Welcome to TiddlyWiki created by Jeremy Ruston, Copyright © 2007 UnaMesa Association
!!!
Date of MSC TiddlyWiki creation: 20080723014940
!!![[00|00-XX]]Axx General and miscellaneous specific topics {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/00Axx.html]]}
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* ''00A05'' General mathematics
* ''00A06'' Mathematics for nonmathematicians (engineering, social sciences, etc.)
* ''00A07'' Problem books
* ''00A08'' Recreational mathematics [See also [[97A20|97Axx]]]
* ''00A09'' --Mathematics and the Arts-- __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|03-XX]]]
* ''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]]}
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* ''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]]}
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* ''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]]]
!!!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]]}
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* ''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]]}
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* ''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
* ''03A05'' Philosophical and critical {For philosophy of mathematics, see also [[00A30|00Axx]]}
* __''03A99''__ __None of the above, but in this section__
!!![[03|03-XX]]Bxx General logic {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/03Bxx.html]]}
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* ''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'' Logic__s__ of knowledge and belief __(including belief change)__
* ''03B44'' Temporal logic
* ''03B45'' Modal logic __(including the logic of norms)__ {For knowledge and belief see 03B42; for temporal logic see 03B44; for provability logic see also [[03F45|03Fxx]]}
* ''03B47'' Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCĭlogics) {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'' --Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.)-- __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]]}
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* ''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]__
* __''03C48''__ __Abstract elementary classes and related topics [See also 03C45]__
* ''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|13-XX]]]
* ''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]
* ''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]]}
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* ''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]]}
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* ''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]__
* ''03E55'' Large cardinals
* __''03E57''__ __Generic absoluteness and forcing axioms [See also 03E50]__
* ''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]]}
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* ''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 --in proof theory -- __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]]}
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* ''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]]}
----
* ''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.
* ''[[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]]}
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* ''03H05'' Nonstandard models in mathematics [See also [[26E35|26Exx]], [[28E05|28Exx]], [[30G06|30Gxx]], [[46S20|46Sxx]], [[47S20|47Sxx]], [[54J05|54-XX]]]
* ''03H10'' Other applications of nonstandard models (economics, physics, etc.)
* ''03H15'' Nonstandard models of arithmetic [See also [[11U10|11Uxx]], [[12L15|12Lxx]], [[13L05|13-XX]]]
* ''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]]}
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* ''05A05'' --Combinatorial choice problems (subsets, representatives, permutations)-- __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'' <html><math><mi>q</mi></math></html>-calculus and related topics [See also --[[03Dxx|03Dxx]]]__[[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]]}
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* ''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]]}
----
* ''05C05'' Trees
* ''05C07'' __Vertex degrees [See also [[05E30|05Exx]]]__ --Degree sequences--
* ''05C10'' __Planar graphs; geometric and topological aspects of__ --Topological-- graph theory--, imbedding-- [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 --, gain and biased-- __and weighted__ graphs
* ''05C25'' Graphs and --groups-- __abstract algebra (groups, rings, fields, etc.)__ [See also [[20F65|20Fxx]]]
* ''05C30'' Enumeration --of graphs and maps-- __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 --matrices-- __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 --types-- __families__ of graphs
* __''05C76''__ __Graph operations (line graphs, products, etc.)__
* ''05C78'' Graph labelling (graceful graphs, bandwidth, etc.)
* ''05C80'' Random graphs __[See also [[60B35|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]]}
----
* ''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]]}
----
* ''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]]}
----
* ''05E05'' Symmetric functions __and generalizations__
* ''05E10'' --Tableaux, representations of the symmetric group-- __Combinatorial aspects of representation theory__ [See also [[20C30|20Cxx]]]
* ''05E15'' Combinatorial __aspects of groups and algebras __ --problems concerning the classical groups -- [See also [[14Nxx|14Nxx]], [[22E45|22Exx]], [[33C80|33Cxx]]]
* --''05E20''-- --Group actions on designs, geometries and codes--
* __''05E18''__ __Group actions on combinatorial structures__
* --''05E25''-- --Group actions on posets and homology groups of posets [See also [[06A11|06Axx]]]--
* ''05E30'' Association schemes, strongly regular graphs
* --''05E35''-- --Orthogonal polynomials [See also [[33C45|33Cxx]], [[33C50|33Cxx]], [[33D45|33Dxx]]]--
* __''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]]}
----
* ''06A05'' Total order
* ''06A06'' Partial order, general
* ''06A07'' Combinatorics of partially ordered sets
* ''06A11'' Algebraic aspects of posets [See also [[05E25|05Exx]]]
* ''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]]}
----
* ''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, [[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]]}
----
* ''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]]}
----
* ''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, \L ukasiewicz 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]]}
----
* ''06E05'' Structure theory
* ''06E10'' Chain conditions, complete algebras
* ''06E15'' --Stone space and related constructions-- __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]]}
----
* ''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
* __''06Z05''__ __Miscellaneous applications of order, lattices or ordered algebraic structures__
!!![[06|06-XX]]Fxx Ordered structures {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/06Fxx.html]]}
----
* ''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]]}
----
* ''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]]}
----
* ''08B05'' Equational logic, Mal{\cprime}cev (Mal{\cprime}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]]}
----
* ''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]]}
----
* ''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]]}
----
* ''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]]}
----
* ''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 <html><math><mi>m</mi></math></html>)
* ''11B57'' Farey sequences; the sequences <html><math><mo fence="true">{</mo><msup><mn>1</mn><mi>k</mi></msup><mo separator="true">,</mo><msup><mn>2</mn><mi>k</mi></msup><mo separator="true">,</mo><mo>…</mo><mo fence="true">}</mo></math></html>)
* ''11B65'' Binomial coefficients; factorials; <html><math><mi>q</mi></math></html>-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]]}
----
* ''11C08'' Polynomials [See also [[13F20|13Fxx]]]
* ''11C20'' Matrices, determinants [See also [[15A36|15Axx]]]
* ''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]]}
----
* ''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'' <html><math><mi>p</mi></math></html>-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]]}
----
* ''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'' <html><math><mi>K</mi></math></html>-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'' <html><math><mi>p</mi></math></html>-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]]}
----
* ''11F03'' Modular and automorphic functions
* ''11F06'' Structure of modular groups and generalizations; arithmetic groups [See also [[20H05|20Hxx]], [[20H10|20Hxx]], [[22E40|22Exx]]]
* ''11F11'' --Modular forms, one variable-- __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 <html><math><mi>p</mi></math></html>-adic modular forms [See also [[14G20|14Gxx]], [[22E50|22Exx]]]
* ''11F37'' Forms of half-integer weight; nonholomorphic modular forms
* ''11F41'' __Automorphic forms on 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 --and their modular-- __; Siegel and ~Hilbert-Siegel modular__ and automorphic forms
* ''11F50'' Jacobi forms
* ''11F52'' Modular forms associated to Drinfel{\cprime}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 <html><math><mi>L</mi></math></html>-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'' <html><math><mi>p</mi></math></html>-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]]}
----
* ''11G05'' Elliptic curves over global fields [See also [[14H52|14Hxx]]]
* ''11G07'' Elliptic curves over local fields [See also [[14G20|14Gxx]], [[14H52|14Hxx]]]
* ''11G09'' Drinfel{\cprime}d modules; higher-dimensional motives, etc. [See also [[14L05|14Lxx]]]
* ''11G10'' Abelian varieties of dimension <html><math><mo>></mo><mn>1,</mn></math></html> [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 <html><math><mo>≠</mo><mi>1</mi></math></html> over global fields [See also [[14H25|14Hxx]]]
* __''11G32''__ __Dessins d'enfants, Belyĭ theory__
* ''11G35'' Varieties over global fields [See also [[14G25|14Gxx]]]
* ''11G40'' <html><math><mi>L</mi></math></html>-functions of varieties over global fields; ~Birch-Swinnerton-Dyer conjecture [See also [[14G10|14Gxx]]]
* __''11G42''__ __Arithmetic mirror symmetry [See also 14J32]__
* ''11G45'' Geometric class field theory [See also [[11R37|11Rxx]], [[14C35|14Cxx]], [[19F05|19Fxx]]]
* ''11G50'' Heights [See also [[14G40|14Gxx]]]
* ''11G55'' Polylogarithms and relations with <html><math><mi>K</mi></math></html>-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]]}
----
* ''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]]}
----
* ''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{\cprime}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{\cprime}d and <html><math><mi>t</mi></math></html>-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 <html><math><mi>1</mi></math></html>; metric theory of algorithms {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Kxx.html]]}
----
* ''11K06'' General theory of distribution modulo <html><math><mi>1</mi></math></html> [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, <html><math><mi>p</mi></math></html>-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]]}
----
* ''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 <html><math><mi>L</mi></math></html>-functions: analytic theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Mxx.html]]}
----
* ''11M06'' <html><math><mi>ζ</mi><mo fence="true">(</mo><mi>s</mi><mo fence="true">)</mo></math></html>) and <html><math display="block"><mi>L</mi><mo fence="true">(</mo><mi>s</mi><mo separator="true">,</mo><mi>χ</mi><mo fence="true">)</mo></math></html>
* ''11M20'' Real zeros of <html><math display="block"><mi>L</mi><mo fence="true">(</mo><mi>s</mi><mo separator="true">,</mo><mi>χ</mi><mo fence="true">)</mo></math></html>; results on <html><math display="block"><mi>L</mi><mo fence="true">(</mo><mn>1</mn><mo separator="true">,</mo><mi>χ</mi><mo fence="true">)</mo></math></html>
* ''11M26'' Nonreal zeros of <html><math><mi>ζ</mi><mo fence="true">(</mo><mi>s</mi><mo fence="true">)</mo></math></html>) and <html><math display="block"><mi>L</mi><mo fence="true">(</mo><mi>s</mi><mo separator="true">,</mo><mi>χ</mi><mo fence="true">)</mo></math></html>; 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 <html><math><mi>L</mi></math></html>-functions in characteristic <html><math><mi>p</mi></math></html>
* ''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]]}
----
* ''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]]}
----
* ''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]]}
----
* ''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]]--, [[16H05|16-XX]]], [[19A31|19Axx]]--
* ''11R37'' Class field theory
* ''11R39'' ~Langlands-Weil conjectures, nonabelian class field theory [See also [[11Fxx|11Fxx]], [[22E55|22Exx]]]
* ''11R42'' Zeta functions and <html><math><mi>L</mi></math></html>-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 <html><math><mi>L</mi></math></html>-functions [See also [[11S45|11Sxx]], --[[16H05|16-XX]]]__[[16-XX|16-XX]]__ , [[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'' <html><math><mi>K</mi></math></html>-theory of global fields [See also [[19Fxx|19Fxx]]]
* ''11R80'' Totally real--and totally positive-- fields [See also [[12J15|12Jxx]]]
* ''11R99'' None of the above, but in this section
!!![[11|11-XX]]Sxx Algebraic number theory: local and <html><math><mi>p</mi></math></html>-adic fields {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Sxx.html]]}
----
* ''11S05'' Polynomials
* ''11S15'' Ramification and extension theory
* ''11S20'' Galois theory
* ''11S23'' Integral representations
* ''11S25'' Galois cohomology [See also [[12Gxx|12Gxx]], [[16H05|16-XX]]]
* ''11S31'' Class field theory; <html><math><mi>p</mi></math></html>-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 <html><math><mi>L</mi></math></html>-functions [See also [[11M41|11Mxx]], [[19F27|19Fxx]]]
* ''11S45'' Algebras and orders, and their zeta functions [See also [[11R52|11Rxx]], [[11R54|11Rxx]], --[[16H05|16-XX]]]__[[16-XX|16-XX]]__ , [[16Kxx|16Kxx]]--
* ''11S70'' <html><math><mi>K</mi></math></html>-theory of local fields [See also [[19Fxx|19Fxx]]]
* ''11S80'' Other analytic theory (analogues of beta and gamma functions, <html><math><mi>p</mi></math></html>-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]]}
----
* ''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]]}
----
* ''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-XX Number theory {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11-XX.html]]}
----
* ''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 <html><math><mi>1</mi></math></html>; metric theory of algorithms
* ''[[11Lxx|11Lxx]]'' Exponential sums and character sums {For finite fields, see [[11Txx|11Txx]]}
* ''[[11Mxx|11Mxx]]'' Zeta and <html><math><mi>L</mi></math></html>-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 <html><math><mi>p</mi></math></html>-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]]]
!!![[11|11-XX]]Yxx Computational number theory [See also [[11-04|11-XX]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/11Yxx.html]]}
----
* ''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
* ''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]]}
----
* ''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]]}
----
* ''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]]}
----
* ''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]]}
----
* ''12G05'' Galois cohomology [See also [[14F22|14Fxx]], [[16H05|16-XX]], [[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]]}
----
* ''12H05'' Differential algebra [See also [[13Nxx|13Nxx]]]
* ''12H10'' Difference algebra [See also [[39Axx|39Axx]]]
* ''12H20'' Abstract differential equations [See also [[34Mxx|34Mxx]]]
* ''12H25'' <html><math><mi>p</mi></math></html>-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]]}
----
* ''12J05'' Normed fields
* ''12J10'' Valued fields
* ''12J12'' Formally <html><math><mi>p</mi></math></html>-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|32-XX]], [[46S10|46Sxx]], [[47S10|47Sxx]]]
* ''12J27'' ~Krasner-Tate algebras [See mainly [[32P05|32-XX]]; 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]]}
----
* ''12K05'' Near-fields [See also [[16Y30|16Yxx]]]
* ''12K10'' Semifields [See also [[16Y60|16Yxx]]]
* ''12K99'' None of the above, but in this section
!!!12-XX Field theory and polynomials {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/12-XX.html]]}
----
* ''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
!!![[12|12-XX]]Lxx Connections with logic {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/12Lxx.html]]}
----
* ''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
* ''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]]}
----
* ''13A02'' Graded rings [See also [[16W50|16Wxx]]]
* ''13A05'' Divisibility; __factorizations__ __[See also [[13F15|13Fxx]]]__
* --''13A10''-- --Radical theory--
* ''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 <html><math><mi>p</mi></math></html> methods (Frobenius endomorphism) and reduction to characteristic <html><math><mi>p</mi></math></html>; 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]]}
----
* ''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.)
* --''13B24''-- --Going up; going down; going between--
* ''13B25'' Polynomials over commutative rings [See also [[11C08|11Cxx]], [[13F20|13Fxx]], [[13M10|13Mxx]]]
* ''13B30'' --Quotients-- __Rings of fractions__ and localization
* ''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]]}
----
* ''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__ --; derived 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]]}
----
* ''13D02'' Syzygies --and-- __, __ 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, <html><math><mi>K</mi></math></html>-theory [See also [[14C35|14Cxx]], [[18F30|18Fxx]], [[19Axx|19Axx]], [[19D50|19Dxx]]]
* ''13D22'' Homological conjectures (intersection theorems)
* --''13D25''-- --Complexes--
* ''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]]}
----
* ''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]]}
----
* ''13F05'' Dedekind, Prüfer --and-- __,__ Krull __and Mori__ rings and their generalizations
* ''13F07'' Euclidean rings and generalizations
* ''13F10'' Principal ideal rings
* ''13F15'' --Factorial rings, unique factorization domains-- __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'' --Face and ~Stanley-Reisner rings-- __~Stanley-Reisner face rings__ ; simplicial complexes [See also [[55U10|55Uxx]]]
* __''13F60''__ __Cluster algebras__
* ''13F99'' None of the above, but in this section
* ''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]]}
----
* ''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]]}
----
* ''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
* ''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]]}
----
* ''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]]}
----
* ''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 rings and algebras {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/13-XX.html]]}
----
* ''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
* ''[[13Hxx|13Hxx]]'' Local rings and semilocal rings
* ''[[13Jxx|13Jxx]]'' Topological rings and modules [See also [[16W60|16Wxx]], [[16W80|16Wxx]]]
* --''13K05''-- --Witt vectors and related rings--
* ''[[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--of commutative algebra-- __and applications__ [See also [[14Qxx|14Qxx]], [[68W30|68Wxx]]]
!!![[13|13-XX]]Pxx Computational aspects--of commutative algebra-- __and applications__ [See also [[14Qxx|14Qxx]], [[68W30|68Wxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/13Pxx.html]]}
----
* ''13P05'' Polynomials, factorization [See also [[12Y05|12-XX]]]
* ''13P10'' --Polynomial ideals,-- Gröbner bases __; other bases for ideals and modules (e.g., Janet and border bases)__ --[See also [[13F20|13Fxx]]]--
* __''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]]}
----
* ''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
* ''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]]}
----
* ''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]]}
----
* ''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 <html><math><mi>K</mi></math></html>-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]]}
----
* ''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)
* ''14D22'' Fine and coarse moduli spaces
* __''14D23''__ __Stacks and moduli problems__
* __''14D24''__ __Geometric Langlands program: algebro-geometric aspects__
* ''14D99'' None of the above, but in this section
!!![[14|14-XX]]Exx Birational geometry {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/14Exx.html]]}
----
* ''14E05'' Rational and birational maps
* ''14E07'' Birational automorphisms, Cremona group and generalizations
* ''14E08'' Rationality questions
* ''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]]}
----
* ''14F05'' --Vector bundles,-- __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 cohomologies
* ''14F22'' Brauer groups of schemes [See also [[12G05|12Gxx]], [[16K50|16Kxx]]]
* ''14F25'' Classical real and complex cohomology
* ''14F30'' <html><math><mi>p</mi></math></html>-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 __ --; motives--
* ''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]]}
----
* ''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]]]
* ''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]]}
----
* ''14H05'' Algebraic functions; function fields [See also [[11R58|11Rxx]]]
* ''14H10'' Families, moduli (algebraic)
* ''14H15'' Families, moduli (analytic) [See also [[30F10|30Fxx]], [[32Gxx|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]]}
----
* ''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'' <html><math><mi>K3</mi></math></html> surfaces and Enriques surfaces
* ''14J29'' Surfaces of general type
* ''14J30'' <html><math><mi>3</mi></math></html>-folds
* ''14J32'' ~Calabi-Yau manifolds--, mirror symmetry--
* __''14J33''__ __Mirror symmetry__
* ''14J35'' <html><math><mi>4</mi></math></html>-folds
* ''14J40'' <html><math><mi>n</mi></math></html>-folds (<html><math><mi>n</mi><mo>></mo><mn>4</mn></math></html>)
* ''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]]}
----
* ''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]], [[11Gxx|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]]}
----
* ''14L05'' Formal groups, <html><math><mi>p</mi></math></html>-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]
* ''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]]}
----
* ''14M05'' Varieties defined by ring conditions (factorial, ~Cohen-Macaulay, seminormal) [See also [[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
* __''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]]}
----
* ''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]]}
----
* ''14P05'' Real algebraic sets [See also [[12Dxx|12Dxx]]]
* ''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|12-XX]], [[13Pxx|13Pxx]], [[68W30|68Wxx]]] {[[Info & Stats|http://msc2010.org/mscwiki/msc2007/14Qxx.html]]}
----
* ''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]]}
----
* ''14R05'' Classification of affine varieties
* ''14R10'' Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
* ''14R15'' Jacobian problem
* ''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]]}
----
* ''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|12-XX]], [[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]]}
----
* ''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]]}
----
* ''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]]]
* ''15A33'' Matrices over special rings (quaternions, finite fields, etc.)
* --''15A36''-- --Matrices of integers [See also [[11C20|11Cxx]]]--
* ''15A39'' Linear inequalities
* ''15A42'' Inequalities involving eigenvalues and eigenvectors
* ''15A45'' Miscellaneous inequalities involving matrices
* --''15A48''-- --Positive matrices and their generalizations; cones of matrices--
* --''15A51''-- --Stochastic matrices--
* --''15A52''-- --Random matrices--
* ''15A54'' Matrices over function rings in one or more variables
* --''15A57''-- --Other types of matrices (Hermitian, skew-Hermitian, etc.)--
* ''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]]}
----
* ''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]]}
----
* __''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]]}
----
* ''16B5