\;","&gt;");        
        newCommand("\&lt;\;","&lt;"); 
        newCommand("\·","\\cdot");
        newCommand("\\colon",": ");
        newCommand("\\{\\scr","\\scr\\{");
        newCommand("\ŋ","\\eta");
        newCommand("\µ","\\mu");
        newCommand("\\cosh","\\mbox{cosh}\\,");
        newCommand("\\sinh","\\mbox{sinh}\\,");
        newCommand("\\bfsigma","\\bf\\sigma");
        newCommand("\\bfvarepsilon","\\bf\\varepsilon");
        newCommand("\\ltimes", "\u22C9");
        newCommand("\\nearrow", "\u2197");
        newCommand("\\exp", "\\mbox{exp}\\,");        
	init();
}
//}}}
$\R$ $\mathbb{\R}$$\mathbb{\mathbb{\R}}$
!Description
This plugin is a modification of  a set of ~JavaScript functions to convert ~LaTeX math notation to Presentation ~MathML written by Douglas Woodall. The original notice can be found at the end of this text. The most important changes were:
#the substitution mechanism of ~LaTeX snippets (enclosed by {{{$...$}}} or {{{$$...$$}}}) was replaced by a couple of ~TiddlyWiki formatters
#centered equations (enclosed by {{{$$...$$}}}) are properly handled
#~MathML output can be decorated by CSS rules such as
{{{
math {
 font-family: sans-serif,arial;
 color: red;
}
}}}
!Installation
To use this plugin with Internet Explorer (IE) it is needed the [[MathPlayer|http://www.dessci.com/en/products/mathplayer/]] plugin for IE and the following lines should be added to the ~MarkupPreHead tiddler:
{{{
<html xmlns:m="http://www.w3.org/1998/Math/MathML">
<object id="mathplayer" classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987"></object>
<?import namespace="m" implementation="#mathplayer"?>
}}}
!Adding new symbols
The standard symbol table can be extended by adding additional symbols. This is done by adding a few lines of ~JavaScript code as in [[here|LaTeXMathMLPluginComp]].
You first have to find the four-digit hexadecimal Unicode value for these symbols by looking them up at, say, [[here|http://www.w3.org/TR/MathML2/chapter6.html#chars.entity.tables]].
!Credits
A final word of appreciation for the work of Douglas Woodall and Peter Jipsen on promoting the presentation of beautiful math in the web.
!Revision history
*1.1 06/10/2007
**Complete refactoring of the code. No more global variables!
*1.0.1 15/09/2007
**Included missing function 'newcommand' that allows the extension of the set of symbols available
*1.0.0 12/09/2007
**Initial release 
!Original notice
{{{
LaTeXMathML.js
==============

This file, in this form, is due to Douglas Woodall, June 2006.
It contains JavaScript functions to convert (most simple) LaTeX
math notation to Presentation MathML.  It was obtained by
downloading the file ASCIIMathML.js from
	http://www1.chapman.edu/~jipsen/mathml/asciimathdownload/
and modifying it so that it carries out ONLY those conversions
that would be carried out in LaTeX.  A description of the original
file, with examples, can be found at
	www1.chapman.edu/~jipsen/mathml/asciimath.html
	ASCIIMathML: Math on the web for everyone

Here is the header notice from the original file:

ASCIIMathML.js
==============
This file contains JavaScript functions to convert ASCII math notation
to Presentation MathML. The conversion is done while the (X)HTML page
loads, and should work with Firefox/Mozilla/Netscape 7+ and Internet
Explorer 6+MathPlayer (http://www.dessci.com/en/products/mathplayer/).
Just add the next line to your (X)HTML page with this file in the same folder:
<script type="text/javascript" src="ASCIIMathML.js"></script>
This is a convenient and inexpensive solution for authoring MathML.

Version 1.4.7 Dec 15, 2005, (c) Peter Jipsen http://www.chapman.edu/~jipsen
Latest version at http://www.chapman.edu/~jipsen/mathml/ASCIIMathML.js
For changes see http://www.chapman.edu/~jipsen/mathml/asciimathchanges.txt
If you use it on a webpage, please send the URL to jipsen@chapman.edu

This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or (at
your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
General Public License (at http://www.gnu.org/copyleft/gpl.html)
for more details.
}}}
/***
|Name|LoadTiddlersPlugin|
|Source|http://www.TiddlyTools.com/#LoadTiddlersPlugin|
|Documentation|http://www.TiddlyTools.com/#LoadTiddlersPluginInfo|
|Version|3.8.1|
|Author|Eric Shulman|
|License|http://www.TiddlyTools.com/#LegalStatements|
|~CoreVersion|2.1|
|Type|plugin|
|Description|macro for automated updates or one-click installations of tiddlers from remote sources|
!!!!!Documentation
>see [[LoadTiddlersPluginInfo]]
!!!!!Configuration
<<<
<<option chkLoadTiddlersShowReport>>after loading tiddlers, automatically display [[ImportedTiddlers]] (if created)
__password-protected server settings //(optional, if needed)//:__
>username: <<option txtRemoteUsername>> password: <<option txtRemotePassword>>
>{{{usage: <<option txtRemoteUsername>> <<option txtRemotePassword>>}}}
>''note: these settings are also used by [[ExternalTiddlersPlugin]] and [[ImportTiddlersPlugin]]''
<<<
!!!!!Revisions
<<<
2009.10.08 3.8.1 removed switchTheme() from doImport()... causes an INFINITE cycle of imports!
|please see [[LoadTiddlersPluginInfo]] for additional revision details|
2005.07.20 1.0.0 Initial Release
<<<
!!!!!Code
***/
//{{{
version.extensions.LoadTiddlersPlugin= {major: 3, minor: 8, revision: 1, date: new Date(2009,10,8)};

if (config.options.chkLoadTiddlersShowReport===undefined)
	config.options.chkLoadTiddlersShowReport=true;

config.macros.loadTiddlers = {
	label: '',
	tip: "add/update tiddlers from '%0'",
	lockedTag: 'noReload',	// if existing tiddler has this tag value, don't overwrite it, even if inbound tiddler is newer
	askMsg: 'Please enter a local path/filename or a remote URL',
	openMsg: 'Opening %0',
	openErrMsg: 'Could not open %0 - error=%1',
	readMsg: 'Read %0 bytes from %1',
	foundMsg: 'Found %0 tiddlers in %1',
	nochangeMsg: "'%0' is up-to-date... skipped.",
	lockedMsg: "'%0' is tagged '%1'... skipped.",
	skippedMsg: 'skipped (cancelled by user)',
	loadedMsg: 'Loaded %0 of %1 tiddlers from %2',
	reportTitle: 'ImportedTiddlers',
	warning: "Warning!!  Processing '%0' as a systemConfig (plugin) tiddler may produce unexpected results! Are you sure you want to proceed?",
	handler: function(place,macroName,params) {
		var label=(params[0] && params[0].substr(0,6)=='label:')?params.shift().substr(6):this.label;
		var tip=(params[0] && params[0].substr(0,7)=='prompt:')?params.shift().substr(7):this.tip;
		var filter='updates';
		if (params[0] && (params[0]=='all' || params[0]=='new' || params[0]=='changes' || params[0]=='updates'
			|| params[0].substr(0,8)=='tiddler:' || params[0].substr(0,4)=='tag:'))
			filter=params.shift();
		var src=params.shift(); if (!src || !src.length) return; // filename is required
		var quiet=(params[0]=='quiet'); if (quiet) params.shift();
		var ask=(params[0]=='confirm'); if (ask) params.shift();
		var force=(params[0]=='force'); if (force) params.shift();
		var init=(params[0]=='init'); if (init) params.shift();
		var nodirty=(params[0]=='nodirty'); if (nodirty) params.shift();
		var norefresh=(params[0]=='norefresh'); if (norefresh) params.shift();
		var noreport=(params[0]=='noreport'); if (noreport) params.shift();
		this.newTags=[]; if (params[0]) this.newTags=params; // any remaining params are used as 'autotags'
		if (label.trim().length) {
			// link triggers load tiddlers from another file/URL and then applies filtering rules to add/replace tiddlers in the store
			createTiddlyButton(place,label.format([src.replace(/%20/g,' ')]),tip.format([src.replace(/%20/g,' ')]), function() {
				if (src=='ask') src=prompt(this.askMsg);
				config.macros.loadTiddlers.loadFile(src,config.macros.loadTiddlers.doImport,{quiet:quiet,ask:ask,filter:filter,force:force,init:init,noreport:noreport});
				return false;
			})
		}
		else {
			// load tiddlers from another file/URL and then apply filtering rules to add/replace tiddlers in the store
			if (src=='ask') src=prompt(this.askMsg);
			config.macros.loadTiddlers.loadFile(src,config.macros.loadTiddlers.doImport,{quiet:quiet,ask:ask,filter:filter,force:force,init:init,nodirty:nodirty,norefresh:norefresh,noreport:noreport});
		}
	},
	loadFile: function(src,callback,params) {
		var quiet=params.quiet;
		if (src==undefined || !src.length) return null; // filename is required
		if (!quiet) clearMessage();
		if (!quiet) displayMessage(this.openMsg.format([src.replace(/%20/g,' ')]));
		// if working locally and src is not a URL, read from local filesystem
		if (document.location.protocol=='file:' && src.substr(0,5)!='http:' && src.substr(0,5)!='file:') {
			var txt=loadFile(src);
			if (!txt) { // file didn't load, might be relative path.. try fixup
				var pathPrefix=document.location.href;  // get current document path and trim off filename
				var slashpos=pathPrefix.lastIndexOf('/'); if (slashpos==-1) slashpos=pathPrefix.lastIndexOf('\\'); 
				if (slashpos!=-1 && slashpos!=pathPrefix.length-1) pathPrefix=pathPrefix.substr(0,slashpos+1);
				src=pathPrefix+src;
				if (pathPrefix.substr(0,5)!='http:') src=getLocalPath(src);
				var txt=loadFile(src);
			}
			if (!txt) { // file still didn't load, report error
				if (!quiet) displayMessage(this.openErrMsg.format([src.replace(/%20/g,' '),'(unknown)']));
			} else {
				if (!quiet) displayMessage(this.readMsg.format([txt.length,src.replace(/%20/g,' ')]));
				if (version.major+version.minor*.1+version.revision*.01!=2.52)
					txt=convertUTF8ToUnicode(txt);
				if (callback) callback(true,params,txt,src,null);
			}
		} else { // use XMLHttpRequest
			doHttp('GET',src,null,null,config.options.txtRemoteUsername,config.options.txtRemotePassword,callback,params,null);
		}
	},
	readTiddlersFromHTML: function(html) {
		// for TW2.2+
		if (TiddlyWiki.prototype.importTiddlyWiki!=undefined) {
			var remoteStore=new TiddlyWiki();
			remoteStore.importTiddlyWiki(html);
			return remoteStore.getTiddlers('title');	
		}
	},
	readTiddlersFromCSV: function(CSV) {
		var remoteStore=new TiddlyWiki();
		// GET NAMES
		var lines=CSV.replace(/\r/g,'').split('\n');
		var names=lines.shift().replace(/"/g,'').split(',');
		CSV=lines.join('\n');
		// ENCODE commas and newlines within quoted values
		var comma='!~comma~!'; var commaRE=new RegExp(comma,'g');
		var newline='!~newline~!'; var newlineRE=new RegExp(newline,'g');
		CSV=CSV.replace(/"([^"]*?)"/g,
			function(x){ return x.replace(/\,/g,comma).replace(/\n/g,newline); });
		// PARSE lines
		var lines=CSV.split('\n');
		for (var i=0; i<lines.length; i++) { if (!lines[i].length) continue;
			var values=lines[i].split(',');
			// DECODE commas, newlines, and doubled-quotes, and remove enclosing quotes (if any)
			for (var v=0; v<values.length; v++)
				values[v]=values[v].replace(commaRE,',').replace(newlineRE,'\n')
					.replace(/^"|"$/g,'').replace(/""/g,'"');
			// EXTRACT tiddler values
			var title=''; var text=''; var tags=[]; var fields={};
			var created=null; var when=new Date(); var who=config.options.txtUserName;
			for (var v=0; v<values.length; v++) { var val=values[v];
				if (names[v]) switch(names[v].toLowerCase()) {
					case 'title':	title=val.replace(/\[\]\|/g,'_'); break;
					case 'created': created=new Date(val); break;
					case 'modified':when=new Date(val); break;
					case 'modifier':who=val; break;
					case 'text':	text=val; break;
					case 'tags':	tags=val.readBracketedList(); break;
					default:	fields[names[v].toLowerCase()]=val; break;
				}
			}
			// CREATE tiddler in temporary store
			if (title.length)
				remoteStore.saveTiddler(title,title,text,who,when,tags,fields,true,created||when);
		}
		return remoteStore.getTiddlers('title');	
	},
	createTiddlerFromFile: function(src,txt) {
		var t=new Tiddler();
		var pos=src.lastIndexOf("/"); if (pos==-1) pos=src.lastIndexOf("\\");
		t.title=pos==-1?src:src.substr(pos+1);
		t.text=txt; 
		t.created=t.modified=new Date();
		t.modifier=config.options.txtUserName;
		if (src.substr(src.length-3,3)=='.js') t.tags=['systemConfig'];
		return [t];
	},
	doImport: function(status,params,html,src,xhr) {
		var cml=config.macros.loadTiddlers; // abbrev
		src=src.split('?')[0]; // strip off "?nocache=..."
		if (!status) {
			displayMessage(cml.openErrMsg.format([src.replace(/%20/g,' '),xhr.status]));
			return false;
		}
		var quiet=params.quiet;
		var ask=params.ask;
		var filter=params.filter;
		var force=params.force;
		var init=params.init;
		var nodirty=params.nodirty;
		var norefresh=params.norefresh;
		var noreport=params.noreport;
		var tiddlers = cml.readTiddlersFromHTML(html);
		if (!tiddlers||!tiddlers.length) tiddlers=cml.readTiddlersFromCSV(html);
		if (!tiddlers||!tiddlers.length) tiddlers=cml.createTiddlerFromFile(src,html);
		var count=tiddlers?tiddlers.length:0;
		if (!quiet) displayMessage(cml.foundMsg.format([count,src.replace(/%20/g,' ')]));
		var wasDirty=store.isDirty();
		store.suspendNotifications();
		var count=0;
		if (tiddlers) for (var t=0;t<tiddlers.length;t++) {
			var inbound = tiddlers[t];
			var theExisting = store.getTiddler(inbound.title);
			if (inbound.title==cml.reportTitle)
				continue; // skip 'ImportedTiddlers' history from the other document...
			if (theExisting && theExisting.tags.contains(cml.lockedTag)) {
				if (!quiet) displayMessage(cml.lockedMsg.format([theExisting.title,cml.lockedTag]));
				continue; // skip existing tiddler if tagged with 'noReload'
			}
			// apply the all/new/changes/updates filter (if any)
			if (filter && filter!='all') {
				if ((filter=='new') && theExisting) // skip existing tiddlers
					continue;
				if ((filter=='changes') && !theExisting) // skip new tiddlers
					continue;
				if ((filter.substr(0,4)=='tag:') && inbound.tags.indexOf(filter.substr(4))==-1) // must match specific tag value
					continue;
				if ((filter.substr(0,8)=='tiddler:') && inbound.title!=filter.substr(8)) // must match specific tiddler name
					continue;
				if (!force && store.tiddlerExists(inbound.title) && ((theExisting.modified.getTime()-inbound.modified.getTime())>=0)) {
					var msg=cml.nochangeMsg;
					if (!quiet&&msg.length) displayMessage(msg.format([inbound.title]));
					continue;
				}
			}
			// get confirmation if required
			var msg=(theExisting?'Update':'Add')+" tiddler '"+inbound.title+"'\n"
				+'from '+src.replace(/%20/g,' ')+'\n\nOK to proceed?';
			if (ask && !confirm(msg))
				{ tiddlers[t].status=cml.skippedMsg; continue; }
			// DO IT!
			var tags=new Array().concat(inbound.tags,cml.newTags);
	                store.saveTiddler(inbound.title, inbound.title, inbound.text, inbound.modifier,
				inbound.modified, tags, inbound.fields, true, inbound.created);
			// force creation date to imported value - needed for TW2.1.3 or earlier
	                store.fetchTiddler(inbound.title).created = inbound.created;
			tiddlers[t].status=theExisting?'updated':'added'
			if (init && tags.contains('systemConfig') && !tags.contains('systemConfigDisable')) {
				var ok=true;
				if (ask||!quiet) ok=confirm(cml.warning.format([inbound.title]))
				if (ok) { // run the plugin
					try { window.eval(inbound.text); tiddlers[t].status+=' (plugin initialized)'; }
					catch(ex) { displayMessage(config.messages.pluginError.format([exceptionText(ex)])); }
				}
			}
			count++;
		}
		store.resumeNotifications();
		if (count) {
			// set/clear 'unsaved changes' flag, refresh page display, and generate a report
			store.setDirty(wasDirty||!nodirty);
			if (!norefresh) {
				story.forEachTiddler(function(t,e){
					if(!story.isDirty(t))story.refreshTiddler(t,null,true)
				});
				store.notifyAll();
			}
			if (!noreport) cml.report(src,tiddlers,count,quiet);
		}
		// show message whenver tiddlers are actually loaded
		if (!quiet||count)
			displayMessage(cml.loadedMsg.format([count,tiddlers.length,src.replace(/%20/g,' ')]));
	},
	showReport: true,
	report: function(src,tiddlers,count,quiet) {
		var cml=config.macros.loadTiddlers; // abbrev
		// format the new report content
		var newText = 'On '+(new Date()).toLocaleString()+', ';
		newText += config.options.txtUserName+' loaded '+count+' tiddlers ';
		newText += 'from\n[['+src+'|'+src+']]:\n';
		newText += '<<<\n';
		for (var t=0; t<tiddlers.length; t++)
			if (tiddlers[t].status)
				newText += '#[['+tiddlers[t].title+']] - '+tiddlers[t].status+'\n';
		newText += '<<<\n';
		var title=cml.reportTitle;
		var currText='';
		var t=store.getTiddler(title);
		if (t) currText=(t.text.length?'\n----\n':'')+t.text;
		store.saveTiddler(title, title, newText+currText,
			config.options.txtUserName, new Date(),	t?t.tags:null, t?t.fields:null);
		if (!quiet) {
			if (config.options.chkLoadTiddlersShowReport)
				story.displayTiddler(null,title);
			story.refreshTiddler(title,null,true);
		}
	}
}
//}}}
/***
|Name|LoadTiddlersPluginInfo|
|Source|http://www.TiddlyTools.com/#LoadTiddlersPlugin|
|Documentation|http://www.TiddlyTools.com/#LoadTiddlersPluginInfo|
|Version|3.8.1|
|Author|Eric Shulman|
|License|http://www.TiddlyTools.com/#LegalStatements|
|~CoreVersion|2.1|
|Type|documentation|
|Description|documentation for LoadTiddlersPlugin|
!!!!!Usage
<<<
{{{
<<loadTiddlers label:... prompt:... filter source
	quiet confirm force init nodirty norefresh noreport
	tag tag tag...>>
}}}
*''label:...'' and ''prompt:...''<br>link and tooltip text to trigger the load tiddler processing.  If a label is NOT provided, then no link is created and the loadTiddlers function is performed whenever the containing tiddler is rendered.
*''filter'' (optional keyword)<br>determines which tiddlers will be automatically selected for importing.  Use one of the following:
**''all''<br>ALL tiddlers from the import source document, even if they have not been changed.
**''new''<br>only tiddlers that are found in the import source document, but do not yet exist in the destination document
**''changes''<br>only tiddlers that exist in both documents for which the import source tiddler is newer than the existing tiddler
**''updates''<br>both ''new'' and ''changes'' (this is the default action when none is specified)
**''tiddler:TiddlerName''<br>only the specified tiddler is retrieved
**''tag:value''<br>only the tiddlers tagged with the indicated value.
*''source'' (required)<br>is the location of the imported document.  It can be either a local document path/filename in whatever format your system requires, or a remote web location (starting with "http://" or "https://").  Use the special keyword, ''ask'', to prompt for a source location whenever the macro is invoked
*''quiet'' (optional)<br>supresses all status message during the import processing.  Note: if any tiddlers are actually imported, a final message will still be displayed, even when 'quiet' is specified.  This ensures that changes to your document cannot occur without any visible indication at all.
*''confirm'' (optional)<br>adds interactive confirmation for each inbound tiddler, so that you can manually bypass any tiddlers that you do not want to import.
*''init'' (optional)<br>invokes tiddlers tagged with <<tag systemConfig>> as plugins as soon as they are imported, without requiring a save-and-reload action first.  For safety, you will be asked to confirm each imported plugin, so that you can manually bypass any that you do not want to invoke.  Note, however, that those tiddlers are still //imported// and saved with your document and will still take effect the next time you save-and-reload the document.
*''force'' (optional)<br>imports all matching tiddlers, even if unchanged
*''noreport'' (optional)<br>suppress generation of [[ImportedTiddlers]] report
*''nodirty'' (optional)<br>loads tiddlers without marking the document as 'dirty' (i.e., needing to be saved)
*''norefresh'' (optional)<br>prevents automatic re-rendering of the page after tiddlers are loaded
*''tag tag tag...'' (optional)<br>any remaining parameters are used as tag values to be added to each imported tiddler (i.e., "tag-on-import")
Note: if a tiddler in the current document is tagged with<<tag noReload>> then it ''will not be overwritten, even if the inbound tiddler has been selected'' by the filtering process.  This allows you to make local changes to imported tiddlers while ensuring that those changes won't be lost due to automatic tiddler updates retrieved from the import source document.
<<<
!!!!!Examples
<<<
{{{<<loadTiddlers "label:load tiddlers from %0" example.html confirm temporary>>}}}
<<loadTiddlers "label:load tiddlers from %0" example.html confirm temporary>>
<<<
!!!!!Configuration
<<<
<<option chkLoadTiddlersShowReport>>after loading tiddlers, automatically display [[ImportedTiddlers]] (if created)
__password-protected server settings //(optional, if needed)//:__
>username: <<option txtRemoteUsername>> password: <<option txtRemotePassword>>
>{{{usage: <<option txtRemoteUsername>> <<option txtRemotePassword>>}}}
>''note: these settings are also used by [[ExternalTiddlersPlugin]] and [[ImportTiddlersPlugin]]''
<<<
!!!!!Revisions
<<<
2009.10.08 3.8.1 removed switchTheme() from doImport()... causes an INFINITE cycle of imports!
2009.10.06 3.8.0 added createTiddlerFromFile (import text files)
2009.10.04 3.7.8 in doImport(), call switchTheme() after loading tiddlers
2009.09.27 3.7.7 in readTiddlersFromCSV(), strip \r from input and fixed handling for quoted values
2009.09.01 3.7.6 added config.options.chkLoadTiddlersShowReport (default=true)
2009.09.01 3.7.6 added config.options.chkLoadTiddlersShowReport (default=true)
2009.08.30 3.7.5 in doImport(), check status and report error, if any
2009.08.29 3.7.4 in handler(), added 'return false' in button function (fixes IE page transition)
2009.08.19 3.7.3 in doImport(), fixed 'init' handling
2009.08.16 3.7.2 in doImport(), corrected check for tiddlers returned by readTiddlersFromHTML();
2009.07.03 3.7.1 fixups for TW252: doHttp() doesn't return XHR and convertUTF8ToUnicode() not needed for local I/O
2009.05.04 3.7.0 read CSV file format
2008.11.14 3.6.4 in loadFile(), force use of XMLHttpRequest if not viewing a local document (supports use of relative file references when online)
2008.10.27 3.6.3 in doImport(), fixed Safari bug by replacing static Array.concat(...) with new Array().concat(...)
2008.08.05 3.6.2 rewrote loadFile() to eliminate use of platform-specific fileExists() test
2008.08.03 3.6.1 in handler(), changed variable 'prompt' to 'tip' to avoid conflict with prompt() function
2008.01.07 3.6.0 added 'init' option to automatically invoke plugin tiddlers as soon as they are loaded (without needing save/reload)
2008.01.03 3.5.0 in loadFile(), use lower-level doHttp() instead of loadRemoteFile() in order to support username/password access to remote server
2007.12.04 *.*.* update for TW2.3.0: replaced deprecated core functions, regexps, and macros
2007.06.27 3.4.8 added missing 'fields' params to saveTiddler() call. Fixes problem where importing tiddlers would lose the custom fields.
2007.06.25 3.4.7 add calls to store.suspendNotifications() and store.resumeNotifications() to eliminate redisplay overhead DURING import activities.
2007.05.27 3.4.6 in handler(), loadRemoteFile() and doImport(), added 'noreport' flag to suppress generation of ImportedTiddlers
2007.05.27 3.4.5 in handler(), initialize 'newTags' to [] (empty array) instead of null... fixes fatal error when loading tiddler without autotagging.
2007.04.22 3.4.4 in readTiddlersFromHTML(), for TW2.2 and above, use importTiddlyWiki() (new core functionality) to get tiddlers from remote file content.  Also, copied updated TW21Loader.prototype.internalizeTiddler() definition from TW2.2b5 so plugin can read tiddlers from TW2.2+ even when running under TW2.1.x
2007.04.05 3.4.3 in doImport(), changed this.readTiddlersFromHTML(html) to config.macros.loadTiddlers.readTiddlersFromHTML(html).
2007.03.26 3.4.2 renamed import() to doImport() to fix IE load-time error ("identifier expected").  "import" is a reserved word in some browsers...
2007.03.22 3.4.1 code cleanup: moved all functions inside object def'n, re-wrote report function
2007.03.21 3.4.0 split ImportTiddlersPlugin and LoadTiddlersPlugin into separate plugins
|please see [[ImportTiddlersPluginInfo]] for additional revision details|
2005.07.20 1.0.0 Initial Release
<<<
Name: Blue
Background: #fff
Foreground: #000
PrimaryPale: #cdf
PrimaryLight: #57c
PrimaryMid: #114
PrimaryDark: #012
SecondaryPale: #ffc
SecondaryLight: #fe8
SecondaryMid: #db4
SecondaryDark: #841
TertiaryPale: #eee
TertiaryLight: #ccc
TertiaryMid: #999
TertiaryDark: #666
Error: #f88

Name: Green
Background: #fff
Foreground: #000
PrimaryPale: #9b9
PrimaryLight: #385
PrimaryMid: #031
PrimaryDark: #020
SecondaryPale: #ffc
SecondaryLight: #fe8
SecondaryMid: #db4
SecondaryDark: #841
TertiaryPale: #eee
TertiaryLight: #ccc
TertiaryMid: #999
TertiaryDark: #666
Error: #f88

Name: MR-colors
Background: #fff
Foreground: #000
PrimaryPale: #8cf
PrimaryLight: #e8793e
PrimaryMid: #ff4500
PrimaryDark: #014
SecondaryPale: #ffc
SecondaryLight: #fe8
SecondaryMid: #db4
SecondaryDark: #841
TertiaryPale: #eee
TertiaryLight: #ccc
TertiaryMid: #999
TertiaryDark: #666
Error: #f88
Name: Red
Background: #fff
Foreground: #000
PrimaryPale: #fdd
PrimaryLight: #c55
PrimaryMid: #711
PrimaryDark: #500
SecondaryPale: #ffc
SecondaryLight: #fe8
SecondaryMid: #db4
SecondaryDark: #841
TertiaryPale: #eee
TertiaryLight: #ccc
TertiaryMid: #999
TertiaryDark: #666
Error: #f88

Name: Smoke
Background: #fff
Foreground: #000
PrimaryPale: #aaa
PrimaryLight: #777
PrimaryMid: #111
PrimaryDark: #000
SecondaryPale: #ffc
SecondaryLight: #fe8
SecondaryMid: #db4
SecondaryDark: #841
TertiaryPale: #eee
TertiaryLight: #ccc
TertiaryMid: #999
TertiaryDark: #666
Error: #f88

Name: Teal
Background: #fff
Foreground: #000
PrimaryPale: #b5d1df
PrimaryLight: #618FA9
PrimaryMid: #1a3844
PrimaryDark: #000
SecondaryPale: #ffc
SecondaryLight: #fe8
SecondaryMid: #db4
SecondaryDark: #841
TertiaryPale: #f8f8f8
TertiaryLight: #bbb
TertiaryMid: #999
TertiaryDark: #888
Error: #f88
!!!A joint revision by Mathematical Reviews and Zentralblatt f&uuml;r Mathematik
* ''[[00-XX]]'' General
* ''[[01-XX]]'' History and biography [See also the classification number –03 in the other sections]
* ''[[03-XX]]'' Mathematical logic and foundations
* ''[[05-XX]]'' Combinatorics {For finite fields, see [[11Txx|11Txx]]}
* ''[[06-XX]]'' Order, lattices, ordered algebraic structures [See also [[18B35|18Bxx]]]
* ''[[08-XX]]'' General algebraic systems
* ''[[11-XX]]'' Number theory
* ''[[12-XX]]'' Field theory and polynomials
* ''[[13-XX]]'' Commutative algebra
* ''[[14-XX]]'' Algebraic geometry
* ''[[15-XX]]'' Linear and multilinear algebra; matrix theory
* ''[[16-XX]]'' Associative rings and algebras {For the commutative case, see [[13-XX|13-XX]]}
* ''[[17-XX]]'' Nonassociative rings and algebras
* ''[[18-XX]]'' Category theory; homological algebra {For commutative rings see [[13Dxx|13Dxx]], for associative rings [[16Exx|16Exx]], for groups [[20Jxx|20Jxx]], for topological groups and related structures [[57Txx|57Txx]]; see also [[55Nxx|55Nxx]] and [[55Uxx|55Uxx]] for algebraic topology}
* ''[[19-XX]]''  <html><math><mi>K</mi></math></html>-theory [See also [[16E20|16Exx]], [[18F25|18Fxx]]]
* ''[[20-XX]]'' Group theory and generalizations
* ''[[22-XX]]'' Topological groups, Lie groups {For transformation groups, see [[54H15|54Hxx]], [[57Sxx|57Sxx]], [[58-XX|58-XX]]. For abstract harmonic analysis, see [[43-XX|43-XX]]}
* ''[[26-XX]]'' Real functions [See also [[54C30|54Cxx]]]
* ''[[28-XX]]'' Measure and integration {For analysis on manifolds, see [[58-XX|58-XX]]}
* ''[[30-XX]]'' Functions of a complex variable {For analysis on manifolds, see [[58-XX|58-XX]]}
* ''[[31-XX]]'' Potential theory {For probabilistic potential theory, see [[60J45|60Jxx]]}
* ''[[32-XX]]'' Several complex variables and analytic spaces {For infinite-dimensional holomorphy, see [[46G20|46Gxx]], [[58B12|58Bxx]]}
* ''[[33-XX]]'' Special functions ([[33-XX|33-XX]] deals with the properties of functions as functions) {For orthogonal functions, see [[42Cxx|42Cxx]]; for aspects of combinatorics see [[05Axx|05Axx]]; for number-theoretic aspects see [[11-XX|11-XX]]; for representation theory see [[22Exx|22Exx]]}
* ''[[34-XX]]'' Ordinary differential equations
* ''[[35-XX]]'' Partial differential equations
* ''[[37-XX]]'' Dynamical systems and ergodic theory [See also [[26A18|26Axx]], [[28Dxx|28Dxx]], [[34Cxx|34Cxx]], [[34Dxx|34Dxx]], [[35Bxx|35Bxx]], [[46Lxx|46Lxx]], [[58Jxx|58Jxx]], [[70-XX|70-XX]]]
* ''[[39-XX]]'' Difference and functional equations
* ''[[40-XX]]'' Sequences, series, summability
* ''[[41-XX]]'' Approximations and expansions {For all approximation theory in the complex domain, see [[30E05|30Exx]] and [[30E10|30Exx]]; for all trigonometric approximation and interpolation, see [[42A10|42Axx]] and [[42A15|42Axx]]; for numerical approximation, see [[65Dxx|65Dxx]]}
* ''[[42-XX]]'' Harmonic analysis on Euclidean spaces
* ''[[43-XX]]'' Abstract harmonic analysis {For other analysis on topological and Lie groups, see [[22Exx|22Exx]]}
* ''[[44-XX]]'' Integral transforms, operational calculus {For fractional derivatives and integrals, see [[26A33|26Axx]]. For Fourier transforms, see [[42A38|42Axx]], [[42B10|42Bxx]]. For integral transforms in distribution spaces, see [[46F12|46Fxx]]. For numerical methods, see [[65R10|65Rxx]]}
* ''[[45-XX]]'' Integral equations
* ''[[46-XX]]'' Functional analysis {For manifolds modeled on topological linear spaces, see [[57Nxx|57Nxx]], [[58Bxx|58Bxx]]}
* ''[[47-XX]]'' Operator theory
* ''[[49-XX]]'' Calculus of variations and optimal control; optimization [See also [[34H05|34-XX]], [[34K35|34Kxx]], [[65Kxx|65Kxx]], [[90Cxx|90Cxx]], [[93-XX|93-XX]]]
* ''[[51-XX]]'' Geometry {For algebraic geometry, see [[14-XX|14-XX]]}
* ''[[52-XX]]'' Convex and discrete geometry
* ''[[53-XX]]'' Differential geometry {For differential topology, see [[57Rxx|57Rxx]]. For foundational questions of differentiable manifolds, see [[58Axx|58Axx]]}
* ''[[54-XX]]'' General topology {For the topology of manifolds of all dimensions, see [[57Nxx|57Nxx]]}
* ''[[55-XX]]'' Algebraic topology
* ''[[57-XX]]'' Manifolds and cell complexes {For complex manifolds, see [[32Qxx|32Qxx]]}
* ''[[58-XX]]'' Global analysis, analysis on manifolds [See also [[32Cxx|32Cxx]], [[32Fxx|32Fxx]], [[32Wxx|32Wxx]], [[46-XX|46-XX]], [[47Hxx|47Hxx]], [[53Cxx|53Cxx]]] {For geometric integration theory, see&nbsp;[[49Q15|49Qxx]]}
* ''[[60-XX]]'' Probability theory and stochastic processes {For additional applications, see [[11Kxx|11Kxx]], [[62-XX|62-XX]], [[90-XX|90-XX]], [[91-XX|91-XX]], [[92-XX|92-XX]], [[93-XX|93-XX]], [[94-XX|94-XX]]}
* ''[[62-XX]]'' Statistics
* ''[[65-XX]]'' Numerical analysis
* ''[[68-XX]]'' Computer science {For papers involving machine computations and programs in a specific mathematical area, see Section –04 in that area}
* ''[[70-XX]]'' Mechanics of particles and systems {For relativistic mechanics, see&nbsp;[[83A05|83-XX]] and [[83C10|83Cxx]]; for statistical mechanics, see&nbsp;[[82-XX|82-XX]]}
* ''[[74-XX]]'' Mechanics of deformable solids
* ''[[76-XX]]'' Fluid mechanics {For general continuum mechanics, see [[74Axx|74Axx]], or other parts of [[74-XX|74-XX]]}
* ''[[78-XX]]'' Optics, electromagnetic theory {For quantum optics, see [[81V80|81Vxx]]}
* ''[[80-XX]]'' Classical thermodynamics, heat transfer {For thermodynamics of solids, see [[74A15|74Axx]]}
* ''[[81-XX]]'' Quantum theory
* ''[[82-XX]]'' Statistical mechanics, structure of matter
* ''[[83-XX]]'' Relativity and gravitational theory
* ''[[85-XX]]'' Astronomy and astrophysics {For celestial mechanics, see [[70F15|70Fxx]]}
* ''[[86-XX]]'' Geophysics [See also [[76U05|76-XX]], [[76V05|76-XX]]]
* ''[[90-XX]]'' Operations research, mathematical programming
* ''[[91-XX]]'' Game theory, economics, social and behavioral sciences
* ''[[92-XX]]'' Biology and other natural sciences
* ''[[93-XX]]'' Systems theory; control {For optimal control, see [[49-XX|49-XX]]}
* ''[[94-XX]]'' Information and communication, circuits
* ''[[97-XX]]'' Mathematics education
<<miniBrowser http://msc2010.org>>
This ~TiddlyWiki version of the current ~MSC2010 is designed to be used locally as a searchable tree-structured version of the MSC which can be privately annotated; it was prepared  by Dean Carlson and Patrick Ion at MR/AMS.  
~MSCbot is the name used as an author by the robot program, written in Perl, that creates this [[TiddlyWWiki|http://www.tiddlywiki.org]] 
form of the MSC from a source file with TeX markup, which is used to prepare a print version of the MSC.
''<<toggleSideBar ToggleSidebar hide hide>>''
''[[MSC2010 Top|MSC2010]]''
<<closeAll>>&nbsp;|&nbsp;<<search>>
''[[Search Help|YourSearch Help]]''&nbsp;|&nbsp;''[[FAQ |FAQ/Help]]''
''<<slider  chkSliderOptionsPanel "More Help" "Toggle More Help">>''
''[[MSC2010 in PDF|http://www.msc2010.org/mscwiki/index.php?title=MSC-PDF]]''
''[[MSC2010 Site|http://msc2010.org/]]''
''[[Get Personal Copy|http://msc2010.org/download.php?file=MSC-2010-personal.html]]''
''[[MSC Conversions|http://msc2010.org/mscwiki/index.php?title=Code_Conversion_Tables]]''
''<<slider chkSliderOptionsPanel Areas "Toggle Areas" >>''
''[[AMS]]''&nbsp;|&nbsp;''[[MathSciNet]]''
''[[EMS]]''&nbsp;|&nbsp;''[[ZblMATH]]''
''[[Other Classifications|Other related classification schemes]]''
''[[Math on the Web]]''
''[[Colophon]]''
''[[DISCLAIMER|Disclaimer]]''
''[[Date of Creation|Date of Creation]]''


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<link rel='alternate' type='application/rss+xml' title='RSS' href='index.xml'/>
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<<miniBrowser http://www.ams.org/mathweb/>>
<<miniBrowser http://www.ams.org/mathscinet/search.html>>
/***
|Name|MiniBrowserPlugin|
|Source|http://www.TiddlyTools.com/#MiniBrowserPlugin|
|Version|1.3.1|
|Author|Eric Shulman - ELS Design Studios|
|License|http://www.TiddlyTools.com/#LegalStatements <br>and [[Creative Commons Attribution-ShareAlike 2.5 License|http://creativecommons.org/licenses/by-sa/2.5/]]|
|~CoreVersion|2.1|
|Type|plugin|
|Requires|PlayerPlugin (optional, recommended)|
|Overrides||
|Options|##Configuration|
|Description|embedded browser-in-browser with favorites lists and media support|
!!!!!Usage
<<<
{{{<<miniBrowser noplayer hidecontrols URL TiddlerName TiddlerName TiddlerName...>>}}}
* ''noplayer'' (optional)<br>disables support for embedded media player (using [[PlayerPlugin]], if installed)
* ''hidecontrols'' (optional)<br>hide initial display of minibrowser controls (except for 'show controls' checkbox)<br>//note: if no initial URL is specified, controls will be shown anyway//
* ''URL'' (optional)<br>specifies an initial URL to open when the mini browser is rendered
* ''TiddlerName'', ''TiddlerName''... (optional)<br>indicates one or more tiddlers containing "HR-separated" lists of favorites.<br>//notes: if no tiddler is specified, [[MiniBrowserList]] is used by default.  In addition, when adding/deleting favorites, the plugin automatically updates [[MiniBrowserList]], regardless of any alternative lists of favorites stored in separate tiddlers.  After changes to [[MiniBrowserList]] are made, you can then use cut/paste to manually move entries from that tiddler into other tiddlers.//
<<<
!!!!!Configuration
<<<
Default mini browser size:
width: <<option txtMiniBrowserWidth>> height: <<option txtMiniBrowserHeight>>
<<<
!!!!!Example
>{{{<<miniBrowser>>}}}<br>{{smallform small{<<miniBrowser>>}}}
>{{{<<miniBrowser hidecontrols http://www.TiddlyWiki.com>>}}}<br>{{smallform small{<<miniBrowser hidecontrols http://www.TiddlyWiki.com>>}}}
!!!!!Revisions
<<<
2008.09.16 [1.3.1] fixed getWikifiedData() when using IE (remove \r and multiple \n)
2008.08.12 [1.3.0] added support for wikifying content from favorites lists to enable use of forEachTiddler or inline script output to generate lists on the fly.
2008.08.06 [1.2.2] corrected size control buttons to use fixed width
2008.04.07 [1.2.1] added txtMiniBrowserWidth and txtMiniBrowserHeight.  cleanup init handling (somewhat)
2008.04.06 [1.2.0] added support for specifying initial URL to view (suggested by Richard Berg).  When opening a URL, select matching entry (if any) in bookmarks droplist.  Added support for hiding minibrowser controls.
2008.01.19 [1.1.0] added support for optional extra favorites lists stored in separate tiddlers
2007.10.15 [1.0.0] combined MiniBrowser and MediaCenter inline scripts and converted to true plugin
2006.03.01 [0.0.0] inline script
<<<
!!!!!Code
***/
//{{{
version.extensions.MiniBrowserPlugin={major: 1, minor: 3, revision: 1, date: new Date(2008,9,16)};
//}}}
//{{{
config.shadowTiddlers.MiniBrowser="<<miniBrowser>>";
//}}}
//{{{
if (config.options.txtMiniBrowserWidth==undefined) config.options.txtMiniBrowserWidth="100%";
if (config.options.txtMiniBrowserHeight==undefined) config.options.txtMiniBrowserHeight="480";
//}}}
//{{{
config.macros.miniBrowser= {
	favoritesList:
		"MiniBrowserList",
	handler: function(place,macroName,params,wikifier,paramString,tiddler) {

		var noPlayer=params[0]&&params[0].toLowerCase()=="noplayer"; if (noPlayer) params.shift();
		if (!config.macros.player) noPlayer=true; // if PlayerPlugin not installed
		var hideControls=params[0]&&params[0].toLowerCase()=="hidecontrols"; if (hideControls) params.shift();
		var url=(params[0]&&!store.tiddlerExists(params[0]))?params.shift():"";
		hideControls=hideControls&&url.length; // if no initial URL, then show controls anyway
		var w=config.options.txtMiniBrowserWidth;
		var h=config.options.txtMiniBrowserHeight;

		// create form
		var guid=new Date().getTime()+Math.random().toString(); // globally unique ID
		var html=this.html;
		html=html.replace(/%id%/g,guid);
		html=html.replace(/%noplayer%/g,noPlayer?"true":"");
		html=html.replace(/%hidecontrols%/g,hideControls?"none":"block");
		html=html.replace(/%favorites%/g,params[0]||config.macros.miniBrowser.favoritesList);
		createTiddlyElement(place,"span").innerHTML=html;

		// init form
		document.getElementById("minibrowser_controls_"+guid).style.display=hideControls?"none":"block";
		document.getElementById("minibrowser_resize_"+guid).style.display=hideControls?"none":"block";
		document.getElementById("minibrowser_togglecontrols_"+guid).checked=!hideControls;
		document.getElementById("minibrowser_form_"+guid).url.value=url;
		document.getElementById("minibrowser_form_"+guid).w.value=w;
		document.getElementById("minibrowser_form_"+guid).h.value=h;
		if (noPlayer) { // hide "type" list no PlayerPlugin
			document.getElementById("minibrowser_type_"+guid).style.display="none";
			document.getElementById("minibrowser_url_"+guid).style.width="36%";
		}

		// load bookmarks droplist from HR-separated tiddler contents
		var b=document.getElementById("minibrowser_bookmarks_"+guid);
		while (b.options[1]) b.options[1]=null; // clear list but leave 'prompt' item
		var p; while (p=params.shift()) this.getFavorites(b,p); // load custom bookmarks
		if (b.length<2) this.getFavorites(b,config.macros.miniBrowser.favoritesList); // default list

		// load initial URL (if any)
		var place=document.getElementById("minibrowser_player_"+guid);
		this.load(place,guid,"","",w,h,true,noPlayer);
		this.go(document.getElementById("minibrowser_form_"+guid));
	},
	getFavorites: function(list,tid) {
		var txt=store.getTiddlerText(tid); if (!txt||!txt.trim().length) return;
		txt=this.getWikifiedData(txt);
		var parts=txt.split("\n----\n");
		for (var p=0; p<parts.length; p++) {
			var lines=parts[p].split("\n");
			var label=lines.shift()||""; // 1st line=display text
			var value=lines.shift()||""; // 2nd line=item value
			var indent=value&&value.length?"\xa0\xa0":"";
			list.options[list.length]=new Option(indent+label,value,false,false);
		}
	},
	getWikifiedData: // wikify tiddler content, then extract text WITH newlines and HRs included
	function(txt) {
		var e=createTiddlyElement(document.body,"div"); wikify(txt,e);
		var breaks=e.getElementsByTagName("br");
		for (var b=0; b<breaks.length; b++)
			breaks[b].parentNode.insertBefore(document.createTextNode("\n"),breaks[b]);
		var lines=e.getElementsByTagName("hr");
		for (var l=0; l<lines.length; l++)
			lines[l].parentNode.insertBefore(document.createTextNode("----\n"),lines[l]);
		var items=e.getElementsByTagName("li");
		for (var i=0; i<items.length; i++)
			items[i].parentNode.insertBefore(document.createTextNode("\n"),items[i]);
		var txt=getPlainText(e);
		removeNode(e);
		return txt.replace(/\r*/g,"").replace(/\n\n/g,"\n");
	},
	load: function(place,id,type,url,w,h,showcontrols,noPlayer) {
		if (noPlayer) {
			if (!place) place=document.getElementById(id).parentNode;
			place.innerHTML="<iframe name='"+id+"' id='"+id+"' \
				src='"+url+"' width='"+w+"' height='"+h+"' \
				style='background:#fff;border:1px solid'></iframe>"
		} else
			config.macros.player.loadURL(place,id,type,url,w,h,showcontrols);
	},
	go: function(f) {
		var url=f.url.value.trim();
		if (!url.length) url=f.url.value=f.bookmarks.value.trim();
		if (!url.length) { this.done(f); return false; }
		var id=f.playerID.value;
		document.getElementById("minibrowser_player_"+id).style.display="block";
		document.getElementById("minibrowser_controls2_"+id).style.display="block";
		this.load(null,id,f.type.value,f.url.value,f.w.value,f.h.value,f.ctrls.checked,f.noPlayer.value=="true");
		var matched=false; for (var i=0; i<f.bookmarks.options.length; i++) // select matching bookmark
			if (f.bookmarks.options[i].value==url) { f.bookmarks.selectedIndex=i; matched=true; break; }
		if (!matched) f.bookmarks.selectedIndex=0;
		f.done.disabled=false;
		return false;
	},
	done: function(f) {
		var id=f.playerID.value;
		this.load(null,id,null,null,f.w.value,0,f.ctrls.checked,f.noPlayer.value=="true");
		document.getElementById("minibrowser_player_"+id).style.display="none";
		document.getElementById("minibrowser_controls2_"+id).style.display="none";
		f.done.disabled=true; 
		return false;
	},
	fit: function(place) {
		var trim=89; 	// fudge factor to account for the other controls + padding + borders.  ADJUST THIS VALUE TO FIT LAYOUT
		var t=story.findContainingTiddler(place);
		if (!t) { t=place; while (t && t.className!='floatingPanel') t=t.parentNode; } if (!t) return;
		var w="100%"; // horizontal stretching via CSS works, but vertical stretching doesn't... so:
		var h=t.offsetHeight-trim; // workaround: get containing panel/tiddler height and subtract "trim" height
		var f=place.form;
		this.load(null,f.playerID.value,f.type.value,f.url.value,w,h,f.ctrls.checked,f.noPlayer.value=="true"); // reload player with new size
		place.form.w.value=w; place.form.h.value=h; // update width/height input fields
	},
	add: function(place,title) {
		var v=place.value; if (!v.length) return;
		var d=prompt("Please enter a description for\n"+place.value); if (!d || !d.length) return;
		var who=config.options.txtUserName;
		var when=new Date();
		var tid=store.getTiddler(title);
		var txt="%0\n%1\n----\n%2".format([d,v,tid?tid.text:""]);
		store.saveTiddler(title,title,txt,who,when,tid?tid.tags:[],tid?tid.fields:{});
		if (!tid) story.displayTiddler(story.findContainingTiddler(place),title);
		else story.refreshTiddler(title,1,true);
		var here=story.findContainingTiddler(place);
		if (here) story.refreshTiddler(here.getAttribute("tiddler"),1,true);
	},
	del: function(place,title) {
		var v=place.value; if (!v.length) return;
		var d=place.options[place.selectedIndex].text; if (!d.length) return;
		if (!confirm("Are you sure you want to remove this favorite?\n\n"+d+"\n"+v)) return;
		var tid=store.getTiddler(title); if (!tid) return;
		var who=config.options.txtUserName;
		var when=new Date();
		var pat='%0\n%1\n----\n'.format([d.replace(/\xa0/g,''),v]); var re=new RegExp(pat,"i");
		var txt=tid.text.replace(re,"");
		store.saveTiddler(title,title,txt,who,when,tid?tid.tags:[],tid?tid.fields:{});
		story.refreshTiddler(title,1,true);
		var here=story.findContainingTiddler(place);
		if (here) story.refreshTiddler(here.getAttribute("tiddler"),1,true);
	},
	html: "<form id='minibrowser_form_%id%' style='display:block;margin:0;padding:0' onsubmit='return config.macros.miniBrowser.go(this);'><!-- \
		--><nobr><input type='hidden' name='playerID' value='%id%'><input type='hidden' name='noPlayer' value='%noplayer%'><!-- \
		--><div id='minibrowser_controls_%id%' style='display:%hidecontrols%'><!-- \
		--><input type='button' value='<' title='back' style='font-size:8pt;width:3%' \
			onclick='try{window.frames[\"player_%id%\"].history.go(-1)}catch(e){window.history.go(-1)}' ><!-- \
		--><input type='button' value='>' title='forward' style='font-size:8pt;width:3%' \
			onclick='try{window.frames[\"player_%id%\"].history.go(+1)}catch(e){window.history.go(+1)}'><!-- \
		--><input type='button' value='+' title='refresh'style='font-size:8pt;width:3%' \
			onclick='try{window.frames[\"player_%id%\"].location.reload()}catch(e){;}'><!-- \
		--><input type='button' value='x' title='stop'style='font-size:8pt;width:3%' \
			onclick='window.stop()'><!-- \
		--><select name='bookmarks' id='minibrowser_bookmarks_%id%' size='1' style='font-size:8pt;width:20%' \
			onchange='this.form.url.value=this.value; return config.macros.miniBrowser.go(this.form);'><!-- \
		--><option value=''>bookmarks...</option><!-- \
		--></select><!-- \
		--><input type='button' value='add' title='add URL to the bookmarks' style='font-size:8pt;width:5%' \
			favorites=\"%favorites%\" \
			onclick='config.macros.miniBrowser.add(this.form.url,this.getAttribute(\"favorites\"));'><!-- \
		--><input type='button' value='del' title='remove URL from the bookmarks' style='font-size:8pt;width:5%' \
			favorites=\"%favorites%\" \
			onclick='config.macros.miniBrowser.del(this.form.bookmarks,this.getAttribute(\"favorites\"));'><!-- \
		--><input type='button' value='edit' title='edit the bookmarks list' style='font-size:8pt;width:5%' \
			favorites=\"%favorites%\" \
			onclick='story.displayTiddler(null,this.getAttribute(\"favorites\"),2)'><!-- \
		--><input type='text' name='url' id='minibrowser_url_%id%' size='60' value='' style='font-size:8pt;width:23%' \
			onfocus='this.select()'><!-- \
		--><select name='type' id='minibrowser_type_%id%' size='1' style='font-size:8pt;width:13%'><!-- \
		--><option value=''>media type...</option><!-- \
		--><option value=''>auto-detect</option><!-- \
		--><option value='iframe'>web page</option><!-- \
		--><option value='windows'>windows media</option><!-- \
		--><option value='realone'>real one</option><!-- \
		--><option value='quicktime'>quicktime</option><!-- \
		--><option value='flash'>flash</option><!-- \
		--><option value='image'>jpg/gif/png</option><!-- \
		--></select><!-- \
		--><input type='submit' value='go' title='view URL in embedded player' style='font-size:8pt;width:4%'><!-- \
		--><input type='button' value='open' title='view URL in a separate player' style='font-size:8pt;width:6%' \
			onclick='if (this.form.url.value.length) window.open(this.form.url.value)'><!-- \
		--><input type='button' value='done' name='done' disabled title='disconnect from URL' style='font-size:8pt;width:6%' \
			onclick='return config.macros.miniBrowser.done(this.form);'><!-- \
		--></div><!-- \
		--><div id='minibrowser_player_%id%' style='display:none;text-align:center'></div><!-- \
		--><span id='minibrowser_controls2_%id%' style='margin-top:2px;display:none;font-size:8pt;'><!-- \
		--><div id='minibrowser_resize_%id%' style='display:%hidecontrols%;float:right;font-size:8pt'><!-- \
		--> size: <input type='text' name='w' size='3' value='' style='font-size:8pt;' \
			onfocus='this.select()'><!-- \
		-->x<input type='text' name='h' size='3' value='' style='font-size:8pt;' \
			onfocus='this.select()'><!-- \
		--> <input type='submit' value='set' style='font-size:8pt;width:5em' \
			onclick='var f=this.form; \
				if(!f.w.value.trim().length) f.w.value=config.options.txtMiniBrowserWidth; \
				if(!f.h.value.trim().length) f.h.value=config.options.txtMiniBrowserHeight; \
				config.options.txtMiniBrowserWidth=f.w.value; config.options.txtMiniBrowserHeight=f.h.value; \
				saveOptionCookie(\"txtMiniBrowserWidth\"); saveOptionCookie(\"txtMiniBrowserHeight\");'><!-- \
		--><input type='submit' value='reset' style='font-size:8pt;width:5em' \
			onclick='var f=this.form; f.ctrls.checked=true; f.w.value=\"100%\"; f.h.value=\"480\"; \
				config.options.txtMiniBrowserWidth=f.w.value; config.options.txtMiniBrowserHeight=f.h.value; \
				saveOptionCookie(\"txtMiniBrowserWidth\"); saveOptionCookie(\"txtMiniBrowserHeight\");'><!-- \
		--><input type='button' value='fit' title='resize player to fit containing window' style='font-size:8pt;width:5em' \
			onclick='config.macros.miniBrowser.fit(this)'><!-- \
		--></div><!-- \
		--> <input type='checkbox' name='ctrls' id='minibrowser_togglecontrols_%id%' title='toggle minibrowser controls' CHECKED  \
			onclick='document.getElementById(\"minibrowser_controls_%id%\").style.display=this.checked?\"block\":\"none\"; \
				document.getElementById(\"minibrowser_resize_%id%\").style.display=this.checked?\"block\":\"none\";' \
		><a href='' title='toggle minibrowser controls' \
			onclick='this.previousSibling.click();return false;'>show controls</a><!-- \
		--></span><!-- \
		--></nobr></form> \
	"
}
//}}}
''[[TiddlyWiki Markup|TiddlyWiki Markup CheatSheet]]
Using the ~MSC2010 is easy but takes some getting used to. Rather than scrolling up and down a long web page or word processing document, you open small chunks of information ("microcontent") written in boxes called "tiddlers." You read what you need from a tiddler, then close it with the ''close'' button at the top right hand corner of the tiddler.

Tiddlers are linked to each other in different ways: 
*[[through a MainMenu]]
*[[through hyperlinks]]
When a tiddler is opened up, it appears at the top of the screen or below the tiddler used to link to it. After opening a few tiddlers in succession, you might feel overwhelmed by all the open tiddlers. Not to worry. 
*You can close every tiddler but the one you are using by clicking on the ''close others'' button.
*If you have multiple tiddlers open, you can use the ''jump'' button to quickly go to the open tiddler you desire without having to scroll up and down.
*See [[here|Anatomy of a Tiddler]] for information on the other buttons at the top right of the tiddler.
To ''search for a tiddler'', you can use the search window in the ~MainMenu at your left. All the tiddlers that contain the word that you search for will appear. 
<<selectPalette>>

These Interface Options for customising ~TiddlyWiki are saved in your browser

Your username for signing your edits. Write it as a ~WikiWord (eg ~JoeBloggs)

<<option txtUserName>>
<<option chkAutoSave>> ~AutoSave
<<option chkRegExpSearch>> ~RegExpSearch
<<option chkCaseSensitiveSearch>> ~CaseSensitiveSearch
<<option chkAnimate>> ~EnableAnimations

----
Also see [[Advanced Options|AdvancedOptions]]
[[Physics and Astronomy Classification Scheme (PACS)]]
[[American Computing Machinery (ACM) Classification Scheme]]
[[Insurance: Mathematics and Economics Classification]]
[[ArXiv Mathematics categories]]
[[Guide to Available Mathematical Software (GAMS)]]
[[Journal of Economic Literature (JEL)|http://www.aeaweb.org/journal/jel_class_system.html]]
All of the above classifications schemes open in a minibrowser inside a tiddler except for the last one (JEL) which opens either in a separate window or tab depending on how your browser is set.
<!--{{{-->
<div class='header' macro='gradient vert [[ColorPalette::PrimaryLight]] [[ColorPalette::PrimaryMid]]'>
<div class='headerShadow'>
<span class='siteTitle' refresh='content' tiddler='SiteTitle'></span>&nbsp;
<span class='siteSubtitle' refresh='content' tiddler='SiteSubtitle'></span>
</div>
<div class='headerForeground'>
<span class='siteTitle' refresh='content' tiddler='SiteTitle'></span>&nbsp;
<span class='siteSubtitle' refresh='content' tiddler='SiteSubtitle'></span>
</div>
</div>
<div id='mainMenu' refresh='content' tiddler='MainMenu'></div>
<div id='sidebar'>
<div id='sidebarOptions' refresh='content' tiddler='SideBarOptions'></div>
<!-- Removed to eliminate long list of tiddlers in right sidebar -->
<!-- <div id='sidebarTabs' refresh='content' force='true' tiddler='SideBarTabs'></div>-->
</div>
<div id='displayArea'>
<div id='messageArea'></div>
<div id='tiddlerDisplay'></div>
</div>
<!--}}}-->
<<miniBrowser http://publish.aps.org/PACS/>>
<<plugins>>
/***
| Name|SelectPalettePlugin|
| Description|Lets you easily change colour palette|
| Version|3.0 ($Rev: 1845 $)|
| Date|$Date: 2007-03-16 15:19:22 +1000 (Fri, 16 Mar 2007) $|
| Source|http://mptw.tiddlyspot.com/#SelectPalettePlugin|
| Author|Simon Baird <simon.baird@gmail.com>|
| License|http://mptw.tiddlyspot.com/#TheBSDLicense|
/***
!!Usage:
{{{<<<selectPalette>>}}}
<<selectPalette>>

!!WARNING
Will overwrite your ColorPalette tiddler.
***/

//{{{

merge(config.macros,{

	setPalette: {

		handler: function(place,macroName,params,wikifier,paramString,tiddler) {
			var paletteName = params[0] ? params[0] : tiddler.title;
			createTiddlyButton(place,"apply","Apply this palette",function(e) {
				config.macros.selectPalette.updatePalette(tiddler.title);
				return false;
			});
		}
	},

	selectPalette: {

		handler: function(place,macroName,params,wikifier,paramString,tiddler) {
			createTiddlyDropDown(place,this.onPaletteChange,this.getPalettes());
		},

		getPalettes: function() {
			var result = [
				{caption:"-palette-", name:""},
				{caption:"(Default)", name:"(default)"}
			];
			var tagged = store.getTaggedTiddlers("palette","title");
			for(var t=0; t<tagged.length; t++) {
				var caption = tagged[t].title;
				var sliceTitle = store.getTiddlerSlice(caption,"Name");
				if (sliceTitle)
					caption = sliceTitle;
				result.push({caption:sliceTitle, name:tagged[t].title});
			}
			return result;
		},

		onPaletteChange: function(e) {
			config.macros.selectPalette.updatePalette(this.value);
			return true;
		},

		updatePalette: function(title) {
			if (title != "") {
				store.deleteTiddler("ColorPalette");
				if (title != "(default)")
					store.saveTiddler("ColorPalette","ColorPalette",store.getTiddlerText(title),
								config.options.txtUserName,undefined,"");
				this.refreshPalette();
				if(config.options.chkAutoSave)
					saveChanges(true);
			}
		},

		refreshPalette: function() {
			config.macros.refreshDisplay.onClick();
		}
	}
});

config.shadowTiddlers.OptionsPanel = "<<selectPalette>>\n\n" + config.shadowTiddlers.OptionsPanel;

//}}}

/***
|Name|ShowUpdatesPlugin|
|Created by|SaqImtiaz|
|Version|0.2 |
|Requires|~TW2.x|
!!!Description:
Allows you to list tiddlers that have changed since the users last visit. You can list only all changed tiddlers, or filter them to only show tiddlers that have or do not have a specific tag. By default a simple list of the titles of changed tiddlers is created. However, using an extremely versatile syntax you can provide a custom template for the generated text.

!!!Examples: 
[[ShowUpdatesDocs]]

!!!Installation:
Copy the contents of this tiddler to your TW, tag with systemConfig, save and reload your TW.

!!!Syntax:
{{{<<showUpdates>>}}}
additional optional params:
{{{<showUpdates excludeTag:TagToExclude onlyTag:TagToList maxEntries:10 write:CustomWriteParameter >>}}}
excludeTag: ~TagToExclude
onlyTag: ~TagToList
maxEntries: max number of entries displayed when there are no updates. (default is 10, which can be changed in the config.macros.showUpdates.settings part of the code)
write: if a write parameter is not provided, an un-numbered list of the updates is generated. Alternatively, you can specify a custom 'template' for the text generated. The syntax for the write parameter is identical to that of the forEachTiddler macro. Additonal documentation on this syntax will be provided soon.
Some of the variables available in the write parameter are 'index', 'count' and 'lastVisit' where lastVisit is the date of the last visit in the format YYYYMMDDHHMM. Also areUpdates is a boolean that is true if there are new updates since the users last visit.

!!!To Do:
*refactor code to facilitate translations
*a streamlined version without the custom write parameter


!!!Code
***/
//{{{
window.lewcidLastVisit = '';
window.old_lewcid_whatsnew_restart = window.restart;
window.restart = function()
{
        if(config.options.txtLastVisit)
                 lewcidLastVisit= config.options.txtLastVisit;
        config.options.txtLastVisit = (new Date()).convertToYYYYMMDDHHMM();
        saveOptionCookie('txtLastVisit');
        window.old_lewcid_whatsnew_restart();
}

TiddlyWiki.prototype.lewcidGetTiddlers = function(field,excludeTag,includeTag,updatesOnly)
{
              var results = [];
              this.forEachTiddler(function(title,tiddler)
                      {
                      if(excludeTag == undefined || !tiddler.isTagged(excludeTag))
                                    if(includeTag == undefined ||  tiddler.isTagged(includeTag))
                                            if ( updatesOnly == false || tiddler.modified.convertToYYYYMMDDHHMM()>lewcidLastVisit)
                                                  results.push(tiddler);
                      });
              if(field)
                  results.sort(function (a,b) {if(a[field] == b[field]) return(0); else return (a[field] < b[field]) ? -1 : +1; });
              return results;
}

config.macros.showUpdates={};
config.macros.showUpdates.settings =
{
         maxEntries: 10  //max items to show, if there are no updates since last visit
}

config.macros.showUpdates.handler = function(place,macroName,params,wikifier,paramString,tiddler)
{
          var args = paramString.parseParams("list",null,true);
          var write = getParam(args, "write", undefined);
          var onlyTag = getParam(args, "onlyTag", undefined);
          var excludeTag = getParam(args, "excludeTag", undefined);
          var sortBy = "modified";
          var maxEntries = getParam(args,"maxEntries",this.settings.maxEntries);

          if (lewcidLastVisit) 
                {var tiddlers = store.lewcidGetTiddlers(sortBy,excludeTag,onlyTag,true);
                 var areUpdates = tiddlers.length>0? true:false;}

          if (!lewcidLastVisit)
               {var countLine = "!!Recent Updates:";
               var tiddlers = store.lewcidGetTiddlers(sortBy,excludeTag,onlyTag,false);
               var areUpdates = false;}
          else if (tiddlers.length == 0)
               {var countLine = "!!@@color:red;No new updates@@ since your last visit. @@color:#999;font-size:70%;" + (Date.convertFromYYYYMMDDHHMM(lewcidLastVisit)).formatString(" (DD/MM/YY)") + "@@\n!!Recent Updates:";
               var tiddlers = store.lewcidGetTiddlers(sortBy,excludeTag,onlyTag,false);}
          else
               {var countLine ="!!@@color:red;"+ tiddlers.length + "@@ new " + (tiddlers.length==1?"update":"updates") + " since your last visit: @@color:#999;font-size:70%;" + (Date.convertFromYYYYMMDDHHMM(lewcidLastVisit)).formatString(" (DD/MM/YY)") + "@@";}

          tiddlers = tiddlers.reverse();
          var lastVisit = lewcidLastVisit? lewcidLastVisit:undefined;
          var count = areUpdates == true? tiddlers.length : maxEntries;
          var sp = createTiddlyElement(place,"span","showUpdates");
          if (write==undefined)
                 {
                  wikify(countLine,sp);
                  var list = createTiddlyElement(sp,"ul");
                  for (var i = 0; i < count; i++)
                          {
                           var tiddler = tiddlers[i];
                           createTiddlyLink(createTiddlyElement(list,"li"), tiddler.title, true);
                          }
                 }
          else
                {
                 var list = '';
                 for (var index = 0; index < count; index++) {
                 var tiddler = tiddlers[index];
                 list += eval(write); }
                 wikify(list, sp);
                }
}
//}}}
<<permaview>><<slider chkSliderOptionsPanel OptionsPanel "options" "Change TiddlyWiki advanced options">>
Public ~TiddlyWiki version of the Mathematical Sciences Classification --  [December 2009 version] {{right{<html>
<style type="text/css">
ul {list-style-type:none; padding: 0;padding-right: 100px; padding-bottom: 5px;  margin-top:-2px;}
li {padding: 0; margin:0; margin-bottom:-3px;}
img,  a {padding: 0; margin:0; }
.ccssdiv {position: relative; top: -2em;  padding:0; margin:0;}
</style>
<div id="ccssdiv"><ul>
<a  href="http://creativecommons.org/licenses/by-nc-sa/3.0/">
<li><img alt="Creative Commons" src="http://msc2010.org/images/cc.png" height="22" width="22" /></li>
<li><img alt="Please Attribute" src="http://msc2010.org/images/by.png" height="22" width="22" /></li>
<li><img alt="Nonprofit" src="http://msc2010.org/images/nc.png" height="22" width="22" /></li>
<li><img alt="Share Alike" src="http://msc2010.org/images/sa.png" height="22" width="22" /></li>
</ a>
</ul></div>
</html>}}}
 ~MSC2010: &nbsp; Server Copy{{right{[img[http://www.ams.org/images/mathweb-logo.gif]]}}}
If you are using Internet Explorer (IE) to open this document, please keep in mind the following items:
# For reading ~TiddlyWikis, almost any browser will do. But for editing a TW file or creating your own, Mozilla's free Firefox browser is optimal, whereas Internet Explorer will require you to take the steps below. You can download Firefox for free from [[here|http://www.mozilla.com/firefox/]]. It really is a great browser. Think about it!
# However, ''if you prefer to continue using Internet Explorer'', you will need version 6.x or higher, preferably version 7. If you want to upgrade to the latest version of IE, you can do so [[here|http://www.microsoft.com/windows/ie/downloads/default.mspx]]. 
# If you are using anything less than version 7, you will just need to ''enable active content''. Go to Tools >> Internet Options >> Advanced >> and check the boxes that say "Allow active content to run on files in My Computer", "Java logging enabled" and "Java Console enabled." Also you will want to click on the options link on the right-hand side of ~TiddlyWiki and check the "Auto Save" option.
# The ''only known issues with Internet Explorer'' itself have to do with gradients and series of consecutive spaces in Tiddler titles, neither of which should be on this version.
# ''If you have Micrososft XP Service Pack 2'', there is one hiccup. Internet Explorer Windows XP ~SP2 keeps track of html files saved from the internet, and stores saved changes in an 'Internet' zone regardless of attempts to rename or modify the file. But, in order to be able to save changes, ~TiddlyWiki needs to run in the 'My Computer' zone. The solution is to right-click on the ~TiddlyWiki html file and choose Properties. If the file is blocked, you'll see an 'Unblock' button on the resulting property sheet that removes the protection and allows the file to open in the 'My Computer' zone. Then open the file in Internet Explorer - it might put up its information bar asking you whether you want to run it. You need to 'Allow blocked content' to let ~TiddlyWiki do its stuff.
This tiddler was taken from the [[Tiddlywiki for the rest of us website|http://www.giffmex.org/twfortherestofus.html]], an excellent information page written by Dave Gifford about ~TiddlyWikis .
/*{{{*/
.headerShadow .left, 
.headerShadow .right { position: absolute; top: 22px;  } 
.headerShadow .left { left: 0px; } 
.headerShadow .right { right: 0px; } 
.headerShadow {margin-top: -0.1em; margin-left: 3px; margin-bottom: 0;}
.headerForeground .left, 
.headerForeground .right { display: none; } 
.moveright { float:right; top:50px; margin-top: -2em;}
.siteSubTitle {padding-bottom: 2em;}
msup > * + *
	{vertical-align:0.7em;
	padding-left:0.5ex;}
msub > * + *
	{vertical-align:-0.5em;}
msup > * + *, msub > * + *, munderover > * + *
	{font-size:0.7em;}
munderover
	{display:inline-table;
	vertical-align:middle;
	text-align:center;}
munderover > *
	{display:table-row;}
munderover > * + * + *
	{display:table-header-group;}
mi
	{font-style:italic;}
mi[mathvariant="normal"]
	{font-style:normal;}
mi[mathvariant="bold"]
	{font-weight:bold;}
mo
	{padding:0 0.5ex;}
mo[form="prefix"]
	{padding:0 0 0 0.5ex;}
mo[separator="true"], mo[fence="true"]
	{padding:0;}
menclose[notation="top"]
	{text-decoration:overline;}
/*}}}*/
/*{{{*/
body {
	background: [[ColorPalette::Background]];
	color: [[ColorPalette::Foreground]];
}

a{
	color: [[ColorPalette::PrimaryMid]];
}

a:hover{
	background: [[ColorPalette::PrimaryMid]];
	color: [[ColorPalette::Background]];
}

a img{
	border: 0;
}

h1,h2,h3,h4,h5 {
	color: [[ColorPalette::SecondaryDark]];
	background: [[ColorPalette::PrimaryPale]];
}

.button {
	color: [[ColorPalette::PrimaryDark]];
	border: 1px solid [[ColorPalette::Background]];
}

.button:hover {
	color: [[ColorPalette::PrimaryDark]];
	background: [[ColorPalette::SecondaryLight]];
	border-color: [[ColorPalette::SecondaryMid]];
}

.button:active {
	color: [[ColorPalette::Background]];
	background: [[ColorPalette::SecondaryMid]];
	border: 1px solid [[ColorPalette::SecondaryDark]];
}

.header {
	background: [[ColorPalette::PrimaryMid]];
}

.headerShadow {
	color: [[ColorPalette::Foreground]];
}

.headerShadow a {
	font-weight: normal;
	color: [[ColorPalette::Foreground]];
}

.headerForeground {
	color: [[ColorPalette::Background]];
}

.headerForeground a {
	font-weight: normal;
	color: [[ColorPalette::PrimaryPale]];
}

.tabSelected{
	color: [[ColorPalette::PrimaryDark]];
	background: [[ColorPalette::TertiaryPale]];
	border-left: 1px solid [[ColorPalette::TertiaryLight]];
	border-top: 1px solid [[ColorPalette::TertiaryLight]];
	border-right: 1px solid [[ColorPalette::TertiaryLight]];
}

.tabUnselected {
	color: [[ColorPalette::Background]];
	background: [[ColorPalette::TertiaryMid]];
}

.tabContents {
	color: [[ColorPalette::PrimaryDark]];
	background: [[ColorPalette::TertiaryPale]];
	border: 1px solid [[ColorPalette::TertiaryLight]];
}

.tabContents .button {
	 border: 0;}

#sidebar {
}

#sidebarOptions input {
	border: 1px solid [[ColorPalette::PrimaryMid]];
}

#sidebarOptions .sliderPanel {
	background: [[ColorPalette::PrimaryPale]];
}

#sidebarOptions .sliderPanel a {
	border: none;
	color: [[ColorPalette::PrimaryMid]];
}

#sidebarOptions .sliderPanel a:hover {
	color: [[ColorPalette::Background]];
	background: [[ColorPalette::PrimaryMid]];
}

#sidebarOptions .sliderPanel a:active {
	color: [[ColorPalette::PrimaryMid]];
	background: [[ColorPalette::Background]];
}

.wizard {
	background: [[ColorPalette::SecondaryLight]];
	border-top: 1px solid [[ColorPalette::SecondaryMid]];
	border-left: 1px solid [[ColorPalette::SecondaryMid]];
}

.wizard h1 {
	color: [[ColorPalette::SecondaryDark]];
}

.wizard h2 {
	color: [[ColorPalette::Foreground]];
}

.wizardStep {
	background: [[ColorPalette::Background]];
	border-top: 1px solid [[ColorPalette::SecondaryMid]];
	border-bottom: 1px solid [[ColorPalette::SecondaryMid]];
	border-left: 1px solid [[ColorPalette::SecondaryMid]];
}

.wizard .button {
	color: [[ColorPalette::Background]];
	background: [[ColorPalette::PrimaryMid]];
	border-top: 1px solid [[ColorPalette::PrimaryLight]];
	border-right: 1px solid [[ColorPalette::PrimaryDark]];
	border-bottom: 1px solid [[ColorPalette::PrimaryDark]];
	border-left: 1px solid [[ColorPalette::PrimaryLight]];
}

.wizard .button:hover {
	color: [[ColorPalette::PrimaryLight]];
	background: [[ColorPalette::PrimaryDark]];
	border-color: [[ColorPalette::PrimaryLight]];
}

.wizard .button:active {
	color: [[ColorPalette::Background]];
	background: [[ColorPalette::PrimaryMid]];
	border-top: 1px solid [[ColorPalette::PrimaryLight]];
	border-right: 1px solid [[ColorPalette::PrimaryDark]];
	border-bottom: 1px solid [[ColorPalette::PrimaryDark]];
	border-left: 1px solid [[ColorPalette::PrimaryLight]];
}

#messageArea {
	border: 1px solid [[ColorPalette::SecondaryDark]];
	background: [[ColorPalette::SecondaryMid]];
	color: [[ColorPalette::PrimaryDark]];
}

#messageArea .button {
	padding: 0.2em 0.2em 0.2em 0.2em;
	color: [[ColorPalette::PrimaryDark]];
	background: [[ColorPalette::Background]];
}

.popup {
	background: [[ColorPalette::PrimaryLight]];
	border: 1px solid [[ColorPalette::PrimaryMid]];
}

.popup hr {
	color: [[ColorPalette::PrimaryDark]];
	background: [[ColorPalette::PrimaryDark]];
	border-bottom: 1px;
}

.listBreak div{
	border-bottom: 1px solid [[ColorPalette::PrimaryDark]];
}

.popup li.disabled {
	color: [[ColorPalette::PrimaryMid]];
}

.popup li a, .popup li a:visited {
	color: [[ColorPalette::TertiaryPale]];
	border: none;
}

.popup li a:hover {
	background: [[ColorPalette::PrimaryDark]];
	color: [[ColorPalette::Background]];
	border: none;
}

.tiddler .defaultCommand {
 font-weight: bold;
}

.shadow .title {
	color: [[ColorPalette::TertiaryDark]];
}

.title {
	color: [[ColorPalette::SecondaryDark]];
}

.subtitle {
	color: [[ColorPalette::TertiaryDark]];
}

.toolbar {
	color: [[ColorPalette::PrimaryMid]];
}

.tagging, .tagged {
	border: 1px solid [[ColorPalette::TertiaryPale]];
	background-color: [[ColorPalette::TertiaryPale]];
}

.selected .tagging, .selected .tagged {
	background-color: [[ColorPalette::TertiaryLight]];
	border: 1px solid [[ColorPalette::TertiaryMid]];
}

.tagging .listTitle, .tagged .listTitle {
	color: [[ColorPalette::PrimaryDark]];
}

.tagging .button, .tagged .button {
		border: none;
}

.footer {
	color: [[ColorPalette::TertiaryLight]];
}

.selected .footer {
	color: [[ColorPalette::TertiaryMid]];
}

.sparkline {
	background: [[ColorPalette::PrimaryPale]];
	border: 0;
}

.sparktick {
	background: [[ColorPalette::PrimaryDark]];
}

.error, .errorButton {
	color: [[ColorPalette::Foreground]];
	background: [[ColorPalette::Error]];
}

.warning {
	color: [[ColorPalette::Foreground]];
	background: [[ColorPalette::SecondaryPale]];
}

.cascade {
	background: [[ColorPalette::TertiaryPale]];
	color: [[ColorPalette::TertiaryMid]];
	border: 1px solid [[ColorPalette::TertiaryMid]];
}

.imageLink, #displayArea .imageLink {
	background: transparent;
}

.viewer .listTitle {list-style-type: none; margin-left: -2em;}

.viewer .button {
	border: 1px solid [[ColorPalette::SecondaryMid]];
}

.viewer blockquote {
	border-left: 3px solid [[ColorPalette::TertiaryDark]];
}

.viewer table {
	border: 2px solid [[ColorPalette::TertiaryDark]];
}

.viewer th, thead td {
	background: [[ColorPalette::SecondaryMid]];
	border: 1px solid [[ColorPalette::TertiaryDark]];
	color: [[ColorPalette::Background]];
}

.viewer td, .viewer tr {
	border: 1px solid [[ColorPalette::TertiaryDark]];
}

.viewer pre {
	border: 1px solid [[ColorPalette::SecondaryLight]];
	background: [[ColorPalette::SecondaryPale]];
}

.viewer code {
	color: [[ColorPalette::SecondaryDark]];
}

.viewer hr {
	border: 0;
	border-top: dashed 1px [[ColorPalette::TertiaryDark]];
	color: [[ColorPalette::TertiaryDark]];
}

.highlight, .marked {
	background: [[ColorPalette::SecondaryLight]];
}

.editor input {
	border: 1px solid [[ColorPalette::PrimaryMid]];
}

.editor textarea {
	border: 1px solid [[ColorPalette::PrimaryMid]];
	width: 100%;
}

.editorFooter {
	color: [[ColorPalette::TertiaryMid]];
}

/*}}}*/
~TeX is the name of a typesetting system developed expressly for mathematics by D. E. Knuth, and widely used 
in scientific publishing. In particular, it is used by by Mathematical Reviews and Zentralblatt 
f&uuml;r Mathematik in their production streams.  The word ~TeX is used to mean, according to
context, the typesetting system, the main program of the system, and the markup language that that 
program compiles.
/***
|Name|TemporaryTiddlersPlugin|
|Source|http://www.TiddlyTools.com/#TemporaryTiddlersPlugin|
|Version|1.1.1|
|Author|Eric Shulman - ELS Design Studios|
|License|http://www.TiddlyTools.com/#LegalStatements <br>and [[Creative Commons Attribution-ShareAlike 2.5 License|http://creativecommons.org/licenses/by-sa/2.5/]]|
|~CoreVersion|2.1|
|Type|plugin|
|Requires||
|Overrides|SaverBase.prototype.externalize()|
|Options|##Configuration|
|Description|blocks tiddlers tagged with "temporary" from being saved into the TW file|
!!!!!Usage
<<<
When the TW document is saved (either to local disk or remote URL), any tiddlers tagged with "temporary" will be skipped over, so that they are not written to the file.  To keep a temporary tiddler, simply edit it and remove the tag before saving the file.  This feature can be combined with various plugins that can automatically create new tiddlers, such as [[SearchOptionsPlugin]] ([[SearchResults]]) and [[ImportTiddlersPlugin]] ([[ImportedTiddlers]]) so that these transient results are not retained when you save you document.

You can also use this tag with the {{{<<loadTiddlers>>}}} macro and the //auto-tagging// features provided by [[ImportTiddlersPlugin]], so that each time you open your document, you can automatically retrieve an up-to-date set of common tiddlers that are stored in another document (either local or via remote URL), without those tiddlers being retained when you save your document.
<<<
!!!!!Configuration
<<<
When saving the document:
<<option chkTemporaryQuiet>> Suppress reporting of temporary tiddlers that have not been saved
<<option chkTemporaryKeep>> Keep temporary tiddlers (i.e., ignore the 'temporary' tag)
Enter a tag value to use when marking tiddlers as temporary: <<option txtTemporaryTag>>
<<<
!!!!!Revisions
<<<
2008.04.08 [1.1.1] don't automatically add configuration options to AdvancedOptions tiddler
2008.03.01 [1.1.0] added support for recognizing 'temporary' flag stored as a tiddler *field* (as an optional alternative to using a tag)
2007.02.08 [1.0.0] initial release
<<<
!!!!!Code
***/
//{{{
version.extensions.TemporaryTiddlersPlugin= {major: 1, minor: 1, revision: 1, date: new Date(2008,4,8)};

// configuration defaults
if (config.options.chkTemporaryKeep ==undefined) config.options.chkTemporaryKeep =false;
if (config.options.chkTemporaryQuiet==undefined) config.options.chkTemporaryQuiet=false;
if (config.options.txtTemporaryTag==undefined) config.options.txtTemporaryTag="temporary";
// lingo
config.messages.TemporaryWarning = "'%0' ...temporary tiddler not saved";
// core override
SaverBase.prototype.externalize = function(store) 
{
	var results = [];
	var tiddlers = store.getTiddlers("title");
	for (var t = 0; t < tiddlers.length; t++) {
		if (config.options.chkTemporaryKeep||!(tiddlers[t].fields['temporary']||tiddlers[t].isTagged(config.options.txtTemporaryTag)))
			results.push(this.externalizeTiddler(store, tiddlers[t]));
		else if (!config.options.chkTemporaryQuiet) // notify user that tiddler won't be saved
			displayMessage(config.messages.TemporaryWarning.format([tiddlers[t].title]));
	}
	return results.join("\n");
}
//}}}
/***
|''Name:''|TiddlerNotesPlugin|
|''Description:''|Add notes to tiddlers without modifying the original content|
|''Author:''|Saq Imtiaz ( lewcid@gmail.com )|
|''Source:''|http://tw.lewcid.org/#TiddlerNotesPlugin|
|''Code Repository:''|http://tw.lewcid.org/svn/plugins|
|''Version:''|2.1|
|''Date:''|26/10/07|
|''License:''|[[Creative Commons Attribution-ShareAlike 3.0 License|http://creativecommons.org/licenses/by-sa/3.0/]]|
|''~CoreVersion:''|2.2.3|

!!Concept:
*The TiddlerNotesPlugin allows you to add notes to tiddlers, without needing to edit the original tiddler. This means that your original content will remain unaltered, and if you update it in the future, you won’t lose your notes. Notes are stored in separate tiddlers, but can be viewed and edited from within the original tiddler.
*For a tiddler titled "~MySlide", the notes are by default saved in a tiddler titled "~MySlide-Notes" and is given a tag of "Notes". The suffix and tags of the notes tiddlers are customizable. You can have one or multiple notes per tiddlers. So it is possible to have for example, teacher's notes and student's notes in the same file.
*Notes can be configured to start off blank, or pre-filled with the contents of the original tiddler.

!!Usage:
*{{{<<notes>>}}} is the simplest usage form.
* additional optional parameters include:
**{{{heading:}}} the heading to use for the notes box
**{{{tag:}}} the tag to be given to the notes tiddler
**{{{suffix:}}} the suffix to be used when naming the notes tiddler
* a full macro call could look like: {{{<<notes heading:"My Notes" tag:"NoteTiddlers" suffix:"Comments">>}}}
* To avoid adding {{{<<notes>>}}} to each tiddler you want notes for, you could add the macro call to the ViewTemplate
** below the line {{{<div class='viewer' macro='view text wikified'></div>}}} add the following line: <br> {{{<div class='viewer' macro='notes'></div>}}}
** Used in combination with the ~HideWhenPlugin or ~PublisherPlugin, you could have notes be shown only for tiddlers with specific tags. The ~PublisherPlugin would allow you for instance to only have the ~TeachersNotes visible to the teacher, and the ~StudentsNotes for the same tiddler visible to the Student.

!!Configuration
*<<option chkPrefillNotes>> Enable to pre-fill notes with the original tiddler's contents

!!Demo:
* [[MySlide]]

***/
// /%
//!BEGIN-PLUGIN-CODE

if (!config.options.chkPrefillNotes)
	config.options.chkPrefillNotes = false;
	
function createTiddlyElement(theParent,theElement,theID,theClass,theText,attribs)
{
	var e = document.createElement(theElement);
	if(theClass != null)
		e.className = theClass;
	if(theID != null)
		e.setAttribute("id",theID);
	if(theText != null)
		e.appendChild(document.createTextNode(theText));
	if(attribs){
		for(var n in attribs){
			e.setAttribute(n,attribs[n]);
		}
	}
	if(theParent != null)
		theParent.appendChild(e);
	return e;
}

function createTiddlyButton(theParent,theText,theTooltip,theAction,theClass,theId,theAccessKey,attribs)
{
	var theButton = document.createElement("a");
	if(theAction) {
		theButton.onclick = theAction;
		theButton.setAttribute("href","javascript:;");
	}
	if(theTooltip)
		theButton.setAttribute("title",theTooltip);
	if(theText)
		theButton.appendChild(document.createTextNode(theText));
	if(theClass)
		theButton.className = theClass;
	else
		theButton.className = "button";
	if(theId)
		theButton.id = theId;
	if(attribs){
		for(var n in attribs){
			e.setAttribute(n,attribs[n]);
		}
	}
	if(theParent)
		theParent.appendChild(theButton);
	if(theAccessKey)
		theButton.setAttribute("accessKey",theAccessKey);
	return theButton;
}

config.macros.notes={
	
	cancelWarning: "Are you sure you want to abandon changes to your notes for '%0'?",
	editLabel: "edit notes",
	editTitle: "double click to edit",
	saveLabel: "save notes",
	saveTitle: "double click to save",
	cancelLabel: "cancel",
	heading: "Notes",
	suffix: "Notes",
	tag: "Notes",
	
	saveNotes: function(ev){
		e = ev? ev : window.event;
		var theTarget = resolveTarget(e);
		if (theTarget.nodeName.toLowerCase() == "textarea")
			return false;
		var title = story.findContainingTiddler(theTarget).getAttribute("tiddler");
		story.setDirty(title,false);
		var box = document.getElementById("notesContainer"+title);
		var textarea = document.getElementById("notesTextArea"+title);
		if(textarea.getAttribute("oldText")!=textarea.value && !hasClass(theTarget,"cancelNotesButton")){
			var suffix = box.getAttribute("suffix");
			var t = store.getTiddler(title+"-"+suffix);
			store.saveTiddler(title+"-"+suffix,title+"-"+suffix,textarea.value,config.options.txtUserName,new Date(),t?t.tags:box.getAttribute("tag"),t?t.fields:{});
		}
		story.refreshTiddler(title,1,true);
		autoSaveChanges(true);
		return false;
	},
	
	editNotes: function(box,tiddler){
		removeChildren(box);
		story.setDirty(tiddler,true);
		box.title = this.saveTitle;
		box.ondblclick = this.saveNotes;
		createTiddlyButton(box,this.cancelLabel,this.cancelLabel,this.saveNotes,"cancelNotesButton");
		createTiddlyButton(box,this.saveLabel,this.saveLabel,this.saveNotes,"saveNotesButton");
		wikify("!!"+box.getAttribute("heading")+"\n",box);
		addClass(box,"editor");
		var wrapper1 = createTiddlyElement(null,"fieldset",null,"fieldsetFix");
		var wrapper2 = createTiddlyElement(wrapper1,"div");
		var e = createTiddlyElement(wrapper2,"textarea","notesTextArea"+tiddler);
		var v = store.getValue(tiddler+"-"+box.getAttribute("suffix"),"text");
		if(!v) 
			v = config.options.chkPrefillNotes? store.getValue(tiddler,"text"):'';
		e.value = v;
		e.setAttribute("oldText",v);
		var rows = 10;
		var lines = v.match(/\n/mg);
		var maxLines = Math.max(parseInt(config.options.txtMaxEditRows),5);
		if(lines != null && lines.length > rows)
			rows = lines.length + 5;
		rows = Math.min(rows,maxLines);
		e.setAttribute("rows",rows);
		box.appendChild(wrapper1);
	},
	
	editNotesButtonOnclick: function(e){
		var title = story.findContainingTiddler(this).getAttribute("tiddler");
		var box = document.getElementById("notesContainer"+title);
		config.macros.notes.editNotes(box,title);
		return false;
	},
	
	ondblclick : function(ev){
		e = ev? ev : window.event;
		var theTarget = resolveTarget(e);
		var title = story.findContainingTiddler(theTarget).getAttribute("tiddler");
		var box = document.getElementById("notesContainer"+title);
		config.macros.notes.editNotes(box,title);
		e.cancelBubble = true;
		if(e.stopPropagation) e.stopPropagation();
		return false;
	},
	
	handler : function(place,macroName,params,wikifier,paramString,tiddler){
		
		params = paramString.parseParams("anon",null,true,false,false);
		var heading = getParam(params,"heading",this.heading);
		var tag = getParam(params,"tag",this.tag);
		var suffix = getParam(params,"suffix",this.suffix);
		var box = createTiddlyElement(place,"div","notesContainer"+tiddler.title,"TiddlerNotes",null,{"source":tiddler.title,params:paramString,heading:heading,tag:tag,suffix:suffix});
		createTiddlyButton(box,this.editLabel,this.editLabel,this.editNotesButtonOnclick,"editNotesButton");
		wikify("!!"+heading+"\n",box);
		box.title=this.editTitle;
		box.ondblclick = this.ondblclick;
		wikify("<<tiddler [["+tiddler.title+"-"+suffix+"]]>>",box);
	}		
};

Story.prototype.old_notes_closeTiddler = Story.prototype.closeTiddler;
Story.prototype.closeTiddler = function(title,animate,unused){
	if(story.isDirty(title)) {
		if(!confirm(config.macros.notes.cancelWarning.format([title])))
			return false;
	}
	return this.old_notes_closeTiddler.apply(this,arguments);
}

setStylesheet(".TiddlerNotes {\n"+ " background:#eee;\n"+ " border:1px solid #ccc;\n"+ " padding:10px;\n"+ " margin:15px;\n"+ "}\n"+ "\n"+ ".cancelNotesButton,.editNotesButton, .saveNotesButton {\n"+ " float:right;\n"+ " border:1px solid #ccc;\n"+ " padding:2px 5px;\n"+ "}\n"+ "\n"+ ".saveNotesButton{\n"+ " margin-right:0.5em;\n"+ "}\n"+ "\n"+ ".TiddlerNotes.editor textarea{\n"+ " border:1px solid #ccc;\n"+ "}","NotesPluginStyles");
//!END-PLUGIN-CODE
// %/
!Inline Formatting /% DEBUG: buggy (-> monospaced) %/
|!Option|!Syntax|!Output|
|bold font|{{{''bold''}}}|''bold''|
|italic type|{{{//italic//}}}|//italic//|
|underlined text|{{{__underlined__}}}|__underlined__|
|strikethrough text|{{{--strikethrough--}}}|--strikethrough--|
|superscript text|{{{^^super^^script}}}|^^super^^script|
|subscript text|{{{~~sub~~script}}}|~~sub~~script|
|highlighted text|{{{@@highlighted@@}}}|@@highlighted@@|
|preformatted text|{{{{{{preformatted}}}}}}|{{{preformatted}}}|
!Block Elements
!!Headings
{{{
!Heading 1
!!Heading 2
!!!Heading 3
!!!!Heading 4
!!!!!Heading 5
}}}
<<<
!Heading 1
!!Heading 2
!!!Heading 3
!!!!Heading 4
!!!!!Heading 5
<<<
!!Lists
{{{
* unordered list, level 1
** unordered list, level 2
*** unordered list, level 3

# ordered list, level 1
## ordered list, level 2
### unordered list, level 3

; definition list, term
: definition list, description
}}}
<<<
* unordered list, level 1
** unordered list, level 2
*** unordered list, level 3

# ordered list, level 1
## ordered list, level 2
### unordered list, level 3

; definition list, term
: definition list, description
<<<
!!Blockquotes /% DEBUG: hack %/
{{{
> blockquote, level 1
>> blockquote, level 2
>>> blockquote, level 3

<<<
blockquote
<<<
}}}
<<<
> blockquote, level 1
>> blockquote, level 2
>>> blockquote, level 3

> blockquote
<<<
!!Preformatted Text /% DEBUG: hack %/
{{{
 {{{
 preformatted (e.g. code)
 }}}
}}}
<<<
{{{
preformatted (e.g. code)
}}}
<<<
!!Tables
{{{
|CssClass|k
|!heading column 1|!heading column 2|
|row 1, column 1|row 1, column 2|
|row 2, column 1|row 2, column 2|
|>|COLSPAN|
|ROWSPAN| … |
|~| … |
|CssProperty:value;…| … |
|caption|c
}}}
''Annotation:''
* The {{{>}}} marker creates a "colspan", causing the current cell to merge with the one to the right.
* The {{{~}}} marker creates a "rowspan", causing the current cell to merge with the one above.
<<<
|CssClass|k
|!heading column 1|!heading column 2|
|row 1, column 1|row 1, column 2|
|row 2, column 1|row 2, column 2|
|>|COLSPAN|
|ROWSPAN| … |
|~| … |
|CssProperty:value;…| … |
|caption|c
<<<
!!Images /% DEBUG: to do %/
cf. [[TiddlyWiki.com|http://www.tiddlywiki.com/#EmbeddedImages]]
!Hyperlinks
* [[WikiWords|WikiWord]] are automatically transformed to hyperlinks to the respective tiddler
** the automatic transformation can be suppressed by preceding the respective WikiWord with a tilde ({{{~}}}): {{{~WikiWord}}}
* [[PrettyLinks]] are enclosed in square brackets and contain the desired tiddler name: {{{[[tiddler name]]}}}
** optionally, a custom title or description can be added, separated by a pipe character ({{{|}}}): {{{[[title|target]]}}}<br>'''N.B.:''' In this case, the target can also be any website (i.e. URL).
!Custom Styling
* {{{@@CssProperty:value;CssProperty:value;…@@}}}<br>''N.B.:'' CSS color definitions should use lowercase letters to prevent the inadvertent creation of WikiWords.
* {{{{{customCssClass{…}}}}}} /% DEBUG: buggy %/
* raw HTML can be inserted by enclosing the respective code in HTML tags: {{{<html> … </html>}}}
!Special Markers
* {{{<br>}}} forces a manual line break
* {{{----}}} creates a horizontal ruler
* [[HTML entities|http://www.tiddlywiki.com/#HtmlEntities]]
* {{{<<macroName>>}}} calls the respective [[macro|Macros]]
* To hide text within a tiddler so that it is not displayed, it can be wrapped in {{{/%}}} and {{{%/}}}.<br/>This can be a useful trick for hiding drafts or annotating complex markup.
* To prevent wiki markup from taking effect for a particular section, that section can be enclosed in three double quotes: e.g. {{{"""WikiWord"""}}}.
Sometimes when opening a lot of tiddlers (e.g., especially in search) a popup window about an unresponsive script  will appear.  Clicking on the continue button will allow the process to continue, but you can stop this popup from occuring as much by  performing the following steps

1) enter about:config into the address field in Firefox
2) search for dom.max_script_run_time in the resulting list of
configuration parameters
3) double-click that entry to change the value from the default of 5 to 20.
4) restart Firefox.

If 'unresponsive' messages continue to appear repeat the above steps and increase the value.

For more tips  see those collected by Morris Gray  at [[Tiddlyspot.com|http://tiddlyspot.com/twhelp/#%5B%5BFireFox%20Tips%5D%5D]] at his excellent tutorial.
This tiddler was taken from the ~TiddlyWiki for the rest of us website, an excellent information page written by Dave Gifford about ~TiddlyWikis.
/%
|Name|ToggleScrollingSidebars|
|Source|http://www.TiddlyTools.com/#ToggleScrollingSidebars|
|Version|1.1.0|
|Author|Eric Shulman|
|License|http://www.TiddlyTools.com/#LegalStatements <br>and [[Creative Commons Attribution-ShareAlike 2.5 License|http://creativecommons.org/licenses/by-sa/2.5/]]|
|~CoreVersion|2.1|
|Type|script|
|Requires|InlineJavascriptPlugin|
|Overrides||
|Description|enable/disable 'fixed' positioning of left and right sidebars|
%/<script>
	if (config.options.chkScrollSidebars==undefined)
		config.options.chkScrollSidebars=true;
	if (!config.options.txtOuterTabHeight||!config.options.txtOuterTabHeight.length)
		config.options.txtOuterTabHeight="25em";
	if (!config.options.txtInnerTabHeight||!config.options.txtInnerTabHeight.length)
		config.options.txtInnerTabHeight="21em";

	window.ToggleScrollingSidebars_setscroll = function() {
		var scroll=config.options.chkScrollSidebars?'':'fixed';
		document.getElementById('mainMenu').style.position=scroll;
		<!-- document.getElementById('sidebar').style.position=scroll; -->
		var outer=config.options.txtOuterTabHeight;
		if (config.options.chkScrollSidebars) outer="auto";
		var inner=config.options.txtInnerTabHeight;
		if (config.options.chkScrollSidebars) inner="auto";
		var css='#sidebarTabs .tabContents { height:'+outer+'; overflow:'+(outer!='auto'?'auto':'visible')+'; width:92.5%; }';
		css+='#sidebarTabs .tabContents .tabContents { height:'+inner+' !important; }';
		setStylesheet(css,'shortSidebarTabs');
	}
	window.ToggleScrollingSidebars_setscroll();
</script><<option chkScrollSidebars>><script>
	place.lastChild.checked=config.options.chkScrollSidebars;
	place.lastChild.onchange=function() {
		config.options.chkScrollSidebars=this.checked;
		saveOptionCookie("chkScrollSidebars");
		window.ToggleScrollingSidebars_setscroll();
	};
</script> sidebars scroll with page
/***

|Name|ToggleSideBarMacro|
|Created by|SaqImtiaz|
|Location|http://tw.lewcid.org/#ToggleSideBarMacro|
|Version|1.0|
|Requires|~TW2.x|
!Description:
Provides a button for toggling visibility of the SideBar. You can choose whether the SideBar should initially be hidden or displayed.

!Demo
<<toggleSideBar "Toggle Sidebar">>

!Usage:
{{{<<toggleSideBar>>}}} <<toggleSideBar>>
additional options:
{{{<<toggleSideBar label tooltip show/hide>>}}} where:
label = custom label for the button,
tooltip = custom tooltip for the button,
show/hide = use one or the other, determines whether the sidebar is shown at first or not.
(default is to show the sidebar)

You can add it to your tiddler toolbar, your MainMenu, or where you like really.
If you are using a horizontal MainMenu and want the button to be right aligned, put the following in your StyleSheet:
{{{ .HideSideBarButton {float:right;} }}}

!History
*23-07-06: version 1.0: completely rewritten, now works with custom stylesheets too, and easier to customize start behaviour. 
*20-07-06: version 0.11
*27-04-06: version 0.1: working.

!Code
***/
//{{{
config.macros.toggleSideBar={};

config.macros.toggleSideBar.settings={
         styleHide :  "#sidebar { display: none;}\n"+"#contentWrapper #displayArea { margin-right: 1em;}\n"+"",
         styleShow : " ",
         arrow1: "«",
         arrow2: "»"
};

config.macros.toggleSideBar.handler=function (place,macroName,params,wikifier,paramString,tiddler)
{
          var tooltip= params[1]||'toggle sidebar';
          var mode = (params[2] && params[2]=="hide")? "hide":"show";
          var arrow = (mode == "hide")? this.settings.arrow1:this.settings.arrow2;
          var label= (params[0]&&params[0]!='.')?params[0]+" "+arrow:arrow;
          var theBtn = createTiddlyButton(place,label,tooltip,this.onToggleSideBar,"button HideSideBarButton");
          if (mode == "hide")
             { 
             (document.getElementById("sidebar")).setAttribute("toggle","hide");
              setStylesheet(this.settings.styleHide,"ToggleSideBarStyles");
             }
};

config.macros.toggleSideBar.onToggleSideBar = function(){
          var sidebar = document.getElementById("sidebar");
          var settings = config.macros.toggleSideBar.settings;
          if (sidebar.getAttribute("toggle")=='hide')
             {
              setStylesheet(settings.styleShow,"ToggleSideBarStyles");
              sidebar.setAttribute("toggle","show");
              this.firstChild.data= (this.firstChild.data).replace(settings.arrow1,settings.arrow2);
              }
          else
              {    
               setStylesheet(settings.styleHide,"ToggleSideBarStyles");
               sidebar.setAttribute("toggle","hide");
               this.firstChild.data= (this.firstChild.data).replace(settings.arrow2,settings.arrow1);
              }

     return false;
}

setStylesheet(".HideSideBarButton .button {font-weight:bold; padding: 0 5px;}\n","ToggleSideBarButtonStyles");

//}}}
<!--{{{-->
<div class='toolbar' macro='toolbar closeTiddler closeOthers  jump > permalink editTiddler  backup'></div>
<div class='title' macro='view title'></div>
<!-- <div class='subtitle'><span macro='view modifier link'></span>, <span macro='view modified date'></span> (<span macro='message views.wikified.createdPrompt'></span> <span macro='view created date'></span>)</div> 
--><div class='viewer' macro='view text wikified'></div>
<div class='viewer' macro='notes'></div>
<div class='tagClear'></div>
<!--}}}-->
!Field Search
With the Field Search you can restrict your search to certain fields of a tiddler, e.g only search the tags or only the titles. The general form is //fieldname//'':''//textToSearch// (e.g. {{{title:intro}}}). In addition one-character shortcuts are also supported for the standard fields {{{title}}}, {{{text}}} and {{{tags}}}:
|!What you want|!What you type|!Example|
|Search ''titles only''|start word with ''!''|{{{!jonny}}} (shortcut for {{{title:jonny}}})|
|Search ''contents/text only''|start word with ''%''|{{{%football}}} (shortcut for {{{text:football}}})|
|Search ''tags only''|start word with ''#''|{{{#Plugin}}} (shortcut for {{{tags:Plugin}}})|

Using this feature you may also search the extended fields ("Metadata") introduced with TiddlyWiki 2.1, e.g. use {{{priority:1}}} to find all tiddlers with the priority field set to "1".

You may search a word in more than one field. E.g. {{{!#Plugin}}} (or {{{title:tags:Plugin}}} in the "long form") finds tiddlers containing "Plugin" either in the title or in the tags (but does not look for "Plugin" in the text). 

!Boolean Search
The Boolean Search is useful when searching for multiple words.
|!What you want|!What you type|!Example|
|''All words'' must exist|List of words|{{{jonny jeremy}}} (or {{{jonny and jeremy}}})|
|''At least one word'' must exist|Separate words by ''or''|{{{jonny or jeremy}}}|
|A word ''must not exist''|Start word with ''-''|{{{-jonny}}} (or {{{not jonny}}})|

''Note:'' When you specify two words, separated with a space, YourSearch finds all tiddlers that contain both words, but not necessarily next to each other. If you want to find a sequence of word, e.g. '{{{John Brown}}}', you need to put the words into quotes. I.e. you type: {{{"john brown"}}}.

Using parenthesis you may change the default "left to right" evaluation of the boolean search. E.g. {{{not (jonny or jeremy)}}} finds all tiddlers that contain neither "jonny" nor "jeremy. In contrast to this {{{not jonny or jeremy}}} (i.e. without parenthesis) finds all tiddlers that either don't contain "jonny" or that contain "jeremy".

!'Exact Word' Search
By default a search result all matches that 'contain' the searched text. E.g. if you search for {{{Task}}} you will get all tiddlers containing 'Task', but also '~CompletedTask', '~TaskForce' etc.

If you only want to get the tiddlers that contain 'exactly the word' you need to prefix it with a '='. E.g. typing '=Task' will find the tiddlers that contain the word 'Task', ignoring words that just contain 'Task' as a substring.

!~CaseSensitiveSearch and ~RegExpSearch
The standard search options ~CaseSensitiveSearch and ~RegExpSearch are fully supported by YourSearch. However when ''~RegExpSearch'' is on Filtered and Boolean Search are disabled.

In addition you may do a "regular expression" search even with the ''~RegExpSearch'' set to false by directly entering the regular expression into the search field, framed with {{{/.../}}}. 

Example: {{{/m[ae][iy]er/}}} will find all tiddlers that contain either "maier", "mayer", "meier" or "meyer".

!~JavaScript Expression Filtering
If you are familiar with JavaScript programming and know some TiddlyWiki internals you may also use JavaScript expression for the search. Just enter a JavaScript boolean expression into the search field, framed with {{{ { ... } }}}. In the code refer to the variable tiddler and evaluate to {{{true}}} when the given tiddler should be included in the result. 

Example: {{{ { tiddler.modified > new Date("Jul 4, 2005")} }}} returns all tiddler modified after July 4th, 2005.

!Combined Search
You are free to combine the various search options. 

''Examples''
|!What you type|!Result|
|{{{!jonny !jeremy -%football}}}|all tiddlers with both {{{jonny}}} and {{{jeremy}}} in its titles, but no {{{football}}} in content.|
|{{{#=Task}}}|All tiddlers tagged with 'Task' (the exact word). Tags named '~CompletedTask', '~TaskForce' etc. are not considered.|

!Access Keys
You are encouraged to use the access keys (also called "shortcut" keys) for the most frequently used operations. For quick reference these shortcuts are also mentioned in the tooltip for the various buttons etc.

|!Key|!Operation|
|{{{Alt-F}}}|''The most important keystroke'': It moves the cursor to the search input field so you can directly start typing your query. Pressing {{{Alt-F}}} will also display the previous search result. This way you can quickly display multiple tiddlers using "Press {{{Alt-F}}}. Select tiddler." sequences.|
|{{{ESC}}}|Closes the [[YourSearch Result]]. When the [[YourSearch Result]] is already closed and the cursor is in the search input field the field's content is cleared so you start a new query.|
|{{{Alt-1}}}, {{{Alt-2}}},... |Pressing these keys opens the first, second etc. tiddler from the result list.|
|{{{Alt-O}}}|Opens all found tiddlers.|
|{{{Alt-P}}}|Toggles the 'Preview Text' mode.|
|{{{Alt-'<'}}}, {{{Alt-'>'}}}|Displays the previous or next page in the [[YourSearch Result]].|
|{{{Return}}}|When you have turned off the 'as you type' search mode pressing the {{{Return}}} key actually starts the search (as does pressing the 'search' button).|

//If some of these shortcuts don't work for you check your browser if you have other extensions installed that already "use" these shortcuts.//
<!--{{{-->
<span class='yourSearchNumber' macro='foundTiddler number'></span>
<span class='yourSearchTitle' macro='foundTiddler title'/></span>&nbsp;-&nbsp;
<span macro='foundTiddler field includeURL'/></span>&nbsp;-&nbsp;
<span class='yourSearchTags' macro='foundTiddler field tags 50'/></span>
<span macro="yourSearch if previewText"><div class='yourSearchText' macro='foundTiddler field text 250'/></div></span>
<!--}}}-->
/***
|''Name:''|YourSearchPlugin|
|''Version:''|2.1.3 (2008-04-16)|
|''Source:''|http://tiddlywiki.abego-software.de/#YourSearchPlugin|
|''Author:''|UdoBorkowski (ub [at] abego-software [dot] de)|
|''Licence:''|[[BSD open source license (abego Software)|http://www.abego-software.de/legal/apl-v10.html]]|
|''Copyright:''|&copy; 2005-2008 [[abego Software|http://www.abego-software.de]]|
|''~CoreVersion:''|2.1.0|
|''Community:''|[[del.icio.us|http://del.icio.us/post?url=http://tiddlywiki.abego-software.de/index.html%23YourSearchPlugin]]|
|''Browser:''|Firefox 1.0.4+; Firefox 1.5; ~InternetExplorer 6.0|
!About YourSearch
YourSearch gives you a bunch of new features to simplify and speed up your daily searches in TiddlyWiki. It seamlessly integrates into the standard TiddlyWiki search: just start typing into the 'search' field and explore!

For more information see [[Help|YourSearch Help]].
!Compatibility
This plugin requires TiddlyWiki 2.1. 
Check the [[archive|http://tiddlywiki.abego-software.de/archive]] for ~YourSearchPlugins supporting older versions of TiddlyWiki.
!Source Code
***/
/***
This plugin's source code is compressed (and hidden). Use this [[link|http://tiddlywiki.abego-software.de/archive/YourSearchPlugin/Plugin-YourSearch-src.2.1.3.js]] to get the readable source code.
***/
///%
if(!version.extensions.YourSearchPlugin){version.extensions.YourSearchPlugin={major:2,minor:1,revision:3,source:"http://tiddlywiki.abego-software.de/#YourSearchPlugin",licence:"[[BSD open source license (abego Software)|http://www.abego-software.de/legal/apl-v10.html]]",copyright:"Copyright (c) abego Software GmbH, 2005-2008 (www.abego-software.de)"};if(!window.abego){window.abego={};}
if(!Array.forEach){Array.forEach=function(_1,_2,_3){for(var i=0,len=_1.length;i<len;i++){_2.call(_3,_1[i],i,_1);}};Array.prototype.forEach=function(_5,_6){for(var i=0,len=this.length;i<len;i++){_5.call(_6,this[i],i,this);}};}
abego.toInt=function(s,_9){if(!s){return _9;}
var n=parseInt(s);return(n==NaN)?_9:n;};abego.createEllipsis=function(_b){var e=createTiddlyElement(_b,"span");e.innerHTML="&hellip;";};abego.shallowCopy=function(_d){if(!_d){return _d;}
var _e={};for(var n in _d){_e[n]=_d[n];}
return _e;};abego.copyOptions=function(_10){return!_10?{}:abego.shallowCopy(_10);};abego.countStrings=function(_11,s){if(!s){return 0;}
var len=s.length;var n=0;var _15=0;while(1){var i=_11.indexOf(s,_15);if(i<0){return n;}
n++;_15=i+len;}
return n;};abego.getBracedText=function(_17,_18,_19){if(!_18){_18=0;}
var re=/\{([^\}]*)\}/gm;re.lastIndex=_18;var m=re.exec(_17);if(m){var s=m[1];var _1d=abego.countStrings(s,"{");if(!_1d){if(_19){_19.lastIndex=re.lastIndex;}
return s;}
var len=_17.length;for(var i=re.lastIndex;i<len&&_1d;i++){var c=_17.charAt(i);if(c=="{"){_1d++;}else{if(c=="}"){_1d--;}}}
if(!_1d){if(_19){_19.lastIndex=i-1;}
return _17.substring(m.index+1,i-1);}}};abego.select=function(_21,_22,_23,_24){if(!_24){_24=[];}
_21.forEach(function(t){if(_22.call(_23,t)){_24.push(t);}});return _24;};abego.consumeEvent=function(e){if(e.stopPropagation){e.stopPropagation();}
if(e.preventDefault){e.preventDefault();}
e.cancelBubble=true;e.returnValue=true;};abego.TiddlerFilterTerm=function(_27,_28){if(!_28){_28={};}
var _29=_27;if(!_28.textIsRegExp){_29=_27.escapeRegExp();if(_28.fullWordMatch){_29="\\b"+_29+"\\b";}}
var _2a=new RegExp(_29,"m"+(_28.caseSensitive?"":"i"));this.tester=new abego.MultiFieldRegExpTester(_2a,_28.fields,_28.withExtendedFields);};abego.TiddlerFilterTerm.prototype.test=function(_2b){return this.tester.test(_2b);};abego.parseNewTiddlerCommandLine=function(s){var m=/(.*?)\.(?:\s+|$)([^#]*)(#.*)?/.exec(s);if(!m){m=/([^#]*)()(#.*)?/.exec(s);}
if(m){var r;if(m[3]){var s2=m[3].replace(/#/g,"");r=s2.parseParams("tag");}else{r=[[]];}
var _30=m[2]?m[2].trim():"";r.push({name:"text",value:_30});r[0].text=[_30];return{title:m[1].trim(),params:r};}else{return{title:s.trim(),params:[[]]};}};abego.parseTiddlerFilterTerm=function(_31,_32,_33){var re=/\s*(?:(?:\{([^\}]*)\})|(?:(=)|([#%!])|(?:(\w+)\s*\:(?!\/\/))|(?:(?:("(?:(?:\\")|[^"])+")|(?:\/((?:(?:\\\/)|[^\/])+)\/)|(\w+\:\/\/[^\s]+)|([^\s\)\-\"]+)))))/mg;var _35={"!":"title","%":"text","#":"tags"};var _36={};var _37;re.lastIndex=_32;while(1){var i=re.lastIndex;var m=re.exec(_31);if(!m||m.index!=i){throw"Word or String literal expected";}
if(m[1]){var _3a={};var _3b=abego.getBracedText(_31,0,_3a);if(!_3b){throw"Invalid {...} syntax";}
var f=Function("tiddler","return ("+_3b+");");return{func:f,lastIndex:_3a.lastIndex,markRE:null};}
if(m[2]){_37=true;}else{if(m[3]){_36[_35[m[3]]]=1;}else{if(m[4]){_36[m[4]]=1;}else{var _3d=m[6];var _3e=m[5]?window.eval(m[5]):m[6]?m[6]:m[7]?m[7]:m[8];var _33=abego.copyOptions(_33);_33.fullWordMatch=_37;_33.textIsRegExp=_3d;var _3f=[];for(var n in _36){_3f.push(n);}
if(_3f.length==0){_33.fields=_33.defaultFields;}else{_33.fields=_3f;_33.withExtendedFields=false;}
var _41=new abego.TiddlerFilterTerm(_3e,_33);var _42=_3d?_3e:_3e.escapeRegExp();if(_42&&_37){_42="\\b"+_42+"\\b";}
return{func:function(_43){return _41.test(_43);},lastIndex:re.lastIndex,markRE:_42?"(?:"+_42+")":null};}}}}};abego.BoolExp=function(s,_45,_46){this.s=s;var _47=_46&&_46.defaultOperationIs_OR;var _48=/\s*(?:(\-|not)|(\())/gi;var _49=/\s*\)/g;var _4a=/\s*(?:(and|\&\&)|(or|\|\|))/gi;var _4b=/\s*[^\)\s]/g;var _4c=/\s*(\-|not)?(\s*\()?/gi;var _4d;var _4e=function(_4f){_4c.lastIndex=_4f;var m=_4c.exec(s);var _51;var _52;if(m&&m.index==_4f){_4f+=m[0].length;_51=m[1];if(m[2]){var e=_4d(_4f);_49.lastIndex=e.lastIndex;if(!_49.exec(s)){throw"Missing ')'";}
_52={func:e.func,lastIndex:_49.lastIndex,markRE:e.markRE};}}
if(!_52){_52=_45(s,_4f,_46);}
if(_51){_52.func=(function(f){return function(_55){return!f(_55);};})(_52.func);_52.markRE=null;}
return _52;};_4d=function(_56){var _57=_4e(_56);while(1){var l=_57.lastIndex;_4a.lastIndex=l;var m=_4a.exec(s);var _5a;var _5b;if(m&&m.index==l){_5a=!m[1];_5b=_4e(_4a.lastIndex);}else{try{_5b=_4e(l);}
catch(e){return _57;}
_5a=_47;}
_57.func=(function(_5c,_5d,_5e){return _5e?function(_5f){return _5c(_5f)||_5d(_5f);}:function(_60){return _5c(_60)&&_5d(_60);};})(_57.func,_5b.func,_5a);_57.lastIndex=_5b.lastIndex;if(!_57.markRE){_57.markRE=_5b.markRE;}else{if(_5b.markRE){_57.markRE=_57.markRE+"|"+_5b.markRE;}}}};var _61=_4d(0);this.evalFunc=_61.func;if(_61.markRE){this.markRegExp=new RegExp(_61.markRE,_46.caseSensitive?"mg":"img");}};abego.BoolExp.prototype.exec=function(){return this.evalFunc.apply(this,arguments);};abego.BoolExp.prototype.getMarkRegExp=function(){return this.markRegExp;};abego.BoolExp.prototype.toString=function(){return this.s;};abego.MultiFieldRegExpTester=function(re,_63,_64){this.re=re;this.fields=_63?_63:["title","text","tags"];this.withExtendedFields=_64;};abego.MultiFieldRegExpTester.prototype.test=function(_65){var re=this.re;for(var i=0;i<this.fields.length;i++){var s=store.getValue(_65,this.fields[i]);if(typeof s=="string"&&re.test(s)){return this.fields[i];}}
if(this.withExtendedFields){return store.forEachField(_65,function(_69,_6a,_6b){return typeof _6b=="string"&&re.test(_6b)?_6a:null;},true);}
return null;};abego.TiddlerQuery=function(_6c,_6d,_6e,_6f,_70){if(_6e){this.regExp=new RegExp(_6c,_6d?"mg":"img");this.tester=new abego.MultiFieldRegExpTester(this.regExp,_6f,_70);}else{this.expr=new abego.BoolExp(_6c,abego.parseTiddlerFilterTerm,{defaultFields:_6f,caseSensitive:_6d,withExtendedFields:_70});}
this.getQueryText=function(){return _6c;};this.getUseRegExp=function(){return _6e;};this.getCaseSensitive=function(){return _6d;};this.getDefaultFields=function(){return _6f;};this.getWithExtendedFields=function(){return _70;};};abego.TiddlerQuery.prototype.test=function(_71){if(!_71){return false;}
if(this.regExp){return this.tester.test(_71);}
return this.expr.exec(_71);};abego.TiddlerQuery.prototype.filter=function(_72){return abego.select(_72,this.test,this);};abego.TiddlerQuery.prototype.getMarkRegExp=function(){if(this.regExp){return"".search(this.regExp)>=0?null:this.regExp;}
return this.expr.getMarkRegExp();};abego.TiddlerQuery.prototype.toString=function(){return(this.regExp?this.regExp:this.expr).toString();};abego.PageWiseRenderer=function(){this.firstIndexOnPage=0;};merge(abego.PageWiseRenderer.prototype,{setItems:function(_73){this.items=_73;this.setFirstIndexOnPage(0);},getMaxPagesInNavigation:function(){return 10;},getItemsCount:function(_74){return this.items?this.items.length:0;},getCurrentPageIndex:function(){return Math.floor(this.firstIndexOnPage/this.getItemsPerPage());},getLastPageIndex:function(){return Math.floor((this.getItemsCount()-1)/this.getItemsPerPage());},setFirstIndexOnPage:function(_75){this.firstIndexOnPage=Math.min(Math.max(0,_75),this.getItemsCount()-1);},getFirstIndexOnPage:function(){this.firstIndexOnPage=Math.floor(this.firstIndexOnPage/this.getItemsPerPage())*this.getItemsPerPage();return this.firstIndexOnPage;},getLastIndexOnPage:function(){return Math.min(this.getFirstIndexOnPage()+this.getItemsPerPage()-1,this.getItemsCount()-1);},onPageChanged:function(_76,_77){},renderPage:function(_78){if(_78.beginRendering){_78.beginRendering(this);}
try{if(this.getItemsCount()){var _79=this.getLastIndexOnPage();var _7a=-1;for(var i=this.getFirstIndexOnPage();i<=_79;i++){_7a++;_78.render(this,this.items[i],i,_7a);}}}
finally{if(_78.endRendering){_78.endRendering(this);}}},addPageNavigation:function(_7c){if(!this.getItemsCount()){return;}
var _7d=this;var _7e=function(e){if(!e){var e=window.event;}
abego.consumeEvent(e);var _80=abego.toInt(this.getAttribute("page"),0);var _81=_7d.getCurrentPageIndex();if(_80==_81){return;}
var _82=_80*_7d.getItemsPerPage();_7d.setFirstIndexOnPage(_82);_7d.onPageChanged(_80,_81);};var _83;var _84=this.getCurrentPageIndex();var _85=this.getLastPageIndex();if(_84>0){_83=createTiddlyButton(_7c,"Previous","Go to previous page (Shortcut: Alt-'<')",_7e,"prev");_83.setAttribute("page",(_84-1).toString());_83.setAttribute("accessKey","<");}
for(var i=-this.getMaxPagesInNavigation();i<this.getMaxPagesInNavigation();i++){var _87=_84+i;if(_87<0){continue;}
if(_87>_85){break;}
var _88=(i+_84+1).toString();var _89=_87==_84?"currentPage":"otherPage";_83=createTiddlyButton(_7c,_88,"Go to page %0".format([_88]),_7e,_89);_83.setAttribute("page",(_87).toString());}
if(_84<_85){_83=createTiddlyButton(_7c,"Next","Go to next page (Shortcut: Alt-'>')",_7e,"next");_83.setAttribute("page",(_84+1).toString());_83.setAttribute("accessKey",">");}}});abego.LimitedTextRenderer=function(){var _8a=40;var _8b=4;var _8c=function(_8d,_8e,_8f){var n=_8d.length;if(n==0){_8d.push({start:_8e,end:_8f});return;}
var i=0;for(;i<n;i++){var _92=_8d[i];if(_92.start<=_8f&&_8e<=_92.end){var r;var _94=i+1;for(;_94<n;_94++){r=_8d[_94];if(r.start>_8f||_8e>_92.end){break;}}
var _95=_8e;var _96=_8f;for(var j=i;j<_94;j++){r=_8d[j];_95=Math.min(_95,r.start);_96=Math.max(_96,r.end);}
_8d.splice(i,_94-i,{start:_95,end:_96});return;}
if(_92.start>_8f){break;}}
_8d.splice(i,0,{start:_8e,end:_8f});};var _98=function(_99){var _9a=0;for(var i=0;i<_99.length;i++){var _9c=_99[i];_9a+=_9c.end-_9c.start;}
return _9a;};var _9d=function(c){return(c>="a"&&c<="z")||(c>="A"&&c<="Z")||c=="_";};var _9f=function(s,_a1){if(!_9d(s[_a1])){return null;}
for(var i=_a1-1;i>=0&&_9d(s[i]);i--){}
var _a3=i+1;var n=s.length;for(i=_a1+1;i<n&&_9d(s[i]);i++){}
return{start:_a3,end:i};};var _a5=function(s,_a7,_a8){var _a9;if(_a8){_a9=_9f(s,_a7);}else{if(_a7<=0){return _a7;}
_a9=_9f(s,_a7-1);}
if(!_a9){return _a7;}
if(_a8){if(_a9.start>=_a7-_8b){return _a9.start;}
if(_a9.end<=_a7+_8b){return _a9.end;}}else{if(_a9.end<=_a7+_8b){return _a9.end;}
if(_a9.start>=_a7-_8b){return _a9.start;}}
return _a7;};var _aa=function(s,_ac){var _ad=[];if(_ac){var _ae=0;var n=s.length;var _b0=0;do{_ac.lastIndex=_ae;var _b1=_ac.exec(s);if(_b1){if(_ae<_b1.index){var t=s.substring(_ae,_b1.index);_ad.push({text:t});}
_ad.push({text:_b1[0],isMatch:true});_ae=_b1.index+_b1[0].length;}else{_ad.push({text:s.substr(_ae)});break;}}while(true);}else{_ad.push({text:s});}
return _ad;};var _b3=function(_b4){var _b5=0;for(var i=0;i<_b4.length;i++){if(_b4[i].isMatch){_b5++;}}
return _b5;};var _b7=function(s,_b9,_ba,_bb,_bc){var _bd=Math.max(Math.floor(_bc/(_bb+1)),_8a);var _be=Math.max(_bd-(_ba-_b9),0);var _bf=Math.min(Math.floor(_ba+_be/3),s.length);var _c0=Math.max(_bf-_bd,0);_c0=_a5(s,_c0,true);_bf=_a5(s,_bf,false);return{start:_c0,end:_bf};};var _c1=function(_c2,s,_c4){var _c5=[];var _c6=_b3(_c2);var pos=0;for(var i=0;i<_c2.length;i++){var t=_c2[i];var _ca=t.text;if(t.isMatch){var _cb=_b7(s,pos,pos+_ca.length,_c6,_c4);_8c(_c5,_cb.start,_cb.end);}
pos+=_ca.length;}
return _c5;};var _cc=function(s,_ce,_cf){var _d0=_cf-_98(_ce);while(_d0>0){if(_ce.length==0){_8c(_ce,0,_a5(s,_cf,false));return;}else{var _d1=_ce[0];var _d2;var _d3;if(_d1.start==0){_d2=_d1.end;if(_ce.length>1){_d3=_ce[1].start;}else{_8c(_ce,_d2,_a5(s,_d2+_d0,false));return;}}else{_d2=0;_d3=_d1.start;}
var _d4=Math.min(_d3,_d2+_d0);_8c(_ce,_d2,_d4);_d0-=(_d4-_d2);}}};var _d5=function(_d6,s,_d8,_d9,_da){if(_d9.length==0){return;}
var _db=function(_dc,s,_de,_df,_e0){var t;var _e2;var pos=0;var i=0;var _e5=0;for(;i<_de.length;i++){t=_de[i];_e2=t.text;if(_df<pos+_e2.length){_e5=_df-pos;break;}
pos+=_e2.length;}
var _e6=_e0-_df;for(;i<_de.length&&_e6>0;i++){t=_de[i];_e2=t.text.substr(_e5);_e5=0;if(_e2.length>_e6){_e2=_e2.substr(0,_e6);}
if(t.isMatch){createTiddlyElement(_dc,"span",null,"marked",_e2);}else{createTiddlyText(_dc,_e2);}
_e6-=_e2.length;}
if(_e0<s.length){abego.createEllipsis(_dc);}};if(_d9[0].start>0){abego.createEllipsis(_d6);}
var _e7=_da;for(var i=0;i<_d9.length&&_e7>0;i++){var _e9=_d9[i];var len=Math.min(_e9.end-_e9.start,_e7);_db(_d6,s,_d8,_e9.start,_e9.start+len);_e7-=len;}};this.render=function(_eb,s,_ed,_ee){if(s.length<_ed){_ed=s.length;}
var _ef=_aa(s,_ee);var _f0=_c1(_ef,s,_ed);_cc(s,_f0,_ed);_d5(_eb,s,_ef,_f0,_ed);};};(function(){function alertAndThrow(msg){alert(msg);throw msg;}
if(version.major<2||(version.major==2&&version.minor<1)){alertAndThrow("YourSearchPlugin requires TiddlyWiki 2.1 or newer.\n\nCheck the archive for YourSearch plugins\nsupporting older versions of TiddlyWiki.\n\nArchive: http://tiddlywiki.abego-software.de/archive");}
abego.YourSearch={};var _f2;var _f3;var _f4=function(_f5){_f2=_f5;};var _f6=function(){return _f2?_f2:[];};var _f7=function(){return _f2?_f2.length:0;};var _f8=4;var _f9=10;var _fa=2;var _fb=function(s,re){var m=s.match(re);return m?m.length:0;};var _ff=function(_100,_101){var _102=_101.getMarkRegExp();if(!_102){return 1;}
var _103=_100.title.match(_102);var _104=_103?_103.length:0;var _105=_fb(_100.getTags(),_102);var _106=_103?_103.join("").length:0;var _107=_100.title.length>0?_106/_100.title.length:0;var rank=_104*_f8+_105*_fa+_107*_f9+1;return rank;};var _109=function(_10a,_10b,_10c,_10d,_10e,_10f){_f3=null;var _110=_10a.reverseLookup("tags",_10f,false);try{var _111=[];if(config.options.chkSearchInTitle){_111.push("title");}
if(config.options.chkSearchInText){_111.push("text");}
if(config.options.chkSearchInTags){_111.push("tags");}
_f3=new abego.TiddlerQuery(_10b,_10c,_10d,_111,config.options.chkSearchExtendedFields);}
catch(e){return[];}
var _112=_f3.filter(_110);var _113=abego.YourSearch.getRankFunction();for(var i=0;i<_112.length;i++){var _115=_112[i];var rank=_113(_115,_f3);_115.searchRank=rank;}
if(!_10e){_10e="title";}
var _117=function(a,b){var _11a=a.searchRank-b.searchRank;if(_11a==0){if(a[_10e]==b[_10e]){return(0);}else{return(a[_10e]<b[_10e])?-1:+1;}}else{return(_11a>0)?-1:+1;}};_112.sort(_117);return _112;};var _11b=80;var _11c=50;var _11d=250;var _11e=50;var _11f=25;var _120=10;var _121="yourSearchResult";var _122="yourSearchResultItems";var _123;var _124;var _125;var _126;var _127;var _128=function(){if(version.extensions.YourSearchPlugin.styleSheetInited){return;}
version.extensions.YourSearchPlugin.styleSheetInited=true;setStylesheet(store.getTiddlerText("YourSearchStyleSheet"),"yourSearch");};var _129=function(){return _124!=null&&_124.parentNode==document.body;};var _12a=function(){if(_129()){document.body.removeChild(_124);}};var _12b=function(e){_12a();var _12d=this.getAttribute("tiddlyLink");if(_12d){var _12e=this.getAttribute("withHilite");var _12f=highlightHack;if(_12e&&_12e=="true"&&_f3){highlightHack=_f3.getMarkRegExp();}
story.displayTiddler(this,_12d);highlightHack=_12f;}
return(false);};var _130=function(){if(!_125){return;}
var root=_125;var _132=findPosX(root);var _133=findPosY(root);var _134=root.offsetHeight;var _135=_132;var _136=_133+_134;var _137=findWindowWidth();if(_137<_124.offsetWidth){_124.style.width=(_137-100)+"px";_137=findWindowWidth();}
var _138=_124.offsetWidth;if(_135+_138>_137){_135=_137-_138-30;}
if(_135<0){_135=0;}
_124.style.left=_135+"px";_124.style.top=_136+"px";_124.style.display="block";};var _139=function(){if(_124){window.scrollTo(0,ensureVisible(_124));}
if(_125){window.scrollTo(0,ensureVisible(_125));}};var _13a=function(){_130();_139();};var _13b;var _13c;var _13d=new abego.PageWiseRenderer();var _13e=function(_13f){this.itemHtml=store.getTiddlerText("YourSearchItemTemplate");if(!this.itemHtml){alertAndThrow("YourSearchItemTemplate not found");}
this.place=document.getElementById(_122);if(!this.place){this.place=createTiddlyElement(_13f,"div",_122);}};merge(_13e.prototype,{render:function(_140,_141,_142,_143){_13b=_143;_13c=_141;var item=createTiddlyElement(this.place,"div",null,"yourSearchItem");item.innerHTML=this.itemHtml;applyHtmlMacros(item,null);refreshElements(item,null);},endRendering:function(_145){_13c=null;}});var _146=function(){if(!_124||!_125){return;}
var html=store.getTiddlerText("YourSearchResultTemplate");if(!html){html="<b>Tiddler YourSearchResultTemplate not found</b>";}
_124.innerHTML=html;applyHtmlMacros(_124,null);refreshElements(_124,null);var _148=new _13e(_124);_13d.renderPage(_148);_13a();};_13d.getItemsPerPage=function(){var n=(config.options.chkPreviewText)?abego.toInt(config.options.txtItemsPerPageWithPreview,_120):abego.toInt(config.options.txtItemsPerPage,_11f);return(n>0)?n:1;};_13d.onPageChanged=function(){_146();};var _14a=function(){if(_125==null||!config.options.chkUseYourSearch){return;}
if((_125.value==_123)&&_123&&!_129()){if(_124&&(_124.parentNode!=document.body)){document.body.appendChild(_124);_13a();}else{abego.YourSearch.onShowResult(true);}}};var _14b=function(){_12a();_124=null;_123=null;};var _14c=function(self,e){while(e!=null){if(self==e){return true;}
e=e.parentNode;}
return false;};var _14f=function(e){if(e.target==_125){return;}
if(e.target==_126){return;}
if(_124&&_14c(_124,e.target)){return;}
_12a();};var _151=function(e){if(e.keyCode==27){_12a();}};addEvent(document,"click",_14f);addEvent(document,"keyup",_151);var _153=function(text,_155,_156){_123=text;_f4(_109(store,text,_155,_156,"title","excludeSearch"));abego.YourSearch.onShowResult();};var _157=function(_158,_159,_15a,_15b,_15c,_15d){_128();_123="";var _15e=null;var _15f=function(txt){if(config.options.chkUseYourSearch){_153(txt.value,config.options.chkCaseSensitiveSearch,config.options.chkRegExpSearch);}else{story.search(txt.value,config.options.chkCaseSensitiveSearch,config.options.chkRegExpSearch);}
_123=txt.value;};var _161=function(e){_15f(_125);return false;};var _163=function(e){if(!e){var e=window.event;}
_125=this;switch(e.keyCode){case 13:if(e.ctrlKey&&_127&&_129()){_127.onclick.apply(_127,[e]);}else{_15f(this);}
break;case 27:if(_129()){_12a();}else{this.value="";clearMessage();}
break;}
if(String.fromCharCode(e.keyCode)==this.accessKey||e.altKey){_14a();}
if(this.value.length<3&&_15e){clearTimeout(_15e);}
if(this.value.length>2){if(this.value!=_123){if(!config.options.chkUseYourSearch||config.options.chkSearchAsYouType){if(_15e){clearTimeout(_15e);}
var txt=this;_15e=setTimeout(function(){_15f(txt);},500);}}else{if(_15e){clearTimeout(_15e);}}}
if(this.value.length==0){_12a();}};var _166=function(e){this.select();clearMessage();_14a();};var args=_15c.parseParams("list",null,true);var _169=getFlag(args,"buttonAtRight");var _16a=getParam(args,"sizeTextbox",this.sizeTextbox);var btn;if(!_169){btn=createTiddlyButton(_158,this.label,this.prompt,_161);}
var txt=createTiddlyElement(_158,"input",null,null,null);if(_15a[0]){txt.value=_15a[0];}
txt.onkeyup=_163;txt.onfocus=_166;txt.setAttribute("size",_16a);txt.setAttribute("accessKey",this.accessKey);txt.setAttribute("autocomplete","off");if(config.browser.isSafari){txt.setAttribute("type","search");txt.setAttribute("results","5");}else{txt.setAttribute("type","text");}
if(_169){btn=createTiddlyButton(_158,this.label,this.prompt,_161);}
_125=txt;_126=btn;};var _16d=function(){_12a();var _16e=_f6();var n=_16e.length;if(n){var _170=[];for(var i=0;i<n;i++){_170.push(_16e[i].title);}
story.displayTiddlers(null,_170);}};var _172=function(_173,_174,_175,_176){invokeMacro(_173,"option",_174,_175,_176);var elem=_173.lastChild;var _178=elem.onclick;elem.onclick=function(e){var _17a=_178.apply(this,arguments);_146();return _17a;};return elem;};var _17b=function(s){var _17d=["''","{{{","}}}","//","<<<","/***","***/"];var _17e="";for(var i=0;i<_17d.length;i++){if(i!=0){_17e+="|";}
_17e+="("+_17d[i].escapeRegExp()+")";}
return s.replace(new RegExp(_17e,"mg"),"").trim();};var _180=function(){var i=_13b;return(i>=0&&i<=9)?(i<9?(i+1):0):-1;};var _182=new abego.LimitedTextRenderer();var _183=function(_184,s,_186){_182.render(_184,s,_186,_f3.getMarkRegExp());};var _187=TiddlyWiki.prototype.saveTiddler;TiddlyWiki.prototype.saveTiddler=function(_188,_189,_18a,_18b,_18c,tags,_18e){_187.apply(this,arguments);_14b();};var _18f=TiddlyWiki.prototype.removeTiddler;TiddlyWiki.prototype.removeTiddler=function(_190){_18f.apply(this,arguments);_14b();};config.macros.yourSearch={label:"yourSearch",prompt:"Gives access to the current/last YourSearch result",handler:function(_191,_192,_193,_194,_195,_196){if(_193.length==0){return;}
var name=_193[0];var func=config.macros.yourSearch.funcs[name];if(func){func(_191,_192,_193,_194,_195,_196);}},tests:{"true":function(){return true;},"false":function(){return false;},"found":function(){return _f7()>0;},"previewText":function(){return config.options.chkPreviewText;}},funcs:{itemRange:function(_199){if(_f7()){var _19a=_13d.getLastIndexOnPage();var s="%0 - %1".format([_13d.getFirstIndexOnPage()+1,_19a+1]);createTiddlyText(_199,s);}},count:function(_19c){createTiddlyText(_19c,_f7().toString());},query:function(_19d){if(_f3){createTiddlyText(_19d,_f3.toString());}},version:function(_19e){var t="YourSearch %0.%1.%2".format([version.extensions.YourSearchPlugin.major,version.extensions.YourSearchPlugin.minor,version.extensions.YourSearchPlugin.revision]);var e=createTiddlyElement(_19e,"a");e.setAttribute("href","http://tiddlywiki.abego-software.de/#YourSearchPlugin");e.innerHTML="<font color=\"black\" face=\"Arial, Helvetica, sans-serif\">"+t+"<font>";},copyright:function(_1a1){var e=createTiddlyElement(_1a1,"a");e.setAttribute("href","http://www.abego-software.de");e.innerHTML="<font color=\"black\" face=\"Arial, Helvetica, sans-serif\">&copy; 2005-2008 <b><font color=\"red\">abego</font></b> Software<font>";},newTiddlerButton:function(_1a3){if(_f3){var r=abego.parseNewTiddlerCommandLine(_f3.getQueryText());var btn=config.macros.newTiddler.createNewTiddlerButton(_1a3,r.title,r.params,"new tiddler","Create a new tiddler based on search text. (Shortcut: Ctrl-Enter; Separators: '.', '#')",null,"text");var _1a6=btn.onclick;btn.onclick=function(){_12a();_1a6.apply(this,arguments);};_127=btn;}},linkButton:function(_1a7,_1a8,_1a9,_1aa,_1ab,_1ac){if(_1a9<2){return;}
var _1ad=_1a9[1];var text=_1a9<3?_1ad:_1a9[2];var _1af=_1a9<4?text:_1a9[3];var _1b0=_1a9<5?null:_1a9[4];var btn=createTiddlyButton(_1a7,text,_1af,_12b,null,null,_1b0);btn.setAttribute("tiddlyLink",_1ad);},closeButton:function(_1b2,_1b3,_1b4,_1b5,_1b6,_1b7){var _1b8=createTiddlyButton(_1b2,"close","Close the Search Results (Shortcut: ESC)",_12a);},openAllButton:function(_1b9,_1ba,_1bb,_1bc,_1bd,_1be){var n=_f7();if(n==0){return;}
var _1c0=n==1?"open tiddler":"open all %0 tiddlers".format([n]);var _1c1=createTiddlyButton(_1b9,_1c0,"Open all found tiddlers (Shortcut: Alt-O)",_16d);_1c1.setAttribute("accessKey","O");},naviBar:function(_1c2,_1c3,_1c4,_1c5,_1c6,_1c7){_13d.addPageNavigation(_1c2);},"if":function(_1c8,_1c9,_1ca,_1cb,_1cc,_1cd){if(_1ca.length<2){return;}
var _1ce=_1ca[1];var _1cf=(_1ce=="not");if(_1cf){if(_1ca.length<3){return;}
_1ce=_1ca[2];}
var test=config.macros.yourSearch.tests[_1ce];var _1d1=false;try{if(test){_1d1=test(_1c8,_1c9,_1ca,_1cb,_1cc,_1cd)!=_1cf;}else{_1d1=(!eval(_1ce))==_1cf;}}
catch(ex){}
if(!_1d1){_1c8.style.display="none";}},chkPreviewText:function(_1d2,_1d3,_1d4,_1d5,_1d6,_1d7){var _1d8=_1d4.slice(1).join(" ");var elem=_172(_1d2,"chkPreviewText",_1d5,_1d7);elem.setAttribute("accessKey","P");elem.title="Show text preview of found tiddlers (Shortcut: Alt-P)";return elem;}}};config.macros.foundTiddler={label:"foundTiddler",prompt:"Provides information on the tiddler currently processed on the YourSearch result page",handler:function(_1da,_1db,_1dc,_1dd,_1de,_1df){var name=_1dc[0];var func=config.macros.foundTiddler.funcs[name];if(func){func(_1da,_1db,_1dc,_1dd,_1de,_1df);}},funcs:{title:function(_1e2,_1e3,_1e4,_1e5,_1e6,_1e7){if(!_13c){return;}
var _1e8=_180();var _1e9=_1e8>=0?"Open tiddler (Shortcut: Alt-%0)".format([_1e8.toString()]):"Open tiddler";var btn=createTiddlyButton(_1e2,null,_1e9,_12b,null);btn.setAttribute("tiddlyLink",_13c.title);btn.setAttribute("withHilite","true");_183(btn,_13c.title,_11b);if(_1e8>=0){btn.setAttribute("accessKey",_1e8.toString());}},tags:function(_1eb,_1ec,_1ed,_1ee,_1ef,_1f0){if(!_13c){return;}
_183(_1eb,_13c.getTags(),_11c);},text:function(_1f1,_1f2,_1f3,_1f4,_1f5,_1f6){if(!_13c){return;}
_183(_1f1,_17b(_13c.text),_11d);},field:function(_1f7,_1f8,_1f9,_1fa,_1fb,_1fc){if(!_13c){return;}
var name=_1f9[1];var len=_1f9.length>2?abego.toInt(_1f9[2],_11e):_11e;var v=store.getValue(_13c,name);if(v){_183(_1f7,_17b(v),len);}},number:function(_200,_201,_202,_203,_204,_205){var _206=_180();if(_206>=0){var text="%0)".format([_206.toString()]);createTiddlyElement(_200,"span",null,"shortcutNumber",text);}}}};var opts={chkUseYourSearch:true,chkPreviewText:true,chkSearchAsYouType:true,chkSearchInTitle:true,chkSearchInText:true,chkSearchInTags:true,chkSearchExtendedFields:true,txtItemsPerPage:_11f,txtItemsPerPageWithPreview:_120};for(var n in opts){if(config.options[n]==undefined){config.options[n]=opts[n];}}
config.shadowTiddlers.AdvancedOptions+="\n<<option chkUseYourSearch>> Use 'Your Search' //([[more options|YourSearch Options]]) ([[help|YourSearch Help]])// ";config.shadowTiddlers["YourSearch Help"]="!Field Search\nWith the Field Search you can restrict your search to certain fields of a tiddler, e.g"+" only search the tags or only the titles. The general form is //fieldname//'':''//textToSearch// (e."+"g. {{{title:intro}}}). In addition one-character shortcuts are also supported for the standard field"+"s {{{title}}}, {{{text}}} and {{{tags}}}:\n|!What you want|!What you type|!Example|\n|Search ''titles "+"only''|start word with ''!''|{{{!jonny}}} (shortcut for {{{title:jonny}}})|\n|Search ''contents/text "+"only''|start word with ''%''|{{{%football}}} (shortcut for {{{text:football}}})|\n|Search ''tags only"+"''|start word with ''#''|{{{#Plugin}}} (shortcut for {{{tags:Plugin}}})|\n\nUsing this feature you may"+" also search the extended fields (\"Metadata\") introduced with TiddlyWiki 2.1, e.g. use {{{priority:1"+"}}} to find all tiddlers with the priority field set to \"1\".\n\nYou may search a word in more than one"+" field. E.g. {{{!#Plugin}}} (or {{{title:tags:Plugin}}} in the \"long form\") finds tiddlers containin"+"g \"Plugin\" either in the title or in the tags (but does not look for \"Plugin\" in the text). \n\n!Boole"+"an Search\nThe Boolean Search is useful when searching for multiple words.\n|!What you want|!What you "+"type|!Example|\n|''All words'' must exist|List of words|{{{jonny jeremy}}} (or {{{jonny and jeremy}}}"+")|\n|''At least one word'' must exist|Separate words by ''or''|{{{jonny or jeremy}}}|\n|A word ''must "+"not exist''|Start word with ''-''|{{{-jonny}}} (or {{{not jonny}}})|\n\n''Note:'' When you specify two"+" words, separated with a space, YourSearch finds all tiddlers that contain both words, but not neces"+"sarily next to each other. If you want to find a sequence of word, e.g. '{{{John Brown}}}', you need"+" to put the words into quotes. I.e. you type: {{{\"john brown\"}}}.\n\nUsing parenthesis you may change "+"the default \"left to right\" evaluation of the boolean search. E.g. {{{not (jonny or jeremy)}}} finds"+" all tiddlers that contain neither \"jonny\" nor \"jeremy. In contrast to this {{{not jonny or jeremy}}"+"} (i.e. without parenthesis) finds all tiddlers that either don't contain \"jonny\" or that contain \"j"+"eremy\".\n\n!'Exact Word' Search\nBy default a search result all matches that 'contain' the searched tex"+"t. E.g. if you search for {{{Task}}} you will get all tiddlers containing 'Task', but also '~Complet"+"edTask', '~TaskForce' etc.\n\nIf you only want to get the tiddlers that contain 'exactly the word' you"+" need to prefix it with a '='. E.g. typing '=Task' will find the tiddlers that contain the word 'Tas"+"k', ignoring words that just contain 'Task' as a substring.\n\n!~CaseSensitiveSearch and ~RegExpSearch"+"\nThe standard search options ~CaseSensitiveSearch and ~RegExpSearch are fully supported by YourSearc"+"h. However when ''~RegExpSearch'' is on Filtered and Boolean Search are disabled.\n\nIn addition you m"+"ay do a \"regular expression\" search even with the ''~RegExpSearch'' set to false by directly enterin"+"g the regular expression into the search field, framed with {{{/.../}}}. \n\nExample: {{{/m[ae][iy]er/"+"}}} will find all tiddlers that contain either \"maier\", \"mayer\", \"meier\" or \"meyer\".\n\n!~JavaScript E"+"xpression Filtering\nIf you are familiar with JavaScript programming and know some TiddlyWiki interna"+"ls you may also use JavaScript expression for the search. Just enter a JavaScript boolean expression"+" into the search field, framed with {{{ { ... } }}}. In the code refer to the variable tiddler and e"+"valuate to {{{true}}} when the given tiddler should be included in the result. \n\nExample: {{{ { tidd"+"ler.modified > new Date(\"Jul 4, 2005\")} }}} returns all tiddler modified after July 4th, 2005.\n\n!Com"+"bined Search\nYou are free to combine the various search options. \n\n''Examples''\n|!What you type|!Res"+"ult|\n|{{{!jonny !jeremy -%football}}}|all tiddlers with both {{{jonny}}} and {{{jeremy}}} in its tit"+"les, but no {{{football}}} in content.|\n|{{{#=Task}}}|All tiddlers tagged with 'Task' (the exact wor"+"d). Tags named '~CompletedTask', '~TaskForce' etc. are not considered.|\n\n!Access Keys\nYou are encour"+"aged to use the access keys (also called \"shortcut\" keys) for the most frequently used operations. F"+"or quick reference these shortcuts are also mentioned in the tooltip for the various buttons etc.\n\n|"+"!Key|!Operation|\n|{{{Alt-F}}}|''The most important keystroke'': It moves the cursor to the search in"+"put field so you can directly start typing your query. Pressing {{{Alt-F}}} will also display the pr"+"evious search result. This way you can quickly display multiple tiddlers using \"Press {{{Alt-F}}}. S"+"elect tiddler.\" sequences.|\n|{{{ESC}}}|Closes the [[YourSearch Result]]. When the [[YourSearch Resul"+"t]] is already closed and the cursor is in the search input field the field's content is cleared so "+"you start a new query.|\n|{{{Alt-1}}}, {{{Alt-2}}},... |Pressing these keys opens the first, second e"+"tc. tiddler from the result list.|\n|{{{Alt-O}}}|Opens all found tiddlers.|\n|{{{Alt-P}}}|Toggles the "+"'Preview Text' mode.|\n|{{{Alt-'<'}}}, {{{Alt-'>'}}}|Displays the previous or next page in the [[Your"+"Search Result]].|\n|{{{Return}}}|When you have turned off the 'as you type' search mode pressing the "+"{{{Return}}} key actually starts the search (as does pressing the 'search' button).|\n\n//If some of t"+"hese shortcuts don't work for you check your browser if you have other extensions installed that alr"+"eady \"use\" these shortcuts.//";config.shadowTiddlers["YourSearch Options"]="|>|!YourSearch Options|\n|>|<<option chkUseYourSearch>> Use 'Your Search'|\n|!|<<option chkPreviewText"+">> Show Text Preview|\n|!|<<option chkSearchAsYouType>> 'Search As You Type' Mode (No RETURN required"+" to start search)|\n|!|Default Search Filter:<<option chkSearchInTitle>>Title ('!')     <<option chk"+"SearchInText>>Text ('%')     <<option chkSearchInTags>>Tags ('#')    <<option chkSearchExtendedFiel"+"ds>>Extended Fields<html><br><font size=\"-2\">The fields of a tiddlers that are searched when you don"+"'t explicitly specify a filter in the search text <br>(Explictly specify fields using one or more '!"+"', '%', '#' or 'fieldname:' prefix before the word/text to find).</font></html>|\n|!|Number of items "+"on search result page: <<option txtItemsPerPage>>|\n|!|Number of items on search result page with pre"+"view text: <<option txtItemsPerPageWithPreview>>|\n";config.shadowTiddlers["YourSearchStyleSheet"]="/***\n!~YourSearchResult Stylesheet\n***/\n/*{{{*/\n.yourSearchResult {\n\tposition: absolute;\n\twidth: 800"+"px;\n\n\tpadding: 0.2em;\n\tlist-style: none;\n\tmargin: 0;\n\n\tbackground: #ffd;\n\tborder: 1px solid DarkGra"+"y;\n}\n\n/*}}}*/\n/***\n!!Summary Section\n***/\n/*{{{*/\n.yourSearchResult .summary {\n\tborder-bottom-width:"+" thin;\n\tborder-bottom-style: solid;\n\tborder-bottom-color: #999999;\n\tpadding-bottom: 4px;\n}\n\n.yourSea"+"rchRange, .yourSearchCount, .yourSearchQuery   {\n\tfont-weight: bold;\n}\n\n.yourSearchResult .summary ."+"button {\n\tfont-size: 10px;\n\n\tpadding-left: 0.3em;\n\tpadding-right: 0.3em;\n}\n\n.yourSearchResult .summa"+"ry .chkBoxLabel {\n\tfont-size: 10px;\n\n\tpadding-right: 0.3em;\n}\n\n/*}}}*/\n/***\n!!Items Area\n***/\n/*{{{*"+"/\n.yourSearchResult .marked {\n\tbackground: none;\n\tfont-weight: bold;\n}\n\n.yourSearchItem {\n\tmargin-to"+"p: 2px;\n}\n\n.yourSearchNumber {\n\tcolor: #808080;\n}\n\n\n.yourSearchTags {\n\tcolor: #008000;\n}\n\n.yourSearc"+"hText {\n\tcolor: #808080;\n\tmargin-bottom: 6px;\n}\n\n/*}}}*/\n/***\n!!Footer\n***/\n/*{{{*/\n.yourSearchFoote"+"r {\n\tmargin-top: 8px;\n\tborder-top-width: thin;\n\tborder-top-style: solid;\n\tborder-top-color: #999999;"+"\n}\n\n.yourSearchFooter a:hover{\n\tbackground: none;\n\tcolor: none;\n}\n/*}}}*/\n/***\n!!Navigation Bar\n***/"+"\n/*{{{*/\n.yourSearchNaviBar a {\n\tfont-size: 16px;\n\tmargin-left: 4px;\n\tmargin-right: 4px;\n\tcolor: bla"+"ck;\n\ttext-decoration: underline;\n}\n\n.yourSearchNaviBar a:hover {\n\tbackground-color: none;\n}\n\n.yourSe"+"archNaviBar .prev {\n\tfont-weight: bold;\n\tcolor: blue;\n}\n\n.yourSearchNaviBar .currentPage {\n\tcolor: #"+"FF0000;\n\tfont-weight: bold;\n\ttext-decoration: none;\n}\n\n.yourSearchNaviBar .next {\n\tfont-weight: bold"+";\n\tcolor: blue;\n}\n/*}}}*/\n";config.shadowTiddlers["YourSearchResultTemplate"]="<!--\n{{{\n-->\n<span macro=\"yourSearch if found\">\n<!-- The Summary Header ============================"+"================ -->\n<table class=\"summary\" border=\"0\" width=\"100%\" cellspacing=\"0\" cellpadding=\"0\">"+"<tbody>\n  <tr>\n\t<td align=\"left\">\n\t\tYourSearch Result <span class=\"yourSearchRange\" macro=\"yourSearc"+"h itemRange\"></span>\n\t\t&nbsp;of&nbsp;<span class=\"yourSearchCount\" macro=\"yourSearch count\"></span>\n"+"\t\tfor&nbsp;<span class=\"yourSearchQuery\" macro=\"yourSearch query\"></span>\n\t</td>\n\t<td class=\"yourSea"+"rchButtons\" align=\"right\">\n\t\t<span macro=\"yourSearch chkPreviewText\"></span><span class=\"chkBoxLabel"+"\">preview text</span>\n\t\t<span macro=\"yourSearch newTiddlerButton\"></span>\n\t\t<span macro=\"yourSearch openAllButton\"></span>\n\t\t<span macro=\"yourSearch lin"+"kButton 'YourSearch Options' options 'Configure YourSearch'\"></span>\n\t\t<span macro=\"yourSearch linkB"+"utton 'YourSearch Help' help 'Get help how to use YourSearch'\"></span>\n\t\t<span macro=\"yourSearch clo"+"seButton\"></span>\n\t</td>\n  </tr>\n</tbody></table>\n\n<!-- The List of Found Tiddlers ================="+"=========================== -->\n<div id=\"yourSearchResultItems\" itemsPerPage=\"25\" itemsPerPageWithPr"+"eview=\"10\"></div>\n\n<!-- The Footer (with the Navigation) ==========================================="+"= -->\n<table class=\"yourSearchFooter\" border=\"0\" width=\"100%\" cellspacing=\"0\" cellpadding=\"0\"><tbody"+">\n  <tr>\n\t<td align=\"left\">\n\t\tResult page: <span class=\"yourSearchNaviBar\" macro=\"yourSearch naviBar"+"\"></span>\n\t</td>\n\t<td align=\"right\"><span macro=\"yourSearch version\"></span>, <span macro=\"yourSearc"+"h copyright\"></span>\n\t</td>\n  </tr>\n</tbody></table>\n<!-- end of the 'tiddlers found' case ========="+"================================== -->\n</span>\n\n\n<!-- The \"No tiddlers found\" case ================="+"========================== -->\n<span macro=\"yourSearch if not found\">\n<table class=\"summary\" border="+"\"0\" width=\"100%\" cellspacing=\"0\" cellpadding=\"0\"><tbody>\n  <tr>\n\t<td align=\"left\">\n\t\tYourSearch Resu"+"lt: No tiddlers found for <span class=\"yourSearchQuery\" macro=\"yourSearch query\"></span>.\n\t</td>\n\t<t"+"d class=\"yourSearchButtons\" align=\"right\">\n\t\t<span macro=\"yourSearch newTiddlerButton\"></span>\n\t\t<span macro=\"yourSearch linkButton 'YourSearch Options'"+" options 'Configure YourSearch'\"></span>\n\t\t<span macro=\"yourSearch linkButton 'YourSearch Help' help"+" 'Get help how to use YourSearch'\"></span>\n\t\t<span macro=\"yourSearch closeButton\"></span>\n\t</td>\n  <"+"/tr>\n</tbody></table>\n</span>\n\n\n<!--\n}}}\n-->\n";config.shadowTiddlers["YourSearchItemTemplate"]="<!--\n{{{\n-->\n<span class='yourSearchNumber' macro='foundTiddler number'></span>\n<span class='yourSea"+"rchTitle' macro='foundTiddler title'/></span>&nbsp;-&nbsp;\n<span class='yourSearchTags' macro='found"+"Tiddler field tags 50'/></span>\n<span macro=\"yourSearch if previewText\"><div class='yourSearchText' macro='fo"+"undTiddler field text 250'/></div></span>\n<!--\n}}}\n-->";config.shadowTiddlers["YourSearch"]="<<tiddler [[YourSearch Help]]>>";config.shadowTiddlers["YourSearch Result"]="The popup-like window displaying the result of a YourSearch query.";config.macros.search.handler=_157;var _20a=function(){if(config.macros.search.handler!=_157){alert("Message from YourSearchPlugin:\n\n\nAnother plugin has disabled the 'Your Search' features.\n\n\nYou may "+"disable the other plugin or change the load order of \nthe plugins (by changing the names of the tidd"+"lers)\nto enable the 'Your Search' features.");}};setTimeout(_20a,5000);abego.YourSearch.getStandardRankFunction=function(){return _ff;};abego.YourSearch.getRankFunction=function(){return abego.YourSearch.getStandardRankFunction();};abego.YourSearch.getCurrentTiddler=function(){return _13c;};abego.YourSearch.closeResult=function(){_12a();};abego.YourSearch.getFoundTiddlers=function(){return _f2;};abego.YourSearch.getQuery=function(){return _f3;};abego.YourSearch.onShowResult=function(_20b){highlightHack=_f3?_f3.getMarkRegExp():null;if(!_20b){_13d.setItems(_f6());}
if(!_124){_124=createTiddlyElement(document.body,"div",_121,"yourSearchResult");}else{if(_124.parentNode!=document.body){document.body.appendChild(_124);}}
_146();highlightHack=null;};})();}
//%/
For YourSearchPlugin source code see the [[archive|http://tiddlywiki.abego-software.de/archive]].
<<miniBrowser http://www.zentralblatt-math.org/reviewer/en/>>
<<miniBrowser http://www.zentralblatt-math.org/zmath/en/>>
*The MainMenu is like a table of contents. It is found on the left hand side of the page.  Click on any colored text and either a tiddler will open or  a remote web site will open in a new browser window .
*Hyperlinks are links between files and between places within a file. The hyperlinks in this file are shown in bold, colored text.  Clicking on them will take you to another tiddler or open another website in a new window.