Welcome to TiddlyWiki created by Jeremy Ruston, Copyright © 2007 UnaMesa Association
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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 ab