The Mathematics Subject Classification (MSC) is an alphanumerical classification scheme formulated by the American Mathematical Society based on the coverage of two major reviewing databases Mathematical Reviews and Zentralblatt MATH. It is used by many mathematics journals, which ask authors of research papers and expository articles to list subject codes from the Mathematics Subject Classification in their papers. (Taken from Wikipedia.)

- 00-xx: General
- 00-01: Instructional exposition (textbooks, tutorial papers, etc.)
- 00-02: Research exposition (monographs, survey articles)
- 00Axx: General and miscellaneous specific topics
- 00A05: General mathematics
- 00A06: Mathematics for nonmathematicians (engineering, social sciences, etc.)
- 00A07: Problem books
- 00A08: Recreational mathematics
- 00A15: Bibliographies
- 00A17: External book reviews
- 00A20: Dictionaries and other general reference works
- 00A22: Formularies
- 00A30: Philosophy of mathematics
- 00A35: Methodology of mathematics, didactics
- 00A69: General applied mathematics
- 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

- 00Bxx: Conference proceedings and collections of papers
- 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

- 01-xx: History and biography
- 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: History of mathematics and mathematicians
- 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
- 01A80: Sociology (and profession) of mathematics
- 01A85: Historiography
- 01A90: Bibliographic studies
- 01A99: Miscellaneous topics

- 03-xx: Mathematical logic and foundations
- 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.
- 03A05: Philosophical and critical

- 03Bxx: General logic
- 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
- 03B30: Foundations of classical theories (including reverse mathematics)
- 03B35: Mechanization of proofs and logical operations
- 03B40: Combinatory logic and lambda-calculus
- 03B42: Logic of knowledge and belief
- 03B44: Temporal logic
- 03B45: Modal logic
- 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
- 03B48: Probability and inductive logic
- 03B50: Many-valued logic
- 03B52: Fuzzy logic; logic of vagueness
- 03B53: Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.)
- 03B55: Intermediate logics
- 03B60: Other nonclassical logic
- 03B65: Logic of natural languages
- 03B70: Logic in computer science
- 03B80: Other applications of logic
- 03B99: None of the above, but in this section

- 03Cxx: Model theory
- 03C05: Equational classes, universal algebra
- 03C07: Basic properties of first-order languages and structures
- 03C10: Quantifier elimination, model completeness and related topics
- 03C13: Finite structures
- 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
- 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
- 03C60: Model-theoretic algebra
- 03C62: Models of arithmetic and set theory
- 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
- 03C85: Second- and higher-order model theory
- 03C90: Nonclassical models (Boolean-valued, sheaf, etc.)
- 03C95: Abstract model theory
- 03C98: Applications of model theory
- 03C99: None of the above, but in this section

- 03Dxx: Computability and recursion theory
- 03D03: Thue and Post systems, etc.
- 03D05: Automata and formal grammars in connection with logical questions
- 03D10: Turing machines and related notions
- 03D15: Complexity of computation
- 03D20: Recursive functions and relations, subrecursive hierarchies
- 03D25: Recursively (computably) enumerable sets and degrees
- 03D28: Other Turing degree structures
- 03D30: Other degrees and reducibilities
- 03D35: Undecidability and degrees of sets of sentences
- 03D40: Word problems, etc.
- 03D45: Theory of numerations, effectively presented structures
- 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
- 03D80: Applications of computability and recursion theory
- 03D99: None of the above, but in this section

- 03Exx: Set theory
- 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
- 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
- 03E55: Large cardinals
- 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

- 03Fxx: Proof theory and constructive mathematics
- 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
- 03F40: Gödel numberings in proof theory
- 03F45: Provability logics and related algebras (e.g., diagonalizable algebras)
- 03F50: Metamathematics of constructive systems
- 03F52: Linear logic and other substructural logics
- 03F55: Intuitionistic mathematics
- 03F60: Constructive and recursive analysis
- 03F65: Other constructive mathematics
- 03F99: None of the above, but in this section

- 03Gxx: Algebraic logic
- 03G05: Boolean algebras
- 03G10: Lattices and related structures
- 03G12: Quantum logic
- 03G15: Cylindric and polyadic algebras; relation algebras
- 03G20: Lukasiewicz and Post algebras
- 03G25: Other algebras related to logic
- 03G30: Categorical logic, topoi
- 03G99: None of the above, but in this section

- 03Hxx: Nonstandard models
- 03H05: Nonstandard models in mathematics
- 03H10: Other applications of nonstandard models (economics, physics, etc.)
- 03H15: Nonstandard models of arithmetic
- 03H99: None of the above, but in this section

- 05-xx: Combinatorics
- 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: Enumerative combinatorics
- 05A05: Combinatorial choice problems (subsets, representatives, permutations)
- 05A10: Factorials, binomial coefficients, combinatorial functions
- 05A15: Exact enumeration problems, generating functions
- 05A16: Asymptotic enumeration
- 05A17: Partitions of integers
- 05A18: Partitions of sets
- 05A19: Combinatorial identities
- 05A20: Combinatorial inequalities
- 05A30: $q$-calculus and related topics
- 05A40: Umbral calculus
- 05A99: None of the above, but in this section

- 05Bxx: Designs and configurations
- 05B05: Block designs
- 05B07: Triple systems
- 05B10: Difference sets (number-theoretic, group-theoretic, etc.)
- 05B15: Orthogonal arrays, Latin squares, Room squares
- 05B20: Matrices (incidence, Hadamard, etc.)
- 05B25: Finite geometries
- 05B30: Other designs, configurations
- 05B35: Matroids, geometric lattices
- 05B40: Packing and covering
- 05B45: Tessellation and tiling problems
- 05B50: Polyominoes
- 05B99: None of the above, but in this section

- 05Cxx: Graph theory
- 05C05: Trees
- 05C07: Degree sequences
- 05C10: Topological graph theory, imbedding
- 05C12: Distance in graphs
- 05C15: Coloring of graphs and hypergraphs
- 05C17: Perfect graphs
- 05C20: Directed graphs (digraphs), tournaments
- 05C22: Signed, gain and biased graphs
- 05C25: Graphs and groups
- 05C30: Enumeration of graphs and maps
- 05C35: Extremal problems
- 05C38: Paths and cycles
- 05C40: Connectivity
- 05C45: Eulerian and Hamiltonian graphs
- 05C50: Graphs and matrices
- 05C55: Generalized Ramsey theory
- 05C60: Isomorphism problems (reconstruction conjecture, etc.)
- 05C62: Graph representations (geometric and intersection representations, etc.)
- 05C65: Hypergraphs
- 05C69: Dominating sets, independent sets, cliques
- 05C70: Factorization, matching, covering and packing
- 05C75: Structural characterization of types of graphs
- 05C78: Graph labelling (graceful graphs, bandwidth, etc.)
- 05C80: Random graphs
- 05C83: Graph minors
- 05C85: Graph algorithms
- 05C90: Applications
- 05C99: None of the above, but in this section

- 05Dxx: Extremal combinatorics
- 05D05: Extremal set theory
- 05D10: Ramsey theory
- 05D15: Transversal (matching) theory
- 05D40: Probabilistic methods
- 05D99: None of the above, but in this section

- 05Exx: Algebraic combinatorics
- 05E05: Symmetric functions
- 05E10: Tableaux, representations of the symmetric group
- 05E15: Combinatorial problems concerning the classical groups
- 05E20: Group actions on designs, geometries and codes
- 05E25: Group actions on posets and homology groups of posets
- 05E30: Association schemes, strongly regular graphs
- 05E35: Orthogonal polynomials
- 05E99: None of the above, but in this section

- 06-xx: Order, lattices, ordered algebraic structures
- 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: Ordered sets
- 06A05: Total order
- 06A06: Partial order, general
- 06A07: Combinatorics of partially ordered sets
- 06A11: Algebraic aspects of posets
- 06A12: Semilattices
- 06A15: Galois correspondences, closure operators
- 06A99: None of the above, but in this section

- 06Bxx: Lattices
- 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
- 06B30: Topological lattices, order topologies
- 06B35: Continuous lattices and posets, applications
- 06B99: None of the above, but in this section

- 06Cxx: Modular lattices, complemented lattices
- 06C05: Modular lattices, Desarguesian lattices
- 06C10: Semimodular lattices, geometric lattices
- 06C15: Complemented lattices, orthocomplemented lattices and posets
- 06C20: Complemented modular lattices, continuous geometries
- 06C99: None of the above, but in this section

- 06Dxx: Distributive lattices
- 06D05: Structure and representation theory
- 06D10: Complete distributivity
- 06D15: Pseudocomplemented lattices
- 06D20: Heyting algebras
- 06D22: Frames, locales
- 06D25: Post algebras
- 06D30: De Morgan algebras, Lukasiewicz algebras
- 06D35: MV-algebras
- 06D50: Lattices and duality
- 06D72: Fuzzy lattices (soft algebras) and related topics
- 06D99: None of the above, but in this section

- 06Exx: Boolean algebras (Boolean rings)
- 06E05: Structure theory
- 06E10: Chain conditions, complete algebras
- 06E15: Stone space and related constructions
- 06E20: Ring-theoretic properties
- 06E25: Boolean algebras with additional operations (diagonalizable algebras, etc.)
- 06E30: Boolean functions
- 06E99: None of the above, but in this section

- 06Fxx: Ordered structures
- 06F05: Ordered semigroups and monoids
- 06F07: Quantales
- 06F10: Noether lattices
- 06F15: Ordered groups
- 06F20: Ordered abelian groups, Riesz groups, ordered linear spaces
- 06F25: Ordered rings, algebras, modules
- 06F30: Topological lattices, order topologies
- 06F35: BCK-algebras, BCI-algebras
- 06F99: None of the above, but in this section

- 08-xx: General algebraic systems
- 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: Algebraic structures
- 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
- 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

- 08Bxx: Varieties
- 08B05: Equational logic, Malcev (Maltsev) conditions
- 08B10: Congruence modularity, congruence distributivity
- 08B15: Lattices of varieties
- 08B20: Free algebras
- 08B25: Products, amalgamated products, and other kinds of limits and colimits
- 08B26: Subdirect products and subdirect irreducibility
- 08B30: Injectives, projectives
- 08B99: None of the above, but in this section

- 08Cxx: Other classes of algebras
- 08C05: Categories of algebras
- 08C10: Axiomatic model classes
- 08C15: Quasivarieties
- 08C99: None of the above, but in this section

- 11-xx: Number theory
- 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: Elementary number theory
- 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
- 11A63: Radix representation; digital problems
- 11A67: Other representations
- 11A99: None of the above, but in this section

- 11Bxx: Sequences and sets
- 11B05: Density, gaps, topology
- 11B13: Additive bases
- 11B25: Arithmetic progressions
- 11B34: Representation functions
- 11B37: Recurrences
- 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
- 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

- 11Cxx: Polynomials and matrices
- 11C08: Polynomials
- 11C20: Matrices, determinants
- 11C99: None of the above, but in this section

- 11Dxx: Diophantine equations
- 11D04: Linear equations
- 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
- 11D75: Diophantine inequalities
- 11D79: Congruences in many variables
- 11D85: Representation problems
- 11D88: $p$-adic and power series fields
- 11D99: None of the above, but in this section

- 11Exx: Forms and linear algebraic groups
- 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
- 11E70: $K$-theory of quadratic and Hermitian forms
- 11E72: Galois cohomology of linear algebraic groups
- 11E76: Forms of degree higher than two
- 11E81: Algebraic theory of quadratic forms; Witt groups and rings
- 11E88: Quadratic spaces; Clifford algebras
- 11E95: $p$-adic theory
- 11E99: None of the above, but in this section

- 11Fxx: Discontinuous groups and automorphic forms
- 11F03: Modular and automorphic functions
- 11F06: Structure of modular groups and generalizations; arithmetic groups
- 11F11: Modular forms, one variable
- 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
- 11F30: Fourier coefficients of automorphic forms
- 11F32: Modular correspondences, etc.
- 11F33: Congruences for modular and $p$-adic modular forms
- 11F37: Forms of half-integer weight; nonholomorphic modular forms
- 11F41: Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
- 11F46: Siegel modular groups and their 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: Dirichlet series and functional equations in connection with modular forms
- 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
- 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
- 11F99: None of the above, but in this section

- 11Gxx: Arithmetic algebraic geometry (Diophantine geometry)
- 11G05: Elliptic curves over global fields
- 11G07: Elliptic curves over local fields
- 11G09: Drinfeld modules; higher-dimensional motives, etc.
- 11G10: Abelian varieties of dimension $\gtr 1$
- 11G15: Complex multiplication and moduli of abelian varieties
- 11G16: Elliptic and modular units
- 11G18: Arithmetic aspects of modular and Shimura varieties
- 11G20: Curves over finite and local fields
- 11G25: Varieties over finite and local fields
- 11G30: Curves of arbitrary genus or genus $\ne 1$ over global fields
- 11G35: Varieties over global fields
- 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
- 11G45: Geometric class field theory
- 11G50: Heights
- 11G55: Polylogarithms and relations with $K$-theory
- 11G99: None of the above, but in this section

- 11Hxx: Geometry of numbers
- 11H06: Lattices and convex bodies
- 11H16: Nonconvex bodies
- 11H31: Lattice packing and covering
- 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

- 11Jxx: Diophantine approximation, transcendental number theory
- 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
- 11J54: Small fractional parts of polynomials and generalizations
- 11J61: Approximation in non-Archimedean valuations
- 11J68: Approximation to algebraic numbers
- 11J70: Continued fractions and generalizations
- 11J71: Distribution modulo one
- 11J72: Irrationality; linear independence over a field
- 11J81: Transcendence (general theory)
- 11J82: Measures of irrationality and of transcendence
- 11J83: Metric theory
- 11J85: Algebraic independence; Gelfond's method
- 11J86: Linear forms in logarithms; Baker's method
- 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

- 11Kxx: Probabilistic theory: distribution modulo $1$; metric theory of algorithms
- 11K06: General theory of distribution modulo $1$
- 11K16: Normal numbers, radix expansions, etc.
- 11K31: Special sequences
- 11K36: Well-distributed sequences and other variations
- 11K38: Irregularities of distribution, discrepancy
- 11K41: Continuous, $p$-adic and abstract analogues
- 11K45: Pseudo-random numbers; Monte Carlo methods
- 11K50: Metric theory of continued fractions
- 11K55: Metric theory of other algorithms and expansions; measure and Hausdorff dimension
- 11K60: Diophantine approximation
- 11K65: Arithmetic functions
- 11K70: Harmonic analysis and almost periodicity
- 11K99: None of the above, but in this section

- 11Lxx: Exponential sums and character sums
- 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

- 11Mxx: Zeta and $L$-functions: analytic theory
- 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
- 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
- 11M45: Tauberian theorems
- 11M99: None of the above, but in this section

- 11Nxx: Multiplicative number theory
- 11N05: Distribution of primes
- 11N13: Primes in progressions
- 11N25: Distribution of integers with specified multiplicative constraints
- 11N30: Turán theory
- 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
- 11N80: Generalized primes and integers
- 11N99: None of the above, but in this section

- 11Pxx: Additive number theory; partitions
- 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
- 11P70: Inverse problems of additive number theory
- 11P81: Elementary theory of partitions
- 11P82: Analytic theory of partitions
- 11P83: Partitions; congruences and congruential restrictions
- 11P99: None of the above, but in this section

- 11Rxx: Algebraic number theory: global fields
- 11R04: Algebraic numbers; rings of algebraic integers
- 11R06: PV-numbers and generalizations; other special algebraic numbers
- 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
- 11R34: Galois cohomology
- 11R37: Class field theory
- 11R39: Langlands-Weil conjectures, nonabelian class field theory
- 11R42: Zeta functions and $L$-functions of number fields
- 11R44: Distribution of prime ideals
- 11R45: Density theorems
- 11R47: Other analytic theory
- 11R52: Quaternion and other division algebras: arithmetic, zeta functions
- 11R54: Other algebras and orders, and their zeta and $L$-functions
- 11R56: Adèle rings and groups
- 11R58: Arithmetic theory of algebraic function fields
- 11R60: Cyclotomic function fields (class groups, Bernoulli objects, etc.)
- 11R65: Class groups and Picard groups of orders
- 11R70: $K$-theory of global fields
- 11R80: Totally real and totally positive fields
- 11R99: None of the above, but in this section

- 11Sxx: Algebraic number theory: local and $p$-adic fields
- 11S05: Polynomials
- 11S15: Ramification and extension theory
- 11S20: Galois theory
- 11S23: Integral representations
- 11S25: Galois cohomology
- 11S31: Class field theory; $p$-adic formal groups
- 11S37: Langlands-Weil conjectures, nonabelian class field theory
- 11S40: Zeta functions and $L$-functions
- 11S45: Algebras and orders, and their zeta functions
- 11S70: $K$-theory of local fields
- 11S80: Other analytic theory (analogues of beta and gamma functions, $p$-adic integration, etc.)
- 11S85: Other nonanalytic theory
- 11S90: Prehomogeneous vector spaces
- 11S99: None of the above, but in this section

- 11Txx: Finite fields and commutative rings (number-theoretic aspects)
- 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

- 11Uxx: Connections with logic
- 11U05: Decidability
- 11U07: Ultraproducts
- 11U09: Model theory
- 11U10: Nonstandard arithmetic
- 11U99: None of the above, but in this section

- 11Yxx: Computational number theory
- 11Y05: Factorization
- 11Y11: Primality
- 11Y16: Algorithms; complexity
- 11Y35: Analytic computations
- 11Y40: Algebraic number theory computations
- 11Y50: Computer solution of Diophantine equations
- 11Y55: Calculation of integer sequences
- 11Y60: Evaluation of constants
- 11Y65: Continued fraction calculations
- 11Y70: Values of arithmetic functions; tables
- 11Y99: None of the above, but in this section
- 11Z05: Miscellaneous applications of number theory

- 12-xx: Field theory and polynomials
- 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: Real and complex fields
- 12D05: Polynomials: factorization
- 12D10: Polynomials: location of zeros (algebraic theorems)
- 12D15: Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
- 12D99: None of the above, but in this section

- 12Exx: General field theory
- 12E05: Polynomials (irreducibility, etc.)
- 12E10: Special polynomials
- 12E12: Equations
- 12E15: Skew fields, division rings
- 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

- 12Fxx: Field extensions
- 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

- 12Gxx: Homological methods (field theory)
- 12G05: Galois cohomology
- 12G10: Cohomological dimension
- 12G99: None of the above, but in this section

- 12Hxx: Differential and difference algebra
- 12H05: Differential algebra
- 12H10: Difference algebra
- 12H20: Abstract differential equations
- 12H25: $p$-adic differential equations
- 12H99: None of the above, but in this section

- 12Jxx: Topological fields
- 12J05: Normed fields
- 12J10: Valued fields
- 12J12: Formally $p$-adic fields
- 12J15: Ordered fields
- 12J17: Topological semifields
- 12J20: General valuation theory
- 12J25: Non-Archimedean valued fields
- 12J27: Krasner-Tate algebras
- 12J99: None of the above, but in this section

- 12Kxx: Generalizations of fields
- 12K05: Near-fields
- 12K10: Semifields
- 12K99: None of the above, but in this section

- 12Lxx: Connections with logic
- 12L05: Decidability
- 12L10: Ultraproducts
- 12L12: Model theory
- 12L15: Nonstandard arithmetic
- 12L99: None of the above, but in this section
- 12Y05: Computational aspects of field theory and polynomials

- 13-xx: Commutative rings and algebras
- 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: General commutative ring theory
- 13A02: Graded rings
- 13A05: Divisibility
- 13A10: Radical theory
- 13A15: Ideals; multiplicative ideal theory
- 13A18: Valuations and their generalizations
- 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
- 13A50: Actions of groups on commutative rings; invariant theory
- 13A99: None of the above, but in this section

- 13Bxx: Ring extensions and related topics
- 13B02: Extension theory
- 13B05: Galois theory
- 13B10: Morphisms
- 13B21: Integral dependence
- 13B22: Integral closure of rings and ideals; integrally closed rings, related rings (Japanese, etc.)
- 13B24: Going up; going down; going between
- 13B25: Polynomials over commutative rings
- 13B30: Quotients and localization
- 13B35: Completion
- 13B40: Étale and flat extensions; Henselization; Artin approximation
- 13B99: None of the above, but in this section

- 13Cxx: Theory of modules and ideals
- 13C05: Structure, classification theorems
- 13C10: Projective and free modules and ideals
- 13C11: Injective and flat modules and ideals
- 13C12: Torsion modules and ideals
- 13C13: Other special types
- 13C14: Cohen-Macaulay modules
- 13C15: Dimension theory, depth, related rings (catenary, etc.)
- 13C20: Class groups
- 13C40: Linkage, complete intersections and determinantal ideals
- 13C99: None of the above, but in this section

- 13Dxx: Homological methods
- 13D02: Syzygies and resolutions
- 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.)
- 13D10: Deformations and infinitesimal methods
- 13D15: Grothendieck groups, $K$-theory
- 13D22: Homological conjectures (intersection theorems)
- 13D25: Complexes
- 13D30: Torsion theory
- 13D40: Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
- 13D45: Local cohomology
- 13D99: None of the above, but in this section

- 13Exx: Chain conditions, finiteness conditions
- 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

- 13Fxx: Arithmetic rings and other special rings
- 13F05: Dedekind, Prüfer and Krull rings and their generalizations
- 13F07: Euclidean rings and generalizations
- 13F10: Principal ideal rings
- 13F15: Factorial rings, unique factorization domains
- 13F20: Polynomial rings and ideals; rings of integer-valued polynomials
- 13F25: Formal power series rings
- 13F30: Valuation rings
- 13F40: Excellent rings
- 13F45: Seminormal rings
- 13F50: Rings with straightening laws, Hodge algebras
- 13F55: Face and Stanley-Reisner rings; simplicial complexes
- 13F99: None of the above, but in this section
- 13G05: Integral domains

- 13Hxx: Local rings and semilocal rings
- 13H05: Regular local rings
- 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
- 13H15: Multiplicity theory and related topics
- 13H99: None of the above, but in this section

- 13Jxx: Topological rings and modules
- 13J05: Power series rings
- 13J07: Analytical algebras and rings
- 13J10: Complete rings, completion
- 13J15: Henselian rings
- 13J20: Global topological rings
- 13J25: Ordered rings
- 13J30: Real algebra
- 13J99: None of the above, but in this section
- 13K05: Witt vectors and related rings
- 13L05: Applications of logic to commutative algebra

- 13Mxx: Finite commutative rings
- 13M05: Structure
- 13M10: Polynomials
- 13M99: None of the above, but in this section

- 13Nxx: Differential algebra
- 13N05: Modules of differentials
- 13N10: Rings of differential operators and their modules
- 13N15: Derivations
- 13N99: None of the above, but in this section

- 13Pxx: Computational aspects of commutative algebra
- 13P05: Polynomials, factorization
- 13P10: Polynomial ideals, Gröbner bases
- 13P99: None of the above, but in this section

- 14-xx: Algebraic geometry
- 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: Foundations
- 14A05: Relevant commutative algebra
- 14A10: Varieties and morphisms
- 14A15: Schemes and morphisms
- 14A20: Generalizations (algebraic spaces, stacks)
- 14A22: Noncommutative algebraic geometry
- 14A25: Elementary questions
- 14A99: None of the above, but in this section

- 14Bxx: Local theory
- 14B05: Singularities
- 14B07: Deformations of singularities
- 14B10: Infinitesimal methods
- 14B12: Local deformation theory, Artin approximation, etc.
- 14B15: Local cohomology
- 14B20: Formal neighborhoods
- 14B25: Local structure of morphisms: étale, flat, etc.
- 14B99: None of the above, but in this section

- 14Cxx: Cycles and subschemes
- 14C05: Parametrization (Chow and Hilbert schemes)
- 14C15: Chow groups and rings
- 14C17: Intersection theory, characteristic classes, intersection multiplicities
- 14C20: Divisors, linear systems, invertible sheaves
- 14C21: Pencils, nets, webs
- 14C22: Picard groups
- 14C25: Algebraic cycles
- 14C30: Transcendental methods, Hodge theory, Hodge conjecture
- 14C34: Torelli problem
- 14C35: Applications of methods of algebraic $K$-theory
- 14C40: Riemann-Roch theorems
- 14C99: None of the above, but in this section

- 14Dxx: Families, fibrations
- 14D05: Structure of families (Picard-Lefschetz, monodromy, etc.)
- 14D06: Fibrations, degenerations
- 14D07: Variation of Hodge structures
- 14D10: Arithmetic ground fields (finite, local, global)
- 14D15: Formal methods; deformations
- 14D20: Algebraic moduli problems, moduli of vector bundles
- 14D21: Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
- 14D22: Fine and coarse moduli spaces
- 14D99: None of the above, but in this section

- 14Exx: Birational geometry
- 14E05: Rational and birational maps
- 14E07: Birational automorphisms, Cremona group and generalizations
- 14E08: Rationality questions
- 14E15: Global theory and resolution of singularities
- 14E20: Coverings
- 14E22: Ramification problems
- 14E25: Embeddings
- 14E30: Minimal model program (Mori theory, extremal rays)
- 14E99: None of the above, but in this section

- 14Fxx: (Co)homology theory
- 14F05: Vector bundles, sheaves, related constructions
- 14F10: Differentials and other special sheaves
- 14F17: Vanishing theorems
- 14F20: Étale and other Grothendieck topologies and cohomologies
- 14F22: Brauer groups of schemes
- 14F25: Classical real and complex cohomology
- 14F30: $p$-adic cohomology, crystalline cohomology
- 14F35: Homotopy theory; fundamental groups
- 14F40: de Rham cohomology
- 14F42: Motivic cohomology
- 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

- 14Gxx: Arithmetic problems. Diophantine geometry
- 14G05: Rational points
- 14G10: Zeta-functions and related questions(Birch-Swinnerton-Dyer conjecture)
- 14G15: Finite 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
- 14G40: Arithmetic varieties and schemes; Arakelov theory; heights
- 14G50: Applications to coding theory and cryptography
- 14G99: None of the above, but in this section

- 14Hxx: Curves
- 14H05: Algebraic functions; function fields
- 14H10: Families, moduli (algebraic)
- 14H15: Families, moduli (analytic)
- 14H20: Singularities, local rings
- 14H25: Arithmetic ground fields
- 14H30: Coverings, fundamental group
- 14H37: Automorphisms
- 14H40: Jacobians, Prym varieties
- 14H42: Theta functions; Schottky problem
- 14H45: Special curves and curves of low genus
- 14H50: Plane and space curves
- 14H51: Special divisors (gonality, Brill-Noether theory)
- 14H52: Elliptic curves
- 14H55: Riemann surfaces; Weierstrass points; gap sequences
- 14H60: Vector bundles on curves and their moduli
- 14H70: Relationships with integrable systems
- 14H81: Relationships with physics
- 14H99: None of the above, but in this section

- 14Jxx: Surfaces and higher-dimensional varieties
- 14J10: Families, moduli, classification: algebraic theory
- 14J15: Moduli, classification: analytic theory; relations with modular forms
- 14J17: Singularities
- 14J20: Arithmetic ground fields
- 14J25: Special surfaces
- 14J26: Rational and ruled surfaces
- 14J27: Elliptic surfaces
- 14J28: $K3$ surfaces and Enriques surfaces
- 14J29: Surfaces of general type
- 14J30: $3$-folds
- 14J32: Calabi-Yau manifolds, mirror symmetry
- 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
- 14J70: Hypersurfaces
- 14J80: Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)
- 14J81: Relationships with physics
- 14J99: None of the above, but in this section

- 14Kxx: Abelian varieties and schemes
- 14K02: Isogeny
- 14K05: Algebraic theory
- 14K10: Algebraic moduli, classification
- 14K12: Subvarieties
- 14K15: Arithmetic ground fields
- 14K20: Analytic theory; abelian integrals and differentials
- 14K22: Complex multiplication
- 14K25: Theta functions
- 14K30: Picard schemes, higher Jacobians
- 14K99: None of the above, but in this section

- 14Lxx: Algebraic groups
- 14L05: Formal groups, $p$-divisible groups
- 14L10: Group varieties
- 14L15: Group schemes
- 14L17: Affine algebraic groups, hyperalgebra constructions
- 14L24: Geometric invariant theory
- 14L30: Group actions on varieties or schemes (quotients)
- 14L35: Classical groups (geometric aspects)
- 14L40: Other algebraic groups (geometric aspects)
- 14L99: None of the above, but in this section

- 14Mxx: Special varieties
- 14M05: Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
- 14M06: Linkage
- 14M07: Low codimension problems
- 14M10: Complete intersections
- 14M12: Determinantal varieties
- 14M15: Grassmannians, Schubert varieties, flag manifolds
- 14M17: Homogeneous spaces and generalizations
- 14M20: Rational and unirational varieties
- 14M25: Toric varieties, Newton polyhedra
- 14M30: Supervarieties
- 14M99: None of the above, but in this section

- 14Nxx: Projective and enumerative geometry
- 14N05: Projective techniques
- 14N10: Enumerative problems (combinatorial problems)
- 14N15: Classical problems, Schubert calculus
- 14N20: Configurations of linear subspaces
- 14N25: Varieties of low degree
- 14N30: Adjunction problems
- 14N35: Gromov-Witten invariants, quantum cohomology
- 14N99: None of the above, but in this section

- 14Pxx: Real algebraic and real analytic geometry
- 14P05: Real algebraic sets
- 14P10: Semialgebraic sets and related spaces
- 14P15: Real analytic and semianalytic sets
- 14P20: Nash functions and manifolds
- 14P25: Topology of real algebraic varieties
- 14P99: None of the above, but in this section

- 14Qxx: Computational aspects in algebraic geometry
- 14Q05: Curves
- 14Q10: Surfaces, hypersurfaces
- 14Q15: Higher-dimensional varieties
- 14Q20: Effectivity
- 14Q99: None of the above, but in this section

- 14Rxx: Affine geometry
- 14R05: Classification of affine varieties
- 14R10: Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
- 14R15: Jacobian problem
- 14R20: Group actions on affine varieties
- 14R25: Affine fibrations
- 14R99: None of the above, but in this section

- 15-xx: Linear and multilinear algebra; matrix theory
- 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.
- 15A03: Vector spaces, linear dependence, rank
- 15A04: Linear transformations, semilinear transformations
- 15A06: Linear equations
- 15A09: Matrix inversion, generalized inverses
- 15A12: Conditioning of matrices
- 15A15: Determinants, permanents, other special matrix functions
- 15A18: Eigenvalues, singular values, and eigenvectors
- 15A21: Canonical forms, reductions, classification
- 15A22: Matrix pencils
- 15A23: Factorization of matrices
- 15A24: Matrix equations and identities
- 15A27: Commutativity
- 15A29: Inverse problems
- 15A30: Algebraic systems of matrices
- 15A33: Matrices over special rings (quaternions, finite fields, etc.)
- 15A36: Matrices of integers
- 15A39: Linear inequalities
- 15A42: Inequalities involving eigenvalues and eigenvectors
- 15A45: Miscellaneous inequalities involving matrices
- 15A48: Positive matrices and their generalizations; cones of matrices
- 15A51: Stochastic matrices
- 15A52: Random matrices
- 15A54: Matrices over function rings in one or more variables
- 15A57: Other types of matrices (Hermitian, skew-Hermitian, etc.)
- 15A60: Norms of matrices, numerical range, applications of functional analysis to matrix theory
- 15A63: Quadratic and bilinear forms, inner products
- 15A66: Clifford algebras, spinors
- 15A69: Multilinear algebra, tensor products
- 15A72: Vector and tensor algebra, theory of invariants
- 15A75: Exterior algebra, Grassmann algebras
- 15A78: Other algebras built from modules
- 15A90: Applications of matrix theory to physics
- 15A99: Miscellaneous topics

- 16-xx: Associative rings and algebras
- 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: General and miscellaneous
- 16B50: Category-theoretic methods and results (except as in 16D90)
- 16B70: Applications of logic
- 16B99: None of the above, but in this section

- 16Dxx: Modules, bimodules and ideals
- 16D10: General module theory
- 16D20: Bimodules
- 16D25: Ideals
- 16D30: Infinite-dimensional simple rings (except as in 16Kxx)
- 16D40: Free, projective, and flat modules and ideals
- 16D50: Injective modules, self-injective rings
- 16D60: Simple and semisimple modules, primitive rings and ideals
- 16D70: Structure and classification (except as in 16Gxx), direct sum decomposition, cancellation
- 16D80: Other classes of modules and ideals
- 16D90: Module categories; module theory in a category-theoretic context; Morita equivalence and duality
- 16D99: None of the above, but in this section

- 16Exx: Homological methods
- 16E05: Syzygies, resolutions, complexes
- 16E10: Homological dimension
- 16E20: Grothendieck groups, $K$-theory, etc.
- 16E30: Homological functors on modules (Tor, Ext, etc.)
- 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

- 16Gxx: Representation theory of rings and algebras
- 16G10: Representations of Artinian rings
- 16G20: Representations of quivers and partially ordered sets
- 16G30: Representations of orders, lattices, algebras over commutative rings
- 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
- 16H05: Orders and arithmetic, separable algebras, Azumaya algebras

- 16Kxx: Division rings and semisimple Artin rings
- 16K20: Finite-dimensional
- 16K40: Infinite-dimensional and general
- 16K50: Brauer groups
- 16K99: None of the above, but in this section

- 16Lxx: Local rings and generalizations
- 16L30: Noncommutative local and semilocal rings, perfect rings
- 16L60: Quasi-Frobenius rings
- 16L99: None of the above, but in this section

- 16Nxx: Radicals and radical properties of rings
- 16N20: Jacobson radical, quasimultiplication
- 16N40: Nil and nilpotent radicals, sets, ideals, rings
- 16N60: Prime and semiprime rings
- 16N80: General radicals and rings
- 16N99: None of the above, but in this section

- 16Pxx: Chain conditions, growth conditions, and other forms of finiteness
- 16P10: Finite rings and finite-dimensional algebras
- 16P20: Artinian rings and modules
- 16P40: Noetherian rings and modules
- 16P50: Localization and Noetherian rings
- 16P60: Chain conditions on annihilators and summands: Goldie-type conditions, 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

- 16Rxx: Rings with polynomial identity
- 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)
- 16R99: None of the above, but in this section

- 16Sxx: Rings and algebras arising under various constructions
- 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
- 16S32: Rings of differential operators
- 16S34: Group rings, Laurent polynomial rings
- 16S35: Twisted and skew group rings, crossed products
- 16S36: Ordinary and skew polynomial rings and semigroup rings
- 16S37: Quadratic and Koszul algebras
- 16S38: Rings arising from non-commutative algebraic geometry
- 16S40: Smash products of general Hopf actions
- 16S50: Endomorphism rings; matrix rings
- 16S60: Rings of functions, subdirect products, sheaves of rings
- 16S70: Extensions of rings by ideals
- 16S80: Deformations of rings
- 16S90: Maximal ring of quotients, torsion theories, radicals on module categories
- 16S99: None of the above, but in this section

- 16Uxx: Conditions on elements
- 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

- 16Wxx: Rings and algebras with additional structure
- 16W10: Rings with involution; Lie, Jordan and other nonassociative structures
- 16W20: Automorphisms and endomorphisms
- 16W22: Actions of groups and semigroups; invariant theory
- 16W25: Derivations, actions of Lie algebras
- 16W30: Coalgebras, bialgebras, Hopf algebras; rings, modules, etc. on which these act
- 16W35: Ring-theoretic aspects of quantum groups
- 16W50: Graded rings and modules
- 16W55: ``Super'' (or ``skew'') structure
- 16W60: Valuations, completions, formal power series and related constructions
- 16W70: Filtered rings; filtrational and graded techniques
- 16W80: Topological and ordered rings and modules
- 16W99: None of the above, but in this section

- 16Yxx: Generalizations
- 16Y30: Near-rings
- 16Y60: Semirings
- 16Y99: None of the above, but in this section
- 16Z05: Computational aspects of associative rings

- 17-xx: Nonassociative rings and algebras
- 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: General nonassociative rings
- 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

- 17Bxx: Lie algebras and Lie superalgebras
- 17B01: Identities, free Lie (super)algebras
- 17B05: Structure theory
- 17B10: Representations, algebraic theory (weights)
- 17B15: Representations, analytic theory
- 17B20: Simple, semisimple, reductive (super)algebras (roots)
- 17B25: Exceptional (super)algebras
- 17B30: Solvable, nilpotent (super)algebras
- 17B35: Universal enveloping (super)algebras
- 17B37: Quantum groups (quantized enveloping algebras) and related deformations
- 17B40: Automorphisms, derivations, other operators
- 17B45: Lie algebras of linear algebraic groups
- 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.)
- 17B62: Lie bialgebras
- 17B63: Poisson algebras
- 17B65: Infinite-dimensional Lie (super)algebras
- 17B66: Lie algebras of vector fields and related (super) algebras
- 17B67: Kac-Moody (super)algebras (structure and representation theory)
- 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

- 17Cxx: Jordan algebras (algebras, triples and pairs)
- 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
- 17C55: Finite-dimensional structures
- 17C60: Division algebras
- 17C65: Jordan structures on Banach spaces and algebras
- 17C70: Super structures
- 17C90: Applications to physics
- 17C99: None of the above, but in this section

- 17Dxx: Other nonassociative rings and algebras
- 17D05: Alternative rings
- 17D10: Malcev (Maltsev) 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-xx: Category theory; homological algebra
- 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: General theory of categories and functors
- 18A05: Definitions, generalizations
- 18A10: Graphs, diagram schemes, precategories
- 18A15: Foundations, relations to logic and deductive systems
- 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

- 18Bxx: Special categories
- 18B05: Category of sets, characterizations
- 18B10: Category of relations, additive relations
- 18B15: Embedding theorems, universal categories
- 18B20: Categories of machines, automata, operative categories
- 18B25: Topoi
- 18B30: Categories of topological spaces and continuous mappings
- 18B35: Preorders, orders and lattices (viewed as categories)
- 18B40: Groupoids, semigroupoids, semigroups, groups (viewed as categories)
- 18B99: None of the above, but in this section

- 18Cxx: Categories and theories
- 18C05: Equational categories
- 18C10: Theories (e.g. algebraic theories), structure, and semantics
- 18C15: Triples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples
- 18C20: Algebras and Kleisli categories associated with monads
- 18C30: Sketches and generalizations
- 18C35: Accessible and locally presentable categories
- 18C50: Categorical semantics of formal languages
- 18C99: None of the above, but in this section

- 18Dxx: Categories with structure
- 18D05: Double categories, $2$-categories, bicategories and generalizations
- 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories
- 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
- 18D99: None of the above, but in this section

- 18Exx: Abelian categories
- 18E05: Preadditive, additive categories
- 18E10: Exact categories, abelian categories
- 18E15: Grothendieck categories
- 18E20: Embedding theorems
- 18E25: Derived functors and satellites
- 18E30: Derived categories, triangulated categories
- 18E35: Localization of categories
- 18E40: Torsion theories, radicals
- 18E99: None of the above, but in this section

- 18Fxx: Categories and geometry
- 18F05: Local categories and functors
- 18F10: Grothendieck topologies
- 18F15: Abstract manifolds and fiber bundles
- 18F20: Presheaves and sheaves
- 18F25: Algebraic $K$-theory and $L$-theory
- 18F30: Grothendieck groups
- 18F99: None of the above, but in this section

- 18Gxx: Homological algebra
- 18G05: Projectives and injectives
- 18G10: Resolutions; derived functors
- 18G15: Ext and Tor, generalizations, Künneth formula
- 18G20: Homological dimension
- 18G25: Relative homological algebra, projective classes
- 18G30: Simplicial sets, simplicial objects (in a category)
- 18G35: Chain complexes
- 18G40: Spectral sequences, hypercohomology
- 18G50: Nonabelian homological algebra
- 18G55: Homotopical algebra
- 18G60: Other (co)homology theories
- 18G99: None of the above, but in this section

- 19-xx: $K$-theory
- 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: Grothendieck groups and $K_0$
- 19A13: Stability for projective modules
- 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

- 19Bxx: Whitehead groups and $K_1$
- 19B10: Stable range conditions
- 19B14: Stability for linear groups
- 19B28: $K_1$ of group rings and orders
- 19B37: Congruence subgroup problems
- 19B99: None of the above, but in this section

- 19Cxx: Steinberg groups and $K_2$
- 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

- 19Dxx: Higher algebraic $K$-theory
- 19D06: $Q$- and plus-constructions
- 19D10: Algebraic $K$-theory of spaces
- 19D23: Symmetric monoidal categories
- 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
- 19D55: $K$-theory and homology; cyclic homology and cohomology
- 19D99: None of the above, but in this section

- 19Exx: $K$-theory in geometry
- 19E08: $K$-theory of schemes
- 19E15: Algebraic cycles and motivic cohomology
- 19E20: Relations with cohomology theories
- 19E99: None of the above, but in this section

- 19Fxx: $K$-theory in number theory
- 19F05: Generalized class field theory
- 19F15: Symbols and arithmetic
- 19F27: Étale cohomology, higher regulators, zeta and $L$-functions
- 19F99: None of the above, but in this section

- 19Gxx: $K$-theory of forms
- 19G05: Stability for quadratic modules
- 19G12: Witt groups of rings
- 19G24: $L$-theory of group rings
- 19G38: Hermitian $K$-theory, relations with $K$-theory of rings
- 19G99: None of the above, but in this section

- 19Jxx: Obstructions from topology
- 19J05: Finiteness and other obstructions in $K_0$
- 19J10: Whitehead (and related) torsion
- 19J25: Surgery obstructions
- 19J35: Obstructions to group actions
- 19J99: None of the above, but in this section

- 19Kxx: $K$-theory and operator algebras
- 19K14: $K_0$ as an ordered group, traces
- 19K33: EXT and $K$-homology
- 19K35: Kasparov theory ($KK$-theory)
- 19K56: Index theory
- 19K99: None of the above, but in this section

- 19Lxx: Topological $K$-theory
- 19L10: Riemann-Roch theorems, Chern characters
- 19L20: $J$-homomorphism, Adams operations
- 19L41: Connective $K$-theory, cobordism
- 19L47: Equivariant $K$-theory
- 19L64: Computations, geometric applications
- 19L99: None of the above, but in this section
- 19M05: Miscellaneous applications of $K$-theory

- 20-xx: Group theory and generalizations
- 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: Foundations
- 20A05: Axiomatics and elementary properties
- 20A10: Metamathematical considerations
- 20A15: Applications of logic to group theory
- 20A99: None of the above, but in this section

- 20Bxx: Permutation groups
- 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
- 20B27: Infinite automorphism groups
- 20B30: Symmetric groups
- 20B35: Subgroups of symmetric groups
- 20B40: Computational methods
- 20B99: None of the above, but in this section

- 20Cxx: Representation theory of groups
- 20C05: Group rings of finite groups and their modules
- 20C07: Group rings of infinite groups and their modules
- 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

- 20Dxx: Abstract finite groups
- 20D05: Classification of simple and nonsolvable groups
- 20D06: Simple groups: alternating groups and groups of Lie type
- 20D08: Simple groups: sporadic groups
- 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $\pi$-length, ranks
- 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

- 20Exx: Structure and classification of infinite or finite groups
- 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
- 20E10: Quasivarieties and varieties of groups
- 20E15: Chains and lattices of subgroups, subnormal subgroups
- 20E18: Limits, profinite groups
- 20E22: Extensions, wreath products, and other compositions
- 20E25: Local properties
- 20E26: Residual properties and generalizations
- 20E28: Maximal subgroups
- 20E32: Simple groups
- 20E34: General structure theorems
- 20E36: General theorems concerning automorphisms of groups
- 20E42: Groups with a $BN$-pair; buildings
- 20E45: Conjugacy classes
- 20E99: None of the above, but in this section

- 20Fxx: Special aspects of infinite or finite groups
- 20F05: Generators, relations, and presentations
- 20F06: Cancellation theory; application of van Kampen diagrams
- 20F10: Word problems, other decision problems, connections with logic and automata
- 20F12: Commutator calculus
- 20F14: Derived series, central series, and generalizations
- 20F16: Solvable groups, supersolvable groups
- 20F17: Formations of groups, Fitting classes
- 20F18: Nilpotent groups
- 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
- 20F29: Representations of groups as automorphism groups of algebraic systems
- 20F34: Fundamental groups and their automorphisms
- 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
- 20F60: Ordered groups
- 20F65: Geometric group theory
- 20F67: Hyperbolic groups and nonpositively curved groups
- 20F69: Asymptotic properties of groups
- 20F99: None of the above, but in this section

- 20Gxx: Linear algebraic groups (classical groups)
- 20G05: Representation 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
- 20G42: Quantum groups (quantized function algebras) and their representations
- 20G45: Applications to physics
- 20G99: None of the above, but in this section

- 20Hxx: Other groups of matrices
- 20H05: Unimodular groups, congruence subgroups
- 20H10: Fuchsian groups and their generalizations
- 20H15: Other geometric groups, including crystallographic groups
- 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

- 20Jxx: Connections with homological algebra and category theory
- 20J05: Homological methods in group theory
- 20J06: Cohomology of groups
- 20J15: Category of groups
- 20J99: None of the above, but in this section

- 20Kxx: Abelian groups
- 20K01: Finite abelian groups
- 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
- 20K99: None of the above, but in this section
- 20L05: Groupoids (i.e. small categories in which all morphisms are isomorphisms)

- 20Mxx: Semigroups
- 20M05: Free semigroups, generators and relations, word problems
- 20M07: Varieties of semigroups
- 20M10: General structure theory
- 20M11: Radical theory
- 20M12: Ideal theory
- 20M14: Commutative semigroups
- 20M15: Mappings of semigroups
- 20M17: Regular semigroups
- 20M18: Inverse semigroups
- 20M19: Orthodox semigroups
- 20M20: Semigroups of transformations, etc.
- 20M25: Semigroup rings, multiplicative semigroups of rings
- 20M30: Representation of semigroups; actions of semigroups on sets
- 20M35: Semigroups in automata theory, linguistics, etc.
- 20M50: Connections of semigroups with homological algebra and category theory
- 20M99: None of the above, but in this section

- 20Nxx: Other generalizations of groups
- 20N02: Sets with a single binary operation (groupoids)
- 20N05: Loops, quasigroups
- 20N10: Ternary systems (heaps, semiheaps, heapoids, etc.)
- 20N15: $n$-ary systems $(n\ge 3)$
- 20N20: Hypergroups
- 20N25: Fuzzy groups
- 20N99: None of the above, but in this section
- 20P05: Probabilistic methods in group theory

- 22-xx: Topological groups, Lie groups
- 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: Topological and differentiable algebraic systems
- 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)
- 22A25: Representations of general topological groups and semigroups
- 22A26: Topological semilattices, lattices and applications
- 22A30: Other topological algebraic systems and their representations
- 22A99: None of the above, but in this section

- 22Bxx: Locally compact abelian groups (LCA groups)
- 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
- 22C05: Compact groups

- 22Dxx: Locally compact groups and their algebras
- 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
- 22D30: Induced representations
- 22D35: Duality theorems
- 22D40: Ergodic theory on groups
- 22D45: Automorphism groups of locally compact groups
- 22D99: None of the above, but in this section

- 22Exx: Lie groups
- 22E05: Local Lie groups
- 22E10: General properties and structure of complex Lie groups
- 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
- 22E35: Analysis on $p$-adic Lie groups
- 22E40: Discrete subgroups of Lie groups
- 22E41: Continuous cohomology
- 22E43: Structure and representation of the Lorentz group
- 22E45: Representations of Lie and linear algebraic groups over real fields: analytic methods
- 22E46: Semisimple Lie groups and their representations
- 22E47: Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
- 22E50: Representations of Lie and linear algebraic groups over local fields
- 22E55: Representations of Lie and linear algebraic groups over global fields and adèle rings
- 22E60: Lie algebras of Lie groups
- 22E65: Infinite-dimensional Lie groups and their Lie algebras
- 22E67: Loop groups and related constructions, group-theoretic treatment
- 22E70: Applications of Lie groups to physics; explicit representations
- 22E99: None of the above, but in this section

- 22Fxx: Noncompact transformation groups
- 22F05: General theory of group and pseudogroup actions
- 22F10: Measurable group actions
- 22F30: Homogeneous spaces
- 22F50: Groups as automorphisms of other structures

- 26-xx: Real functions
- 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: Functions of one variable
- 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
- 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)
- 26A16: Lipschitz (Hölder) classes
- 26A18: Iteration
- 26A21: Classification of real functions; Baire classification of sets and functions
- 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems
- 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
- 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

- 26Bxx: Functions of several variables
- 26B05: Continuity and differentiation questions
- 26B10: Implicit function theorems, Jacobians, transformations with several variables
- 26B12: Calculus of vector functions
- 26B15: Integration: length, area, volume
- 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

- 26Cxx: Polynomials, rational functions
- 26C05: Polynomials: analytic properties, etc.
- 26C10: Polynomials: location of zeros
- 26C15: Rational functions
- 26C99: None of the above, but in this section

- 26Dxx: Inequalities
- 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

- 26Exx: Miscellaneous topics
- 26E05: Real-analytic functions
- 26E10: $C^\infty$-functions, quasi-analytic functions
- 26E15: Calculus of functions on infinite-dimensional spaces
- 26E20: Calculus of functions taking values in infinite-dimensional spaces
- 26E25: Set-valued functions
- 26E30: Non-Archimedean analysis
- 26E35: Nonstandard analysis
- 26E40: Constructive real analysis
- 26E50: Fuzzy real analysis
- 26E60: Means
- 26E99: None of the above, but in this section

- 28-xx: Measure and integration
- 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: Classical measure theory
- 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets
- 28A10: Real- or complex-valued set functions
- 28A12: Contents, measures, outer measures, capacities
- 28A15: Abstract differentiation theory, differentiation of set functions
- 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
- 28A35: Measures and integrals in product spaces
- 28A50: Integration and disintegration of measures
- 28A51: Lifting theory
- 28A60: Measures on Boolean rings, measure algebras
- 28A75: Length, area, volume, other geometric measure theory
- 28A78: Hausdorff and packing measures
- 28A80: Fractals
- 28A99: None of the above, but in this section

- 28Bxx: Set functions, measures and integrals with values in abstract spaces
- 28B05: Vector-valued set functions, measures and integrals
- 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
- 28B99: None of the above, but in this section

- 28Cxx: Set functions and measures on spaces with additional structure
- 28C05: Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
- 28C10: Set functions and measures on topological groups, Haar measures, invariant measures
- 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.)
- 28C99: None of the above, but in this section

- 28Dxx: Measure-theoretic ergodic theory
- 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

- 28Exx: Miscellaneous topics in measure theory
- 28E05: Nonstandard measure theory
- 28E10: Fuzzy measure theory
- 28E15: Other connections with logic and set theory
- 28E99: None of the above, but in this section

- 30-xx: Functions of a complex variable
- 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: General properties
- 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

- 30Bxx: Series expansions
- 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
- 30B60: Completeness problems, closure of a system of functions
- 30B70: Continued fractions
- 30B99: None of the above, but in this section

- 30Cxx: Geometric function theory
- 30C10: Polynomials
- 30C15: Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral)
- 30C20: Conformal mappings of special domains
- 30C25: Covering theorems in conformal mapping theory
- 30C30: Numerical methods in conformal mapping theory
- 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 $<B>R</B>^n$, 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
- 30C99: None of the above, but in this section

- 30Dxx: Entire and meromorphic functions, and related topics
- 30D05: Functional equations in the complex domain, iteration and composition of analytic functions
- 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
- 30D50: Blaschke products, bounded mean oscillation, bounded characteristic, bounded functions, functions with positive real part
- 30D55: ${H]^p$-classes
- 30D60: Quasi-analytic and other classes of functions
- 30D99: None of the above, but in this section

- 30Exx: Miscellaneous topics of analysis in the complex domain
- 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
- 30E25: Boundary value problems
- 30E99: None of the above, but in this section

- 30Fxx: Riemann surfaces
- 30F10: Compact Riemann surfaces and uniformization
- 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
- 30F40: Kleinian groups
- 30F45: Conformal metrics (hyperbolic, Poincaré, distance functions)
- 30F50: Klein surfaces
- 30F60: Teichmüller theory
- 30F99: None of the above, but in this section

- 30Gxx: Generalized function theory
- 30G06: Non-Archimedean function theory; nonstandard function theory
- 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
- 30H05: Spaces and algebras of analytic functions

- 31-xx: Potential theory
- 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: Two-dimensional theory
- 31A05: Harmonic, subharmonic, superharmonic functions
- 31A10: Integral representations, integral operators, integral equations methods
- 31A15: Potentials and capacity, harmonic measure, extremal length
- 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

- 31Bxx: Higher-dimensional theory
- 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

- 31Cxx: Other generalizations
- 31C05: Harmonic, subharmonic, superharmonic functions
- 31C10: Pluriharmonic and plurisubharmonic functions
- 31C12: Potential theory on Riemannian manifolds
- 31C15: Potentials and capacities
- 31C20: Discrete potential theory and numerical methods
- 31C25: Dirichlet spaces
- 31C35: Martin boundary theory
- 31C40: Fine potential theory
- 31C45: Other generalizations (nonlinear potential theory, etc.)
- 31C99: None of the above, but in this section
- 31D05: Axiomatic potential theory

- 32-xx: Several complex variables and analytic spaces
- 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: Holomorphic functions of several complex variables
- 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
- 32A25: Integral representations; canonical kernels (Szegó, Bergman, etc.)
- 32A26: Integral representations, constructed kernels (e.g. Cauchy, Fantappiè-type kernels)
- 32A27: Local theory of residues
- 32A30: Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30)
- 32A35: ${H]^p$-spaces, Nevanlinna spaces
- 32A36: Bergman spaces
- 32A37: Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
- 32A38: Algebras of holomorphic functions
- 32A40: Boundary behavior of holomorphic functions
- 32A45: Hyperfunctions
- 32A50: Harmonic analysis of several complex variables
- 32A55: Singular integrals
- 32A60: Zero sets of holomorphic functions
- 32A65: Banach algebra techniques
- 32A70: Functional analysis techniques
- 32A99: None of the above, but in this section

- 32Bxx: Local analytic geometry
- 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
- 32B25: Triangulation and related questions
- 32B99: None of the above, but in this section

- 32Cxx: Analytic spaces
- 32C05: Real-analytic manifolds, real-analytic spaces
- 32C07: Real-analytic sets, complex Nash functions
- 32C09: Embedding of real analytic manifolds
- 32C11: Complex supergeometry
- 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
- 32C35: Analytic sheaves and cohomology groups
- 32C36: Local cohomology of analytic spaces
- 32C37: Duality theorems
- 32C38: Sheaves of differential operators and their modules, $D$-modules
- 32C55: The Levi problem in complex spaces; generalizations
- 32C81: Applications to physics
- 32C99: None of the above, but in this section

- 32Dxx: Analytic continuation
- 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

- 32Exx: Holomorphic convexity
- 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

- 32Fxx: Geometric convexity
- 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

- 32Gxx: Deformations of analytic structures
- 32G05: Deformations of complex structures
- 32G07: Deformations of special (e.g. CR) structures
- 32G08: Deformations of fiber bundles
- 32G10: Deformations of submanifolds and subspaces
- 32G13: Analytic moduli problems
- 32G15: Moduli of Riemann surfaces, Teichmüller theory
- 32G20: Period matrices, variation of Hodge structure; degenerations
- 32G34: Moduli and deformations for ordinary differential equations (e.g. Khnizhnik-Zamolodchikov equation)
- 32G81: Applications to physics
- 32G99: None of the above, but in this section

- 32Hxx: Holomorphic mappings and correspondences
- 32H02: Holomorphic mappings, (holomorphic) embeddings and related questions
- 32H04: Meromorphic mappings
- 32H12: Boundary uniqueness of mappings
- 32H25: Picard-type theorems and generalizations
- 32H30: Value distribution theory in higher dimensions
- 32H35: Proper mappings, finiteness theorems
- 32H40: Boundary regularity of mappings
- 32H50: Iteration problems
- 32H99: None of the above, but in this section

- 32Jxx: Compact analytic spaces
- 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
- 32J27: Compact Kähler manifolds: generalizations, classification
- 32J81: Applications to physics
- 32J99: None of the above, but in this section

- 32Kxx: Generalizations of analytic spaces (should also be assigned at least one other classification number from Section 32 describing the type of problem)
- 32K05: Banach analytic spaces
- 32K07: Formal and graded complex spaces
- 32K15: Differentiable functions on analytic spaces, differentiable spaces
- 32K99: None of the above, but in this section

- 32Lxx: Holomorphic fiber spaces
- 32L05: Holomorphic bundles and generalizations
- 32L10: Sheaves and cohomology of sections of holomorphic vector bundles, general results
- 32L15: Bundle convexity
- 32L20: Vanishing theorems
- 32L25: Twistor theory, double fibrations
- 32L81: Applications to physics
- 32L99: None of the above, but in this section

- 32Mxx: Complex spaces with a group of automorphisms
- 32M05: Complex Lie groups, automorphism groups acting on complex spaces
- 32M10: Homogeneous complex manifolds
- 32M12: Almost homogeneous manifolds and spaces
- 32M15: Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras
- 32M17: Automorphism groups of ${\bf C]^n$ and affine manifolds
- 32M25: Complex vector fields
- 32M99: None of the above, but in this section

- 32Nxx: Automorphic functions
- 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
- 32P05: Non-Archimedean complex analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem)

- 32Qxx: Complex manifolds
- 32Q05: Negative curvature manifolds
- 32Q10: Positive curvature manifolds
- 32Q15: Kähler manifolds
- 32Q20: Kähler-Einstein manifolds
- 32Q25: Calabi-Yau theory
- 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

- 32Sxx: Singularities
- 32S05: Local singularities
- 32S10: Invariants of analytic local rings
- 32S15: Equisingularity (topological and analytic)
- 32S20: Global theory of singularities; cohomological properties
- 32S22: Relations with arrangements of hyperplanes
- 32S25: Surface and hypersurface singularities
- 32S30: Deformations of singularities; vanishing cycles
- 32S35: Mixed Hodge theory of singular varieties
- 32S40: Monodromy; relations with differential equations and $D$-modules
- 32S45: Modifications; resolution of singularities
- 32S50: Topological aspects: Lefschetz theorems, topological classification, invariants
- 32S55: Milnor fibration; relations with knot theory
- 32S60: Stratifications; constructible sheaves; intersection cohomology
- 32S65: Singularities of holomorphic vector fields and foliations
- 32S70: Other operations on singularities
- 32S99: None of the above, but in this section

- 32Txx: Pseudoconvex domains
- 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

- 32Uxx: Pluripotential theory
- 32U05: Plurisubharmonic functions and generalizations
- 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

- 32Vxx: CR manifolds
- 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

- 32Wxx: Differential operators in several variables
- 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-xx: Special functions (33-XX deals with the properties of functions as functions)
- 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: Elementary classical functions
- 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

- 33Cxx: Hypergeometric functions
- 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.)
- 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 ($E$, $G$ and ${H]$ 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

- 33Dxx: Basic hypergeometric functions
- 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

- 33Exx: Other special functions
- 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

- 33Fxx: Computational aspects
- 33F05: Numerical approximation
- 33F10: Symbolic computation (Gosper and Zeilberger algorithms, etc.)
- 33F99: None of the above, but in this section

- 34-xx: Ordinary differential equations
- 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: General theory
- 34A05: Explicit solutions and reductions
- 34A09: Implicit equations, differential-algebraic equations
- 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions
- 34A25: Analytical theory: series, transformations, transforms, operational calculus, etc.
- 34A26: Geometric methods in differential equations
- 34A30: Linear equations and systems, general
- 34A34: Nonlinear equations and systems, general
- 34A35: Differential equations of infinite order
- 34A36: Discontinuous equations
- 34A37: Differential equations with impulses
- 34A40: Differential inequalities
- 34A45: Theoretical approximation of solutions
- 34A55: Inverse problems
- 34A60: Differential inclusions
- 34A99: None of the above, but in this section

- 34Bxx: Boundary value problems
- 34B05: Linear boundary value problems
- 34B07: Linear boundary value problems with nonlinear dependence on the spectral parameter
- 34B08: Multi-parameter boundary value problems
- 34B09: Boundary value problems with an indefinite weight
- 34B10: 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
- 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

- 34Cxx: Qualitative theory
- 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, comparison of solutions
- 34C12: Monotone systems
- 34C14: Symmetries, invariants
- 34C15: Nonlinear oscillations, coupled oscillators
- 34C20: Transformation and reduction of equations and systems, normal forms
- 34C23: Bifurcation
- 34C25: Periodic solutions
- 34C26: Relaxation oscillations
- 34C27: Almost periodic solutions
- 34C28: Complex behavior, chaotic systems
- 34C29: Averaging method
- 34C30: Manifolds of solutions
- 34C37: Homoclinic and heteroclinic solutions
- 34C40: Equations and systems on manifolds
- 34C41: Equivalence, asymptotic equivalence
- 34C45: Method of integral manifolds
- 34C55: Hysteresis
- 34C60: Applications
- 34C99: None of the above, but in this section

- 34Dxx: Stability theory
- 34D05: Asymptotic properties
- 34D08: Characteristic and Lyapunov exponents
- 34D09: Dichotomy, trichotomy
- 34D10: Perturbations
- 34D15: Singular perturbations
- 34D20: Lyapunov stability
- 34D23: Global stability
- 34D30: Structural stability and analogous concepts
- 34D35: Stability of manifolds of solutions
- 34D40: Ultimate boundedness
- 34D45: Attractors
- 34D99: None of the above, but in this section

- 34Exx: Asymptotic theory
- 34E05: Asymptotic expansions
- 34E10: Perturbations, asymptotics
- 34E13: Multiple scale methods
- 34E15: Singular perturbations, general theory
- 34E18: Methods of nonstandard analysis
- 34E20: Singular perturbations, turning point theory, WKB methods
- 34E99: None of the above, but in this section
- 34F05: Equations and systems with randomness

- 34Gxx: Differential equations in abstract spaces
- 34G10: Linear equations
- 34G20: Nonlinear equations
- 34G25: Evolution inclusions
- 34G99: None of the above, but in this section
- 34H05: Control problems

- 34Kxx: Functional-differential and differential-difference equations
- 34K05: General theory
- 34K06: Linear functional-differential equations
- 34K07: Theoretical approximation of solutions
- 34K10: Boundary value problems
- 34K11: Oscillation theory
- 34K12: Growth, boundedness, comparison of solutions
- 34K13: Periodic solutions
- 34K14: Almost periodic solutions
- 34K17: Transformation and reduction of equations and systems, normal forms
- 34K18: Bifurcation theory
- 34K19: Invariant manifolds
- 34K20: Stability theory
- 34K23: Complex (chaotic) behavior of solutions
- 34K25: Asymptotic theory
- 34K26: Singular perturbations
- 34K28: Numerical approximation of solutions
- 34K29: Inverse problems
- 34K30: Equations in abstract spaces
- 34K35: Control problems
- 34K40: Neutral equations
- 34K45: Equations with impulses
- 34K50: Stochastic delay equations
- 34K60: Applications
- 34K99: None of the above, but in this section

- 34Lxx: Ordinary differential operators
- 34L05: General spectral theory
- 34L10: Eigenfunction expansions, completeness of eigenfunctions
- 34L15: 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
- 34L30: Nonlinear ordinary differential operators
- 34L40: Particular operators (Dirac, one-dimensional Schrödinger, etc.)
- 34L99: None of the above, but in this section

- 34Mxx: Differential equations in the complex domain
- 34M05: Entire and meromorphic solutions
- 34M10: Oscillation, growth of solutions
- 34M15: Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical)
- 34M20: Nonanalytic aspects
- 34M25: Formal solutions, transform techniques
- 34M30: Asymptotics, summation methods
- 34M35: Singularities, monodromy, local behavior of solutions, normal forms
- 34M37: Resurgence phenomena
- 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; isomonodromic deformations
- 34M60: Singular perturbation problems in the complex domain (complex WKB, turning points, steepest descent)
- 34M99: None of the above, but in this section

- 35-xx: Partial differential equations
- 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: General theory
- 35A05: General existence and uniqueness theorems
- 35A07: Local existence and uniqueness theorems
- 35A08: Fundamental solutions
- 35A10: Cauchy-Kovalevskaya theorems
- 35A15: Variational methods
- 35A17: Parametrices
- 35A18: Wave front sets
- 35A20: Analytic methods, singularities
- 35A21: Propagation of singularities
- 35A22: Transform methods (e.g. integral transforms)
- 35A25: Other special methods
- 35A27: Microlocal methods; methods of sheaf theory and homological algebra in PDE
- 35A30: Geometric theory, characteristics, transformations
- 35A35: Theoretical approximation to solutions
- 35A99: None of the above, but in this section

- 35Bxx: Qualitative properties of solutions
- 35B05: General behavior of solutions of PDE (comparison theorems; oscillation, zeros and growth of solutions; mean value theorems)
- 35B10: Periodic solutions
- 35B15: Almost periodic solutions
- 35B20: Perturbations
- 35B25: Singular perturbations
- 35B27: Homogenization; partial differential equations in media with periodic structure
- 35B30: Dependence of solutions of PDE on initial and boundary data, parameters
- 35B32: Bifurcation
- 35B33: Critical exponents
- 35B34: Resonances
- 35B35: Stability, boundedness
- 35B37: PDE in connection with control problems
- 35B38: Critical points
- 35B40: Asymptotic behavior of solutions
- 35B41: Attractors
- 35B42: Inertial manifolds
- 35B45: A priori estimates
- 35B50: Maximum principles
- 35B60: Continuation and prolongation of solutions of PDE
- 35B65: Smoothness and regularity of solutions of PDE
- 35B99: None of the above, but in this section

- 35Cxx: Representations of solutions
- 35C05: Solutions in closed form
- 35C10: Series solutions, expansion theorems
- 35C15: Integral representations of solutions of PDE
- 35C20: Asymptotic expansions
- 35C99: None of the above, but in this section

- 35Dxx: Generalized solutions of partial differential equations
- 35D05: Existence of generalized solutions
- 35D10: Regularity of generalized solutions
- 35D99: None of the above, but in this section

- 35Exx: Equations and systems with constant coefficients
- 35E05: Fundamental solutions
- 35E10: Convexity properties
- 35E15: Initial value problems
- 35E20: General theory
- 35E99: None of the above, but in this section

- 35Fxx: General first-order equations and systems
- 35F05: General theory of linear first-order PDE
- 35F10: Initial value problems for linear first-order PDE, linear evolution equations
- 35F15: Boundary value problems for linear first-order PDE
- 35F20: General theory of nonlinear first-order PDE
- 35F25: Initial value problems for nonlinear first-order PDE, nonlinear evolution equations
- 35F30: Boundary value problems for nonlinear first-order PDE
- 35F99: None of the above, but in this section

- 35Gxx: General higher-order equations and systems
- 35G05: General theory of linear higher-order PDE
- 35G10: Initial value problems for linear higher-order PDE, linear evolution equations
- 35G15: Boundary value problems for linear higher-order PDE
- 35G20: General theory of nonlinear higher-order PDE
- 35G25: Initial value problems for nonlinear higher-order PDE, nonlinear evolution equations
- 35G30: Boundary value problems for nonlinear higher-order PDE
- 35G99: None of the above, but in this section

- 35Hxx: Close-to-elliptic equations
- 35H10: Hypoelliptic equations
- 35H20: Subelliptic equations
- 35H30: Quasi-elliptic equations
- 35H99: None of the above, but in this section

- 35Jxx: Partial differential equations of elliptic type
- 35J05: Laplace equation, reduced wave equation (Helmholtz), Poisson equation
- 35J10: Schrödinger operator
- 35J15: General theory of second-order, elliptic equations
- 35J20: Variational methods for second-order, elliptic equations
- 35J25: Boundary value problems for second-order, elliptic equations
- 35J30: General theory of higher-order, elliptic equations
- 35J35: Variational methods for higher-order, elliptic equations
- 35J40: Boundary value problems for higher-order, elliptic equations
- 35J45: General theory of elliptic systems of PDE
- 35J50: Variational methods for elliptic systems
- 35J55: Boundary value problems for elliptic systems
- 35J60: Nonlinear PDE of elliptic type
- 35J65: Nonlinear boundary value problems for linear elliptic PDE; boundary value problems for nonlinear elliptic PDE
- 35J67: Boundary values of solutions to elliptic PDE
- 35J70: Elliptic partial differential equations of degenerate type
- 35J85: Unilateral problems and variational inequalities for elliptic PDE
- 35J99: None of the above, but in this section

- 35Kxx: Parabolic equations and systems
- 35K05: Heat equation
- 35K10: General theory of second-order, parabolic equations
- 35K15: Initial value problems for second-order, parabolic equations
- 35K20: Boundary value problems for second-order, parabolic equations
- 35K25: General theory of higher-order, parabolic equations
- 35K30: Initial value problems for higher-order, parabolic equations
- 35K35: Boundary value problems for higher-order, parabolic equations
- 35K40: General theory of parabolic systems of PDE
- 35K45: Initial value problems for parabolic systems
- 35K50: Boundary value problems for parabolic systems
- 35K55: Nonlinear PDE of parabolic type
- 35K57: Reaction-diffusion equations
- 35K60: Nonlinear boundary value problems for linear parabolic PDE; boundary value problems for nonlinear parabolic PDE
- 35K65: Parabolic partial differential equations of degenerate type
- 35K70: Ultraparabolic, pseudoparabolic PDE, etc.
- 35K85: Unilateral problems and variational inequalities for parabolic PDE
- 35K90: Abstract parabolic evolution equations
- 35K99: None of the above, but in this section

- 35Lxx: Partial differential equations of hyperbolic type
- 35L05: Wave equation
- 35L10: General theory of second-order, hyperbolic equations
- 35L15: Initial value problems for second-order, hyperbolic equations
- 35L20: Boundary value problems for second-order, hyperbolic equations
- 35L25: General theory of higher-order, hyperbolic equations
- 35L30: Initial value problems for higher-order, hyperbolic equations
- 35L35: Boundary value problems for higher-order, hyperbolic equations
- 35L40: General theory of hyperbolic systems of first-order PDE
- 35L45: Initial value problems for hyperbolic systems of first-order PDE
- 35L50: Boundary value problems for hyperbolic systems of first-order PDE
- 35L55: Hyperbolic systems of higher-order PDE
- 35L60: Nonlinear first-order PDE of hyperbolic type
- 35L65: Conservation laws
- 35L67: Shocks and singularities
- 35L70: Nonlinear second-order PDE of hyperbolic type
- 35L75: Nonlinear hyperbolic PDE of higher ($\gtr 2$) order
- 35L80: Hyperbolic PDE of degenerate type
- 35L82: Pseudohyperbolic equations
- 35L85: Unilateral problems; variational inequalities for hyperbolic PDE
- 35L90: Abstract hyperbolic evolution equations
- 35L99: None of the above, but in this section

- 35Mxx: Partial differential equations of special type (mixed, composite, etc.)
- 35M10: PDE of mixed type
- 35M20: PDE of composite type
- 35M99: None of the above, but in this section

- 35Nxx: Overdetermined systems
- 35N05: Overdetermined systems with constant coefficients
- 35N10: Overdetermined systems with variable coefficients (general)
- 35N15: $\overline\partial$-Neumann problem and generalizations; formal complexes
- 35N99: None of the above, but in this section

- 35Pxx: Spectral theory and eigenvalue problems for partial differential operators
- 35P05: General spectral theory of PDE
- 35P10: Completeness of eigenfunctions, eigenfunction expansions for PDO
- 35P15: Estimation of eigenvalues, upper and lower bounds
- 35P20: Asymptotic distribution of eigenvalues and eigenfunctions for PDO
- 35P25: Scattering theory for PDE
- 35P30: Nonlinear eigenvalue problems, nonlinear spectral theory for PDO
- 35P99: None of the above, but in this section

- 35Qxx: Equations of mathematical physics and other areas of application
- 35Q05: Euler-Poisson-Darboux equation and generalizations
- 35Q15: Riemann-Hilbert problems
- 35Q30: Stokes and Navier-Stokes equations
- 35Q35: Other equations arising in fluid mechanics
- 35Q40: Equations from quantum mechanics
- 35Q51: Solitons
- 35Q53: KdV-like equations (Korteweg-de Vries, Burgers, sine-Gordon, sinh-Gordon, etc.)
- 35Q55: NLS-like (nonlinear Schrödinger) equations
- 35Q58: Other completely integrable equations
- 35Q60: Equations of electromagnetic theory and optics
- 35Q72: Other equations from mechanics
- 35Q75: PDE in relativity
- 35Q80: Applications of PDE in areas other than physics
- 35Q99: None of the above, but in this section

- 35Rxx: Miscellaneous topics involving partial differential equations
- 35R05: PDE with discontinuous coefficients or data
- 35R10: Partial functional-differential or differential-difference equations, with or without deviating arguments
- 35R12: Impulsive partial differential equations
- 35R15: Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in infinitely many variables)
- 35R20: Partial operator-differential equations (i.e. PDE on finite-dimensional spaces for abstract space valued functions)
- 35R25: Improperly posed problems for PDE
- 35R30: Inverse problems (undetermined coefficients, etc.) for PDE
- 35R35: Free boundary problems for PDE
- 35R45: Partial differential inequalities
- 35R50: Partial differential equations of infinite order
- 35R60: Partial differential equations with randomness
- 35R70: PDE with multivalued right-hand sides
- 35R99: None of the above, but in this section

- 35Sxx: Pseudodifferential operators and other generalizations of partial differential operators
- 35S05: General theory of PsDO
- 35S10: Initial value problems for PsDO
- 35S15: Boundary value problems for PsDO
- 35S30: Fourier integral operators
- 35S35: Topological aspects: intersection cohomology, stratified sets, etc.
- 35S50: Paradifferential operators
- 35S99: None of the above, but in this section

- 37-xx: Dynamical systems and ergodic theory
- 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: Ergodic theory
- 37A05: Measure-preserving transformations
- 37A10: One-parameter continuous families of measure-preserving transformations
- 37A15: General groups of measure-preserving transformations
- 37A17: Homogeneous flows
- 37A20: Orbit equivalence, cocycles, ergodic equivalence relations
- 37A25: Ergodicity, mixing, rates of mixing
- 37A30: Ergodic theorems, spectral theory, Markov operators
- 37A35: Entropy and other invariants, isomorphism, classification
- 37A40: Nonsingular (and infinite-measure preserving) transformations
- 37A45: Relations with number theory and harmonic analysis
- 37A50: Relations with probability theory and stochastic processes
- 37A55: Relations with the theory of $C^*$-algebras
- 37A60: Dynamical systems in statistical mechanics
- 37A99: None of the above, but in this section

- 37Bxx: Topological dynamics
- 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)
- 37B10: Symbolic dynamics
- 37B15: Cellular automata
- 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

- 37Cxx: Smooth dynamical systems: general theory
- 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
- 37C45: Dimension theory of dynamical systems
- 37C50: Approximate trajectories (pseudotrajectories, shadowing, etc.)
- 37C55: Periodic and quasiperiodic flows and diffeomorphisms
- 37C60: Nonautonomous smooth dynamical systems
- 37C65: Monotone flows
- 37C70: Attractors and repellers, topological structure
- 37C75: Stability theory
- 37C80: Symmetries, equivariant dynamical systems
- 37C85: Dynamics of group actions other than <B>Z</B> and <B>R</B>, and foliations
- 37C99: None of the above, but in this section

- 37Dxx: Dynamical systems with hyperbolic behavior
- 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

- 37Exx: Low-dimensional dynamical systems
- 37E05: Maps of the interval (piecewise continuous, continuous, smooth)
- 37E10: Maps of the circle
- 37E15: Combinatorial dynamics (types of periodic orbits)
- 37E20: Universality, renormalization
- 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

- 37Fxx: Complex dynamical systems
- 37F05: Relations and correspondences
- 37F10: Polynomials; rational maps; entire and meromorphic functions
- 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
- 37F99: None of the above, but in this section

- 37Gxx: Local and nonlocal bifurcation theory
- 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

- 37Hxx: Random dynamical systems
- 37H05: Foundations, general theory of cocycles, algebraic ergodic theory
- 37H10: Generation, random and stochastic difference and differential equations
- 37H15: Multiplicative ergodic theory, Lyapunov exponents
- 37H20: Bifurcation theory
- 37H99: None of the above, but in this section

- 37Jxx: Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
- 37J05: General theory, relations with symplectic geometry and topology
- 37J10: Symplectic mappings, fixed points
- 37J15: Symmetries, invariants, invariant manifolds, momentum maps, reduction
- 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, Arnold diffusion
- 37J45: Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
- 37J50: Action-minimizing orbits and measures
- 37J55: Contact systems
- 37J60: Nonholonomic dynamical systems
- 37J99: None of the above, but in this section

- 37Kxx: Infinite-dimensional Hamiltonian systems
- 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
- 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
- 37K65: Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics
- 37K99: None of the above, but in this section

- 37Lxx: Infinite-dimensional dissipative dynamical systems
- 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
- 37L60: Lattice dynamics
- 37L65: Special approximation methods (nonlinear Galerkin, etc.)
- 37L99: None of the above, but in this section

- 37Mxx: Approximation methods and numerical treatment of dynamical systems
- 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

- 37Nxx: Applications
- 37N05: Dynamical systems in classical and celestial mechanics
- 37N10: Dynamical systems in fluid mechanics, oceanography and meteorology
- 37N15: Dynamical systems in solid mechanics
- 37N20: Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
- 37N25: Dynamical systems in biology
- 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

- 39-xx: Difference and functional equations
- 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: Difference equations
- 39A05: General
- 39A10: Difference equations, additive
- 39A11: Stability and asymptotics of difference equations; oscillatory and periodic solutions, etc.
- 39A12: Discrete version of topics in analysis
- 39A13: Difference equations, scaling ($q$-differences)
- 39A20: Multiplicative and other generalized difference equations, e.g. of Lyness type
- 39A70: Difference operators
- 39A99: None of the above, but in this section

- 39Bxx: Functional equations and inequalities
- 39B05: General
- 39B12: Iteration theory, iterative and composite equations
- 39B22: Equations for real functions
- 39B32: Equations for complex functions
- 39B42: Matrix and operator equations
- 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.
- 39B72: Systems of functional equations and inequalities
- 39B82: Stability, separation, extension, and related topics
- 39B99: None of the above, but in this section

- 40-xx: Sequences, series, summability
- 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: Convergence and divergence of infinite limiting processes
- 40A05: Convergence and divergence of series and sequences
- 40A10: Convergence and divergence of integrals
- 40A15: Convergence and divergence of continued fractions
- 40A20: Convergence and divergence of infinite products
- 40A25: Approximation to limiting values (summation of series, etc.)
- 40A30: Convergence and divergence of series and sequences of functions
- 40A99: None of the above, but in this section
- 40B05: Multiple sequences and series {(should also be assigned at least one other classification number in this section)]

- 40Cxx: General summability methods
- 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

- 40Dxx: Direct theorems on summability
- 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

- 40Exx: Inversion theorems
- 40E05: Tauberian theorems, general
- 40E10: Growth estimates
- 40E15: Lacunary inversion theorems
- 40E20: Tauberian constants
- 40E99: None of the above, but in this section
- 40F05: Absolute and strong summability

- 40Gxx: Special methods of summability
- 40G05: Cesàro, Euler, Nörlund and Hausdorff methods
- 40G10: Abel, Borel and power series methods
- 40G99: None of the above, but in this section
- 40H05: Functional analytic methods in summability
- 40J05: Summability in abstract structures

- 41-xx: Approximations and expansions
- 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.
- 41A05: Interpolation
- 41A10: Approximation by polynomials
- 41A15: Spline approximation
- 41A17: Inequalities in approximation (Bernstein, Jackson, Nikol\cprime ski\u\i-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.)
- 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: Miscellaneous topics

- 42-xx: Fourier analysis
- 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: Fourier analysis in one variable
- 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
- 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
- 42A82: Positive definite functions
- 42A85: Convolution, factorization
- 42A99: None of the above, but in this section

- 42Bxx: Fourier analysis in several variables
- 42B05: Fourier series and coefficients
- 42B08: Summability
- 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
- 42B15: Multipliers
- 42B20: Singular integrals (Calderón-Zygmund, etc.)
- 42B25: Maximal functions, Littlewood-Paley theory
- 42B30: $H^p$-spaces
- 42B35: Function spaces arising in harmonic analysis
- 42B99: None of the above, but in this section

- 42Cxx: Nontrigonometric Fourier analysis
- 42C05: Orthogonal functions and polynomials, general theory
- 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
- 42C15: Series of general orthogonal functions, generalized Fourier expansions, nonorthogonal expansions
- 42C20: Rearrangements and other transformations of Fourier and other orthogonal series
- 42C25: Uniqueness and localization for orthogonal series
- 42C30: Completeness of sets of functions
- 42C40: Wavelets
- 42C99: None of the above, but in this section

- 43-xx: Abstract harmonic analysis
- 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.
- 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 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.
- 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.
- 43A70: Analysis on specific locally compact abelian groups
- 43A75: Analysis on specific compact groups
- 43A77: Analysis on general compact groups
- 43A80: Analysis on other specific Lie groups
- 43A85: Analysis on homogeneous spaces
- 43A90: Spherical functions
- 43A95: Categorical methods
- 43A99: Miscellaneous topics

- 44-xx: Integral transforms, operational calculus
- 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.
- 44A05: General transforms
- 44A10: Laplace transform
- 44A12: Radon transform
- 44A15: Special transforms (Legendre, Hilbert, etc.)
- 44A20: Transforms of special functions
- 44A30: Multiple transforms
- 44A35: Convolution
- 44A40: Calculus of Mikusi\'nski and other operational calculi
- 44A45: Classical operational calculus
- 44A55: Discrete operational calculus
- 44A60: Moment problems
- 44A99: Miscellaneous topics

- 45-xx: Integral equations
- 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.
- 45A05: Linear integral equations
- 45B05: Fredholm integral equations
- 45C05: Eigenvalue problems
- 45D05: Volterra integral equations

- 45Exx: Singular integral equations
- 45E05: Integral equations with kernels of Cauchy type
- 45E10: Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
- 45E99: None of the above, but in this section

- 45Fxx: Systems of linear integral equations
- 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

- 45Gxx: Nonlinear integral equations
- 45G05: Singular nonlinear integral equations
- 45G10: Other nonlinear integral equations
- 45G15: Systems of nonlinear integral equations
- 45H05: Miscellaneous special kernels
- 45J05: Integro-ordinary differential equations
- 45K05: Integro-partial differential equations
- 45L05: Theoretical approximation of solutions

- 45Mxx: Qualitative behavior
- 45M05: Asymptotics
- 45M10: Stability theory
- 45M15: Periodic solutions
- 45M20: Positive solutions
- 45M99: None of the above, but in this section
- 45N05: Abstract integral equations, integral equations in abstract spaces
- 45P05: Integral operators
- 45Q05: Inverse problems
- 45R05: Random integral equations

- 46-xx: Functional analysis
- 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: Topological linear spaces and related structures
- 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.)
- 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
- 46A25: Reflexivity and semi-reflexivity
- 46A30: Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness)
- 46A32: Spaces of linear operators; topological tensor products; approximation properties
- 46A35: Summability and bases
- 46A40: Ordered topological linear spaces, vector lattices
- 46A45: Sequence spaces (including Köthe sequence spaces)
- 46A50: Compactness in topological linear spaces; angelic spaces, etc.
- 46A55: Convex sets in topological linear spaces; Choquet theory
- 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

- 46Bxx: Normed linear spaces and Banach spaces; Banach lattices
- 46B03: Isomorphic theory (including renorming) of Banach spaces
- 46B04: Isometric theory of Banach spaces
- 46B07: Local theory of Banach spaces
- 46B08: Ultraproduct techniques in Banach space theory
- 46B09: Probabilistic methods in Banach space theory
- 46B10: Duality and reflexivity
- 46B15: Summability and bases
- 46B20: Geometry and structure of normed linear spaces
- 46B22: Radon-Nikodym, Krein-Milman and related properties
- 46B25: Classical Banach spaces in the general theory
- 46B26: Nonseparable Banach spaces
- 46B28: Spaces of operators; tensor products; approximation properties
- 46B40: Ordered normed spaces
- 46B42: Banach lattices
- 46B45: Banach sequence spaces
- 46B50: Compactness in Banach (or normed) spaces
- 46B70: Interpolation between normed linear spaces
- 46B99: None of the above, but in this section

- 46Cxx: Inner product spaces and their generalizations, Hilbert spaces
- 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.)
- 46C15: Characterizations of Hilbert spaces
- 46C20: Spaces with indefinite inner product (Krein spaces, Pontryagin spaces, etc.)
- 46C50: Generalizations of inner products (semi-inner products, partial inner products, etc.)
- 46C99: None of the above, but in this section

- 46Exx: Linear function spaces and their duals
- 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)
- 46E25: Rings and algebras of continuous, differentiable or analytic functions
- 46E27: Spaces of measures
- 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
- 46E99: None of the above, but in this section

- 46Fxx: Distributions, generalized functions, distribution spaces
- 46F05: Topological linear spaces of test functions, distributions and ultradistributions
- 46F10: Operations with distributions
- 46F12: Integral transforms in distribution spaces
- 46F15: Hyperfunctions, analytic functionals
- 46F20: Distributions and ultradistributions as boundary values of analytic functions
- 46F25: Distributions on infinite-dimensional spaces
- 46F30: Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
- 46F99: None of the above, but in this section

- 46Gxx: Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
- 46G05: Derivatives
- 46G10: Vector-valued measures and integration
- 46G12: Measures and integration on abstract linear spaces
- 46G15: Functional analytic lifting theory
- 46G20: Infinite-dimensional holomorphy
- 46G25: (Spaces of) multilinear mappings, polynomials
- 46G99: None of the above, but in this section

- 46Hxx: Topological algebras, normed rings and algebras, Banach algebras
- 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 or 16-XX)
- 46H30: Functional calculus in topological algebras
- 46H35: Topological algebras of operators
- 46H40: Automatic continuity
- 46H70: Nonassociative topological algebras
- 46H99: None of the above, but in this section

- 46Jxx: Commutative Banach algebras and commutative topological algebras
- 46J05: General theory of commutative topological algebras
- 46J10: Banach algebras of continuous functions, function algebras
- 46J15: Banach algebras of differentiable or analytic functions, ${H]^p$-spaces
- 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

- 46Kxx: Topological (rings and) algebras with an involution
- 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
- 46K99: None of the above, but in this section

- 46Lxx: Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W$*-) algebras, etc.)
- 46L05: General theory of $C^*$-algebras
- 46L06: Tensor products of $C^*$-algebras
- 46L07: Operator spaces and completely bounded maps
- 46L08: $C^*$-modules
- 46L09: Free products of $C^*$-algebras
- 46L10: General theory of von Neumann algebras
- 46L30: States
- 46L35: Classifications of $C^*$-algebras, 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
- 46L57: Derivations, dissipations and positive semigroups in $C^*$-algebras
- 46L60: Applications of selfadjoint operator algebras to physics
- 46L65: Quantizations, deformations
- 46L70: Nonassociative selfadjoint operator algebras
- 46L80: $K$-theory and operator algebras (including cyclic theory)
- 46L85: Noncommutative topology
- 46L87: Noncommutative differential geometry
- 46L89: Other ``noncommutative'' mathematics based on $C^*$-algebra theory
- 46L99: None of the above, but in this section

- 46Mxx: Methods of category theory in functional analysis
- 46M05: Tensor products
- 46M07: Ultraproducts
- 46M10: Projective and injective objects
- 46M15: Categories, functors
- 46M18: Homological methods (exact sequences, right inverses, lifting, etc.)
- 46M20: Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
- 46M35: Abstract interpolation of topological vector spaces
- 46M40: Inductive and projective limits
- 46M99: None of the above, but in this section

- 46Nxx: Miscellaneous applications of functional analysis
- 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
- 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

- 46Sxx: Other (nonclassical) types of functional analysis
- 46S10: Functional analysis over fields other than <B>R</B> or <B>C</B> or the quaternions; non-Archimedean functional analysis
- 46S20: Nonstandard functional analysis
- 46S30: Constructive functional analysis
- 46S40: Fuzzy functional analysis
- 46S50: Functional analysis in probabilistic metric linear spaces
- 46S60: Functional analysis on superspaces (supermanifolds) or graded spaces
- 46S99: None of the above, but in this section

- 46Txx: Nonlinear functional analysis
- 46T05: Infinite-dimensional manifolds
- 46T10: Manifolds of mappings
- 46T12: Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds
- 46T20: Continuous and differentiable maps
- 46T25: Holomorphic maps
- 46T30: Distributions and generalized functions on nonlinear spaces
- 46T99: None of the above, but in this section

- 47-xx: Operator theory
- 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: General theory of linear operators
- 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
- 47A16: Cyclic and hypercyclic vectors
- 47A20: Dilations, extensions, compressions
- 47A25: Spectral sets
- 47A30: Norms (inequalities, more than one norm, etc.)
- 47A35: Ergodic theory
- 47A40: Scattering theory
- 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
- 47A53: (Semi-) Fredholm operators; index theories
- 47A55: Perturbation theory
- 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
- 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
- 47A80: Tensor products of operators
- 47A99: None of the above, but in this section

- 47Bxx: Special classes of linear operators
- 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.)
- 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)
- 47B33: Composition operators
- 47B34: Kernel operators
- 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators
- 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
- 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 (= operators on spaces of operators)
- 47B50: Operators on spaces with an indefinite metric
- 47B60: Operators on ordered spaces
- 47B65: Positive operators and order-bounded operators
- 47B80: Random operators
- 47B99: None of the above, but in this section

- 47Cxx: Individual linear operators as elements of algebraic systems
- 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

- 47Dxx: Groups and semigroups of linear operators, their generalizations and applications
- 47D03: Groups and semigroups of linear operators
- 47D06: One-parameter semigroups and linear evolution equations
- 47D07: Markov semigroups and applications to diffusion processes
- 47D08: Schrödinger and Feynman-Kac semigroups
- 47D09: Operator sine and cosine functions and higher-order Cauchy problems
- 47D60: $C$-semigroups
- 47D62: Integrated semigroups
- 47D99: None of the above, but in this section
- 47E05: Ordinary differential operators
- 47F05: Partial differential operators

- 47Gxx: Integral, integro-differential, and pseudodifferential operators
- 47G10: Integral operators
- 47G20: Integro-differential operators
- 47G30: Pseudodifferential operators
- 47G99: None of the above, but in this section

- 47Hxx: Nonlinear operators and their properties
- 47H04: Set-valued operators
- 47H05: Monotone operators (with respect to duality)
- 47H06: Accretive operators, dissipative operators, etc.
- 47H07: Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
- 47H09: Nonexpansive mappings, and their generalizations (ultimately compact mappings, measures of noncompactness and condensing mappings, $A$-proper mappings, $K$-set contractions, etc.)
- 47H10: Fixed-point theorems
- 47H11: Degree theory
- 47H14: Perturbations of nonlinear operators
- 47H20: Semigroups of nonlinear operators
- 47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytskii, Uryson, etc.)
- 47H40: Random operators
- 47H50: Potential operators
- 47H60: Multilinear and polynomial operators
- 47H99: None of the above, but in this section

- 47Jxx: Equations and inequalities involving nonlinear operators
- 47J05: Equations involving nonlinear operators (general)
- 47J06: Nonlinear ill-posed problems
- 47J07: Abstract inverse mapping and implicit function theorems
- 47J10: Nonlinear eigenvalue problems
- 47J15: Abstract bifurcation theory
- 47J20: Variational and other types of inequalities involving nonlinear operators (general)
- 47J25: Methods for solving nonlinear operator equations (general)
- 47J30: Variational methods
- 47J35: Nonlinear evolution equations
- 47J40: Equations with hysteresis operators
- 47J99: None of the above, but in this section

- 47Lxx: Linear spaces and algebras of operators
- 47L05: Linear spaces of operators
- 47L07: Convex sets and cones of operators
- 47L10: Algebras of operators on Banach spaces and other topological linear spaces
- 47L15: Operator algebras with symbol structure
- 47L20: Operator ideals
- 47L25: Operator spaces (= matricially normed spaces)
- 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

- 47Nxx: Miscellaneous applications of operator theory
- 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
- 47N50: Applications in quantum physics
- 47N55: Applications in statistical physics
- 47N60: Applications in biology and other sciences
- 47N70: Applications in systems theory, circuits, etc.
- 47N99: None of the above, but in this section

- 47Sxx: Other (nonclassical) types of operator theory
- 47S10: Operator theory over fields other than <B>R</B>, <B>C</B> or the quaternions; non-Archimedean operator theory
- 47S20: Nonstandard operator theory
- 47S30: Constructive operator theory
- 47S40: Fuzzy operator theory
- 47S50: Operator theory in probabilistic metric linear spaces
- 47S99: None of the above, but in this section

- 49-xx: Calculus of variations and optimal control; optimization
- 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: Existence theories
- 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
- 49J22: Optimal control problems involving integral equations
- 49J24: Optimal control problems involving differential inclusions
- 49J25: Optimal control problems involving equations with retarded arguments
- 49J27: Problems in abstract spaces
- 49J30: Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
- 49J35: Minimax problems
- 49J40: Variational methods including variational inequalities
- 49J45: Methods involving semicontinuity and convergence; relaxation
- 49J50: Fréchet and Gateaux differentiability
- 49J52: Nonsmooth analysis
- 49J53: Set-valued and variational analysis
- 49J55: Problems involving randomness
- 49J99: None of the above, but in this section

- 49Kxx: Necessary conditions and sufficient conditions for optimality
- 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
- 49K22: Problems involving integral equations
- 49K24: Problems involving differential inclusions
- 49K25: Problems involving equations with retarded arguments
- 49K27: Problems in abstract spaces
- 49K30: Optimal solutions belonging to restricted classes
- 49K35: Minimax problems
- 49K40: Sensitivity, stability, well-posedness
- 49K45: Problems involving randomness
- 49K99: None of the above, but in this section

- 49Lxx: Hamilton-Jacobi theories, including dynamic programming
- 49L20: Dynamic programming method
- 49L25: Viscosity solutions
- 49L99: None of the above, but in this section

- 49Mxx: Methods of successive approximations
- 49M05: Methods based on necessary conditions
- 49M15: Methods of Newton-Raphson, Galerkin and Ritz types
- 49M20: Methods of relaxation type
- 49M25: Discrete approximations
- 49M27: Decomposition methods
- 49M29: Methods involving duality
- 49M30: Other methods, not based on necessary conditions (penalty function, etc.)
- 49M37: Methods of nonlinear programming type
- 49M99: None of the above, but in this section

- 49Nxx: Miscellaneous topics
- 49N05: Linear optimal control problems
- 49N10: Linear-quadratic problems
- 49N15: Duality theory
- 49N20: Periodic optimization
- 49N25: Impulsive optimal control problems
- 49N30: Problems with incomplete information
- 49N35: Optimal feedback synthesis
- 49N45: Inverse problems
- 49N60: Regularity of solutions
- 49N70: Differential games
- 49N75: Pursuit and evasion games
- 49N90: Applications of optimal control and differential games
- 49N99: None of the above, but in this section

- 49Qxx: Manifolds
- 49Q05: Minimal surfaces
- 49Q10: Optimization of shapes other than minimal surfaces
- 49Q12: Sensitivity analysis
- 49Q15: Geometric measure and integration theory, integral and normal currents
- 49Q20: Variational problems in a geometric measure-theoretic setting
- 49Q99: None of the above, but in this section
- 49R50: Variational methods for eigenvalues of operators
- 49S05: Variational principles of physics

- 51-xx: Geometry
- 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: Linear incidence geometry
- 51A05: General theory and projective geometries
- 51A10: Homomorphism, automorphism and dualities
- 51A15: Structures with parallelism
- 51A20: Configuration theorems
- 51A25: Algebraization
- 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

- 51Bxx: Nonlinear incidence geometry
- 51B05: General theory
- 51B10: Möbius geometries
- 51B15: Laguerre geometries
- 51B20: Minkowski geometries
- 51B25: Lie geometries
- 51B99: None of the above, but in this section
- 51C05: Ring geometry (Hjelmslev, Barbilian, etc.)

- 51Dxx: Geometric closure systems
- 51D05: Abstract (Maeda) geometries
- 51D10: Abstract geometries with exchange axiom
- 51D15: Abstract geometries with parallelism
- 51D20: Combinatorial geometries
- 51D25: Lattices of subspaces
- 51D30: Continuous geometries and related topics
- 51D99: None of the above, but in this section

- 51Exx: Finite geometry and special incidence structures
- 51E05: General block designs
- 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
- 51E21: Blocking sets, ovals, $k$-arcs
- 51E22: Linear codes and caps in Galois spaces
- 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
- 51E99: None of the above, but in this section

- 51Fxx: Metric geometry
- 51F05: Absolute planes
- 51F10: Absolute spaces
- 51F15: Reflection groups, reflection geometries
- 51F20: Congruence and orthogonality
- 51F25: Orthogonal and unitary groups
- 51F99: None of the above, but in this section
- 51G05: Ordered geometries (ordered incidence structures, etc.)

- 51Hxx: Topological geometry
- 51H05: General theory
- 51H10: Topological linear incidence structures
- 51H15: Topological nonlinear incidence structures
- 51H20: Topological geometries on manifolds
- 51H25: Geometries with differentiable structure
- 51H30: Geometries with algebraic manifold structure
- 51H99: None of the above, but in this section

- 51Jxx: Incidence groups
- 51J05: General theory
- 51J10: Projective incidence groups
- 51J15: Kinematic spaces
- 51J20: Representation by near-fields and near-algebras
- 51J99: None of the above, but in this section

- 51Kxx: Distance geometry
- 51K05: General theory
- 51K10: Synthetic differential geometry
- 51K99: None of the above, but in this section

- 51Lxx: Geometric order structures
- 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

- 51Mxx: Real and complex geometry
- 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
- 51M20: Polyhedra and polytopes; regular figures, division of spaces
- 51M25: Length, area and volume
- 51M30: Line geometries and their generalizations
- 51M35: Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations)
- 51M99: None of the above, but in this section

- 51Nxx: Analytic and descriptive geometry
- 51N05: Descriptive geometry
- 51N10: Affine analytic geometry
- 51N15: Projective analytic geometry
- 51N20: Euclidean analytic geometry
- 51N25: Analytic geometry with other transformation groups
- 51N30: Geometry of classical groups
- 51N35: Questions of classical algebraic geometry
- 51N99: None of the above, but in this section
- 51P05: Geometry and physics (should also be assigned at least one other classification number from Sections 70--86)

- 52-xx: Convex and discrete geometry
- 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: General convexity
- 52A01: Axiomatic and generalized convexity
- 52A05: Convex sets without dimension restrictions
- 52A07: Convex sets in topological vector spaces
- 52A10: Convex sets in $2$ dimensions (including convex curves)
- 52A15: Convex sets in $3$ dimensions (including convex surfaces)
- 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
- 52A21: Finite-dimensional Banach spaces (including special norms, zonoids, etc.)
- 52A22: Random convex sets and integral geometry
- 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
- 52A39: Mixed volumes and related topics
- 52A40: Inequalities and extremum problems
- 52A41: Convex functions and convex programs
- 52A55: Spherical and hyperbolic convexity
- 52A99: None of the above, but in this section

- 52Bxx: Polytopes and polyhedra
- 52B05: Combinatorial properties (number of faces, shortest paths, etc.)
- 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)
- 52B22: Shellability
- 52B35: Gale and other diagrams
- 52B40: Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.)
- 52B45: Dissections and valuations (Hilbert's third problem, etc.)
- 52B55: Computational aspects related to convexity
- 52B60: Isoperimetric problems for polytopes
- 52B70: Polyhedral manifolds
- 52B99: None of the above, but in this section

- 52Cxx: Discrete geometry
- 52C05: Lattices and convex bodies in $2$ dimensions
- 52C07: Lattices and convex bodies in $n$ dimensions
- 52C10: Erdös problems and related topics of discrete geometry
- 52C15: Packing and covering in $2$ dimensions
- 52C17: Packing and covering in $n$ dimensions
- 52C20: Tilings in $2$ dimensions
- 52C22: Tilings in $n$ dimensions
- 52C23: Quasicrystals, aperiodic tilings
- 52C25: Rigidity and flexibility of structures
- 52C26: Circle packings and discrete conformal geometry
- 52C30: Planar arrangements of lines and pseudolines
- 52C35: Arrangements of points, flats, hyperplanes
- 52C40: Oriented matroids
- 52C45: Combinatorial complexity of geometric structures
- 52C99: None of the above, but in this section

- 53-xx: Differential geometry
- 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: Classical differential geometry
- 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
- 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
- 53A99: None of the above, but in this section

- 53Bxx: Local differential geometry
- 53B05: Linear and affine connections
- 53B10: Projective connections
- 53B15: Other connections
- 53B20: Local Riemannian geometry
- 53B21: Methods of Riemannian geometry
- 53B25: Local submanifolds
- 53B30: Lorentz metrics, indefinite metrics
- 53B35: Hermitian and Kählerian structures
- 53B40: Finsler spaces and generalizations (areal metrics)
- 53B50: Applications to physics
- 53B99: None of the above, but in this section

- 53Cxx: Global differential geometry
- 53C05: Connections, general theory
- 53C07: Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills)
- 53C10: $G$-structures
- 53C12: Foliations (differential geometric aspects)
- 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)
- 53C17: Sub-Riemannian geometry
- 53C20: Global Riemannian geometry, including pinching
- 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions
- 53C22: Geodesics
- 53C23: Global topological methods (à la Gromov)
- 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
- 53C29: Issues of holonomy
- 53C30: Homogeneous manifolds
- 53C35: Symmetric spaces
- 53C38: Calibrations and calibrated geometries
- 53C40: Global submanifolds
- 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
- 53C43: Differential geometric aspects of harmonic maps
- 53C44: Geometric evolution equations (mean curvature flow)
- 53C45: Global surface theory (convex surfaces à la A. D. Aleksandrov)
- 53C50: Lorentz manifolds, manifolds with indefinite metrics
- 53C55: Hermitian and Kählerian manifolds
- 53C56: Other complex differential geometry
- 53C60: Finsler spaces and generalizations (areal metrics)
- 53C65: Integral geometry; differential forms, currents, etc.
- 53C70: Direct methods ($G$-spaces of Busemann, etc.)
- 53C75: Geometric orders, order geometry
- 53C80: Applications to physics
- 53C99: None of the above, but in this section

- 53Dxx: Symplectic geometry, contact geometry
- 53D05: Symplectic manifolds, general
- 53D10: Contact manifolds, general
- 53D12: Lagrangian submanifolds; Maslov index
- 53D15: Almost contact and almost symplectic manifolds
- 53D17: Poisson manifolds
- 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
- 53D40: Floer homology and cohomology, symplectic aspects
- 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
- 53D50: Geometric quantization
- 53D55: Deformation quantization, star products
- 53D99: None of the above, but in this section
- 53Z05: Applications to physics

- 54-xx: General topology
- 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: Generalities
- 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)
- 54A35: Consistency and independence results
- 54A40: Fuzzy topology
- 54A99: None of the above, but in this section

- 54Bxx: Basic constructions
- 54B05: Subspaces
- 54B10: Product spaces
- 54B15: Quotient spaces, decompositions
- 54B17: Adjunction spaces and similar constructions
- 54B20: Hyperspaces
- 54B30: Categorical methods
- 54B35: Spectra
- 54B40: Presheaves and sheaves
- 54B99: None of the above, but in this section

- 54Cxx: Maps and general types of spaces defined by maps
- 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
- 54C35: Function spaces
- 54C40: Algebraic properties of function spaces
- 54C45: $C$- and $C^*$-embedding
- 54C50: Special sets defined by functions
- 54C55: Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)
- 54C56: Shape theory
- 54C60: Set-valued maps
- 54C65: Selections
- 54C70: Entropy
- 54C99: None of the above, but in this section

- 54Dxx: Fairly general properties
- 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

- 54Exx: Spaces with richer structures
- 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

- 54Fxx: Special properties
- 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
- 54F15: Continua and generalizations
- 54F35: Higher-dimensional local connectedness
- 54F45: Dimension theory
- 54F50: Spaces of dimension $\leq 1$; curves, dendrites
- 54F55: Unicoherence, multicoherence
- 54F65: Topological characterizations of particular spaces
- 54F99: None of the above, but in this section

- 54Gxx: Peculiar spaces
- 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

- 54Hxx: Connections with other structures, applications
- 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
- 54H10: Topological representations of algebraic systems
- 54H11: Topological groups
- 54H12: Topological lattices, etc.
- 54H13: Topological fields, rings, etc.
- 54H15: Transformation groups and semigroups
- 54H20: Topological dynamics
- 54H25: Fixed-point and coincidence theorems
- 54H99: None of the above, but in this section
- 54J05: Nonstandard topology

- 55-xx: Algebraic topology
- 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: Classical topics
- 55M05: Duality
- 55M10: Dimension theory
- 55M15: Absolute neighborhood retracts
- 55M20: Fixed points and coincidences
- 55M25: Degree, winding number
- 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirelman) category of a space
- 55M35: Finite groups of transformations (including Smith theory)
- 55M99: None of the above, but in this section

- 55Nxx: Homology and cohomology theories
- 55N05: Cech types
- 55N07: Steenrod-Sitnikov homologies
- 55N10: Singular theory
- 55N15: $K$-theory
- 55N20: Generalized (extraordinary) homology and cohomology theories
- 55N22: Bordism and cobordism theories, formal group laws
- 55N25: Homology with local coefficients, equivariant cohomology
- 55N30: Sheaf 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
- 55N99: None of the above, but in this section

- 55Pxx: Homotopy theory
- 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
- 55P55: Shape theory
- 55P57: Proper homotopy theory
- 55P60: Localization and completion
- 55P62: Rational homotopy theory
- 55P65: Homotopy functors
- 55P91: Equivariant homotopy theory
- 55P92: Relations between equivariant and nonequivariant homotopy theory
- 55P99: None of the above, but in this section

- 55Qxx: Homotopy groups
- 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
- 55Q51: $v_n$-periodicity
- 55Q52: Homotopy groups of special spaces
- 55Q55: Cohomotopy groups
- 55Q70: Homotopy groups of special types
- 55Q91: Equivariant homotopy groups
- 55Q99: None of the above, but in this section

- 55Rxx: Fiber spaces and bundles
- 55R05: Fiber spaces
- 55R10: Fiber bundles
- 55R12: Transfer
- 55R15: Classification
- 55R20: Spectral sequences and homology of fiber spaces
- 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
- 55R45: Homology and homotopy of $B{\rm O]$ and $B{\rm U]$; Bott periodicity
- 55R50: Stable classes of vector space bundles, $K$-theory
- 55R55: Fiberings with singularities
- 55R60: Microbundles and block bundles
- 55R65: Generalizations of fiber spaces and bundles
- 55R70: Fibrewise topology
- 55R80: Discriminantal varieties, configuration spaces
- 55R91: Equivariant fiber spaces and bundles
- 55R99: None of the above, but in this section

- 55Sxx: Operations and obstructions
- 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
- 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
- 55S99: None of the above, but in this section

- 55Txx: Spectral sequences
- 55T05: General
- 55T10: Serre spectral sequences
- 55T15: Adams spectral sequences
- 55T20: Eilenberg-Moore spectral sequences
- 55T25: Generalized cohomology
- 55T99: None of the above, but in this section

- 55Uxx: Applied homological algebra and category theory
- 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-xx: Manifolds and cell complexes
- 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: Low-dimensional topology
- 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
- 57M20: Two-dimensional complexes
- 57M25: Knots and links in $S^3$
- 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)
- 57M50: Geometric structures on low-dimensional manifolds
- 57M60: Group actions in low dimensions
- 57M99: None of the above, but in this section

- 57Nxx: Topological manifolds
- 57N05: Topology of $E^2$, $2$-manifolds
- 57N10: Topology of general $3$-manifolds
- 57N12: Topology of $E^3$ and $S^3$
- 57N13: Topology of $E^4$, $4$-manifolds
- 57N15: Topology of $E^n$, $n$-manifolds ($4 < n < \infty$)
- 57N16: Geometric structures on manifolds
- 57N17: Topology of topological vector spaces
- 57N20: Topology of infinite-dimensional manifolds
- 57N25: Shapes
- 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
- 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

- 57Pxx: Generalized manifolds
- 57P05: Local properties of generalized manifolds
- 57P10: Poincaré duality spaces
- 57P99: None of the above, but in this section

- 57Qxx: PL-topology
- 57Q05: General topology of complexes
- 57Q10: Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
- 57Q12: Wall finiteness obstruction for CW-complexes
- 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)
- 57Q50: Microbundles and block bundles
- 57Q55: Approximations
- 57Q60: Cobordism and concordance
- 57Q65: General position and transversality
- 57Q91: Equivariant PL-topology
- 57Q99: None of the above, but in this section

- 57Rxx: Differential topology
- 57R05: Triangulating
- 57R10: Smoothing
- 57R12: Smooth approximations
- 57R15: Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
- 57R17: Symplectic and contact topology
- 57R19: Algebraic topology on manifolds
- 57R20: Characteristic classes and numbers
- 57R22: Topology of vector bundles and fiber bundles
- 57R25: Vector fields, frame fields
- 57R27: Controllability of vector fields on $C^\infty$ and real-analytic manifolds
- 57R30: Foliations; geometric theory
- 57R32: Classifying spaces for foliations; Gelfand-Fuks cohomology
- 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
- 57R58: Floer homology
- 57R60: Homotopy spheres, Poincaré conjecture
- 57R65: Surgery and handlebodies
- 57R67: Surgery obstructions, Wall groups
- 57R70: Critical points and critical submanifolds
- 57R75: O- and SO-cobordism
- 57R77: Complex cobordism (U- and SU-cobordism)
- 57R80: $h$- and $s$-cobordism
- 57R85: Equivariant cobordism
- 57R90: Other types of cobordism
- 57R91: Equivariant algebraic topology of manifolds
- 57R95: Realizing cycles by submanifolds
- 57R99: None of the above, but in this section

- 57Sxx: Topological transformation groups
- 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

- 57Txx: Homology and homotopy of topological groups and related structures
- 57T05: Hopf algebras
- 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
- 57T35: Applications of Eilenberg-Moore spectral sequences
- 57T99: None of the above, but in this section

- 58-xx: Global analysis, analysis on manifolds
- 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: General theory of differentiable manifolds
- 58A03: Topos-theoretic approach to differentiable manifolds
- 58A05: Differentiable manifolds, foundations
- 58A07: Real-analytic and Nash manifolds
- 58A10: Differential forms
- 58A12: de Rham theory
- 58A14: Hodge theory
- 58A15: Exterior differential systems (Cartan theory)
- 58A17: Pfaffian systems
- 58A20: Jets
- 58A25: Currents
- 58A30: Vector distributions (subbundles of the tangent bundles)
- 58A32: Natural bundles
- 58A35: Stratified sets
- 58A40: Differential spaces
- 58A50: Supermanifolds and graded manifolds
- 58A99: None of the above, but in this section

- 58Bxx: Infinite-dimensional manifolds
- 58B05: Homotopy and topological questions
- 58B10: Differentiability questions
- 58B12: Questions of holomorphy
- 58B15: Fredholm structures
- 58B20: Riemannian, Finsler and other geometric structures
- 58B25: Group structures and generalizations on infinite-dimensional manifolds
- 58B32: Geometry of quantum groups
- 58B34: Noncommutative geometry (à la Connes)
- 58B99: None of the above, but in this section

- 58Cxx: Calculus on manifolds; nonlinear operators
- 58C05: Real-valued functions
- 58C06: Set valued and function-space valued mappings
- 58C07: Continuity properties of mappings
- 58C10: Holomorphic maps
- 58C15: Implicit function theorems; global Newton methods
- 58C20: Differentiation theory (Gateaux, Fréchet, etc.)
- 58C25: Differentiable maps
- 58C30: Fixed point theorems on manifolds
- 58C35: Integration on manifolds; measures on manifolds
- 58C40: Spectral theory; eigenvalue problems
- 58C50: Analysis on supermanifolds or graded manifolds
- 58C99: None of the above, but in this section

- 58Dxx: Spaces and manifolds of mappings (including nonlinear versions of 46Exx)
- 58D05: Groups of diffeomorphisms and homeomorphisms as manifolds
- 58D07: Groups and semigroups of nonlinear operators
- 58D10: Spaces of imbeddings and immersions
- 58D15: Manifolds of mappings
- 58D17: Manifolds of metrics (esp. Riemannian)
- 58D19: Group actions and symmetry properties
- 58D20: Measures (Gaussian, cylindrical, etc.) on manifolds of maps
- 58D25: Equations in function spaces; evolution equations
- 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

- 58Exx: Variational problems in infinite-dimensional spaces
- 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirelman) 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)
- 58E15: Application to extremal problems in several variables; Yang-Mills functionals, etc.
- 58E17: Pareto optimality, etc., applications to economics
- 58E20: Harmonic maps, etc.
- 58E25: Applications to control theory
- 58E30: Variational principles
- 58E35: Variational inequalities (global problems)
- 58E40: Group actions
- 58E50: Applications
- 58E99: None of the above, but in this section

- 58Hxx: Pseudogroups, differentiable groupoids and general structures on manifolds
- 58H05: Pseudogroups and differentiable groupoids
- 58H10: Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.)
- 58H15: Deformations of structures
- 58H99: None of the above, but in this section

- 58Jxx: Partial differential equations on manifolds; differential operators
- 58J05: Elliptic equations on manifolds, general theory
- 58J10: Differential complexes; elliptic complexes
- 58J15: Relations with hyperfunctions
- 58J20: Index theory and related fixed point theorems
- 58J22: Exotic index theories
- 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
- 58J42: Noncommutative global analysis, noncommutative residues
- 58J45: Hyperbolic equations
- 58J47: Propagation of singularities; initial value problems
- 58J50: Spectral problems; spectral geometry; scattering theory
- 58J52: Determinants and determinant bundles, analytic torsion
- 58J53: Isospectrality
- 58J55: Bifurcation
- 58J60: Relations with special manifold structures (Riemannian, Finsler, etc.)
- 58J65: Diffusion processes and stochastic analysis on manifolds
- 58J70: Invariance and symmetry properties
- 58J72: Correspondences and other transformation methods (e.g. Lie-Bäcklund)
- 58J90: Applications
- 58J99: None of the above, but in this section

- 58Kxx: Theory of singularities and catastrophe theory
- 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
- 58Z05: Applications to physics

- 60-xx: Probability theory and stochastic processes
- 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)
- 60Axx: Foundations of probability theory
- 60A05: Axioms; other general questions
- 60A10: Probabilistic measure theory
- 60A99: None of the above, but in this section

- 60Bxx: Probability theory on algebraic and topological structures
- 60B05: Probability measures on topological spaces
- 60B10: Convergence of probability measures
- 60B11: Probability theory on linear topological spaces
- 60B12: Limit theorems for vector-valued random variables (infinite-dimensional case)
- 60B15: Probability measures on groups, Fourier transforms, factorization
- 60B99: None of the above, but in this section
- 60C05: Combinatorial probability
- 60D05: Geometric probability, stochastic geometry, random sets

- 60Exx: Distribution theory
- 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

- 60Fxx: Limit theorems
- 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

- 60Gxx: Stochastic processes
- 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
- 60G25: Prediction theory
- 60G30: Continuity and singularity of induced measures
- 60G35: Applications (signal detection, filtering, etc.)
- 60G40: Stopping times; optimal stopping problems; gambling theory
- 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
- 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

- 60Hxx: Stochastic analysis
- 60H05: Stochastic integrals
- 60H07: Stochastic calculus of variations and the Malliavin calculus
- 60H10: Stochastic ordinary differential equations
- 60H15: Stochastic partial differential equations
- 60H20: Stochastic integral equations
- 60H25: Random operators and equations
- 60H30: Applications of stochastic analysis (to PDE, etc.)
- 60H35: Computational methods for stochastic equations
- 60H40: White noise theory
- 60H99: None of the above, but in this section

- 60Jxx: Markov processes
- 60J05: Markov processes with discrete parameter
- 60J10: Markov chains with discrete parameter
- 60J20: Applications of discrete Markov processes (social mobility, learning theory, industrial processes, etc.)
- 60J22: Computational methods in Markov chains
- 60J25: Markov processes with continuous parameter
- 60J27: Markov chains with continuous parameter
- 60J35: Transition functions, generators and resolvents
- 60J40: Right processes
- 60J45: Probabilistic potential theory
- 60J50: Boundary theory
- 60J55: Local time and additive functionals
- 60J57: Multiplicative functionals
- 60J60: Diffusion processes
- 60J65: Brownian motion
- 60J70: Applications of diffusion theory (population genetics, absorption problems, etc.)
- 60J75: Jump processes
- 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
- 60J85: Applications of branching processes
- 60J99: None of the above, but in this section

- 60Kxx: Special processes
- 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.)
- 60K25: Queueing theory
- 60K30: Applications (congestion, allocation, storage, traffic, etc.)
- 60K35: Interacting random processes; statistical mechanics type models; percolation theory
- 60K37: Processes in random environments
- 60K40: Other physical applications of random processes
- 60K99: None of the above, but in this section

- 62-xx: Statistics
- 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
- 62A01: Foundational and philosophical topics

- 62Bxx: Sufficiency and information
- 62B05: Sufficient statistics and fields
- 62B10: Information-theoretic topics
- 62B15: Theory of statistical experiments
- 62B99: None of the above, but in this section

- 62Cxx: Decision theory
- 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
- 62C99: None of the above, but in this section
- 62D05: Sampling theory, sample surveys

- 62Exx: Distribution theory
- 62E10: Characterization and structure theory
- 62E15: Exact distribution theory
- 62E17: Approximations to distributions (nonasymptotic)
- 62E20: Asymptotic distribution theory
- 62E99: None of the above, but in this section

- 62Fxx: Parametric inference
- 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
- 62F99: None of the above, but in this section

- 62Gxx: Nonparametric inference
- 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
- 62G99: None of the above, but in this section

- 62Hxx: Multivariate analysis
- 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
- 62H35: Image analysis
- 62H99: None of the above, but in this section

- 62Jxx: Linear inference, regression
- 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
- 62J99: None of the above, but in this section

- 62Kxx: Design of experiments
- 62K05: Optimal designs
- 62K10: Block designs
- 62K15: Factorial designs
- 62K20: Response surface designs
- 62K25: Robust parameter designs
- 62K99: None of the above, but in this section

- 62Lxx: Sequential methods
- 62L05: Sequential design
- 62L10: Sequential analysis
- 62L12: Sequential estimation
- 62L15: Optimal stopping
- 62L20: Stochastic approximation
- 62L99: None of the above, but in this section

- 62Mxx: Inference from stochastic processes
- 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.
- 62M15: Spectral analysis
- 62M20: Prediction; filtering
- 62M30: Spatial processes
- 62M40: Random fields; image analysis
- 62M45: Neural nets and related approaches
- 62M99: None of the above, but in this section

- 62Nxx: Survival analysis and censored data
- 62N01: Censored data models
- 62N02: Estimation
- 62N03: Testing
- 62N05: Reliability and life testing
- 62N99: None of the above, but in this section

- 62Pxx: Applications
- 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
- 62P25: Applications to social sciences
- 62P30: Applications in engineering and industry
- 62P35: Applications to physics
- 62P99: None of the above, but in this section
- 62Q05: Statistical tables

- 65-xx: Numerical analysis
- 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.
- 65A05: Tables

- 65Bxx: Acceleration of convergence
- 65B05: Extrapolation to the limit, deferred corrections
- 65B10: Summation of series
- 65B15: Euler-Maclaurin formula
- 65B99: None of the above, but in this section

- 65Cxx: Probabilistic methods, simulation and stochastic differential equations
- 65C05: Monte Carlo methods
- 65C10: Random number generation
- 65C20: Models, numerical methods
- 65C30: Stochastic differential and integral equations
- 65C35: Stochastic particle methods
- 65C40: Computational Markov chains
- 65C50: Other computational problems in probability
- 65C60: Computational problems in statistics
- 65C99: None of the above, but in this section

- 65Dxx: Numerical approximation and computational geometry {Primarily algorithms; for theory, see 41-XX and 68Uxx]
- 65D05: Interpolation
- 65D07: Splines
- 65D10: Smoothing, curve fitting
- 65D15: Algorithms for functional approximation
- 65D17: Computer aided design (modeling of curves and surfaces)
- 65D18: Computer graphics and computational geometry
- 65D20: Computation of special functions, construction of tables
- 65D25: Numerical differentiation
- 65D30: Numerical integration
- 65D32: Quadrature and cubature formulas
- 65D99: None of the above, but in this section
- 65E05: Numerical methods in complex analysis (potential theory, etc.)

- 65Fxx: Numerical linear algebra
- 65F05: Direct methods for linear systems and matrix inversion
- 65F10: Iterative methods for linear systems
- 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
- 65F40: Determinants
- 65F50: Sparse matrices
- 65F99: None of the above, but in this section

- 65Gxx: Error analysis and interval analysis
- 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

- 65Hxx: Nonlinear algebraic or transcendental equations
- 65H05: Single equations
- 65H10: Systems of equations
- 65H17: Eigenvalues, eigenvectors
- 65H20: Global methods, including homotopy approaches
- 65H99: None of the above, but in this section

- 65Jxx: Numerical analysis in abstract spaces
- 65J05: General theory
- 65J10: Equations with linear operators (do not use 65Fxx)
- 65J15: Equations with nonlinear operators (do not use 65Hxx)
- 65J20: Improperly posed problems; regularization
- 65J22: Inverse problems
- 65J99: None of the above, but in this section

- 65Kxx: Mathematical programming, optimization and variational techniques
- 65K05: Mathematical programming {Algorithms; for theory see 90Cxx]
- 65K10: Optimization and variational techniques
- 65K99: None of the above, but in this section

- 65Lxx: Ordinary differential 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
- 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

- 65Mxx: Partial differential equations, initial value and time-dependent initial-boundary value problems
- 65M06: Finite difference methods
- 65M12: Stability and convergence of numerical methods
- 65M15: Error bounds
- 65M20: Method of lines
- 65M25: Method of characteristics
- 65M30: Improperly posed problems
- 65M32: Inverse problems
- 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
- 65M99: None of the above, but in this section

- 65Nxx: Partial differential equations, boundary value problems
- 65N06: Finite difference methods
- 65N12: Stability and convergence of numerical methods
- 65N15: Error bounds
- 65N21: Inverse problems
- 65N22: Solution of discretized equations
- 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
- 65N99: None of the above, but in this section

- 65Pxx: Numerical problems in dynamical systems
- 65P10: Hamiltonian systems including symplectic integrators
- 65P20: Numerical chaos
- 65P30: Bifurcation problems
- 65P40: Nonlinear stabilities
- 65P99: None of the above, but in this section
- 65Q05: Difference and functional equations, recurrence relations

- 65Rxx: Integral equations, integral transforms
- 65R10: Integral transforms
- 65R20: Integral equations
- 65R30: Improperly posed problems
- 65R32: Inverse problems
- 65R99: None of the above, but in this section
- 65S05: Graphical methods

- 65Txx: Numerical methods in Fourier analysis
- 65T40: Trigonometric approximation and interpolation
- 65T50: Discrete and fast Fourier transforms
- 65T60: Wavelets
- 65T99: None of the above, but in this section

- 65Yxx: Computer aspects of numerical algorithms
- 65Y05: Parallel computation
- 65Y10: Algorithms for specific classes of architectures
- 65Y15: Packaged methods
- 65Y20: Complexity and performance of numerical algorithms
- 65Y99: None of the above, but in this section
- 65Z05: Applications to physics

- 68-xx: Computer science
- 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: Computer system organization
- 68M01: General
- 68M07: Mathematical problems of computer architecture
- 68M10: Network design and communication
- 68M12: Network protocols
- 68M14: Distributed systems
- 68M15: Reliability, testing and fault tolerance
- 68M20: Performance evaluation; queueing; scheduling
- 68M99: None of the above, but in this section

- 68Nxx: Software
- 68N01: General
- 68N15: Programming languages
- 68N17: Logic programming
- 68N18: Functional programming and lambda calculus
- 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

- 68Pxx: Theory of data
- 68P01: General
- 68P05: Data structures
- 68P10: Searching and sorting
- 68P15: Database theory
- 68P20: Information storage and retrieval
- 68P25: Data encryption
- 68P30: Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.)
- 68P99: None of the above, but in this section

- 68Qxx: Theory of computing
- 68Q01: General
- 68Q05: Models of computation (Turing machines, etc.)
- 68Q10: Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)
- 68Q15: Complexity classes (hierarchies, relations among complexity classes, etc.)
- 68Q17: Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
- 68Q19: Descriptive complexity and finite models
- 68Q25: Analysis of algorithms and problem complexity
- 68Q30: Algorithmic information theory (Kolmogorov complexity, etc.)
- 68Q32: Computational learning theory
- 68Q42: Grammars and rewriting systems
- 68Q45: Formal languages and automata
- 68Q55: Semantics
- 68Q60: Specification and verification (program logics, model checking, etc.)
- 68Q65: Abstract data types; algebraic specification
- 68Q70: Algebraic theory of languages and automata
- 68Q80: Cellular automata
- 68Q85: Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
- 68Q99: None of the above, but in this section

- 68Rxx: Discrete mathematics in relation to computer science
- 68R01: General
- 68R05: Combinatorics
- 68R10: Graph theory
- 68R15: Combinatorics on words
- 68R99: None of the above, but in this section

- 68Txx: Artificial intelligence
- 68T01: General
- 68T05: Learning and adaptive systems
- 68T10: Pattern recognition, speech recognition
- 68T15: Theorem proving (deduction, resolution, etc.)
- 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
- 68T45: Machine vision and scene understanding
- 68T50: Natural language processing
- 68T99: None of the above, but in this section

- 68Uxx: Computing methodologies and applications
- 68U01: General
- 68U05: Computer graphics; computational geometry
- 68U07: Computer-aided design
- 68U10: Image processing
- 68U15: Text processing; mathematical typography
- 68U20: Simulation
- 68U35: Information systems (hypertext navigation, interfaces, decision support, etc.)
- 68U99: None of the above, but in this section

- 68Wxx: Algorithms
- 68W01: General
- 68W05: Nonnumerical algorithms
- 68W10: Parallel algorithms
- 68W15: Distributed algorithms
- 68W20: Randomized algorithms
- 68W25: Approximation algorithms
- 68W30: Symbolic computation and algebraic computation
- 68W35: VLSI algorithms
- 68W40: Analysis of algorithms
- 68W99: None of the above, but in this section

- 70-xx: Mechanics of particles and systems
- 70-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
- 70-01: Instructional exposition (textbooks, tutorial papers, etc.)
- 70-02: Research exposition (monographs, survey articles)
- 70-03: Historical (must also be assigned at least one classification number from Section 01)
- 70-04: Explicit machine computation and programs (not the theory of computation or programming)
- 70-05: Experimental work
- 70-06: Proceedings, conferences, collections, etc.
- 70-08: Computational methods
- 70A05: Axiomatics, foundations

- 70Bxx: Kinematics
- 70B05: Kinematics of a particle
- 70B10: Kinematics of a rigid body
- 70B15: Mechanisms, robots
- 70B99: None of the above, but in this section
- 70C20: Statics

- 70Exx: Dynamics of a rigid body and of multibody systems
- 70E05: Motion of the gyroscope
- 70E15: Free motion of a rigid body
- 70E17: Motion of a rigid body with a fixed point
- 70E18: Motion of a rigid body in contact with a solid surface
- 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
- 70E99: None of the above, but in this section

- 70Fxx: Dynamics of a system of particles, including celestial mechanics
- 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

- 70Gxx: General models, approaches, and methods
- 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.)
- 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

- 70Hxx: Hamiltonian and Lagrangian mechanics
- 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
- 70H50: Higher-order theories
- 70H99: None of the above, but in this section

- 70Jxx: Linear vibration theory
- 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

- 70Kxx: Nonlinear dynamics
- 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)
- 70K60: General perturbation schemes
- 70K65: Averaging of perturbations
- 70K70: Systems with slow and fast motions
- 70K75: Nonlinear modes
- 70K99: None of the above, but in this section
- 70L05: Random vibrations
- 70M20: Orbital mechanics
- 70P05: Variable mass, rockets
- 70Q05: Control of mechanical systems

- 70Sxx: Classical field theories
- 70S05: Lagrangian formalism and Hamiltonian formalism
- 70S10: Symmetries and conservation laws
- 70S15: Yang-Mills and other gauge theories
- 70S20: More general nonquantum field theories
- 70S99: None of the above, but in this section

- 74-xx: Mechanics of deformable solids
- 74-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
- 74-01: Instructional exposition (textbooks, tutorial papers, etc.)
- 74-02: Research exposition (monographs, survey articles)
- 74-03: Historical (must also be assigned at least one classification number from Section 01)
- 74-04: Explicit machine computation and programs (not the theory of computation or programming)
- 74-05: Experimental work
- 74-06: Proceedings, conferences, collections, etc.
- 74Axx: Generalities, axiomatics, foundations of continuum mechanics of solids
- 74A05: Kinematics of deformation
- 74A10: Stress
- 74A15: Thermodynamics
- 74A20: Theory of constitutive functions
- 74A25: Molecular, statistical, and kinetic theories
- 74A30: Nonsimple materials
- 74A35: Polar materials
- 74A40: Random materials and composite materials
- 74A45: Theories of fracture and damage
- 74A50: Structured surfaces and interfaces, coexistent phases
- 74A55: Theories of friction (tribology)
- 74A60: Micromechanical theories
- 74A65: Reactive materials
- 74A99: None of the above, but in this section

- 74Bxx: Elastic materials
- 74B05: Classical linear elasticity
- 74B10: Linear elasticity with initial stresses
- 74B15: Equations linearized about a deformed state (small deformations superposed on large)
- 74B20: Nonlinear elasticity
- 74B99: None of the above, but in this section

- 74Cxx: Plastic materials, materials of stress-rate and internal-variable type
- 74C05: Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials)
- 74C10: Small-strain, rate-dependent theories (including theories of viscoplasticity)
- 74C15: Large-strain, rate-independent theories (including nonlinear plasticity)
- 74C20: Large-strain, rate-dependent theories
- 74C99: None of the above, but in this section

- 74Dxx: Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
- 74D05: Linear constitutive equations
- 74D10: Nonlinear constitutive equations
- 74D99: None of the above, but in this section

- 74Exx: Material properties given special treatment
- 74E05: Inhomogeneity
- 74E10: Anisotropy
- 74E15: Crystalline structure
- 74E20: Granularity
- 74E25: Texture
- 74E30: Composite and mixture properties
- 74E35: Random structure
- 74E40: Chemical structure
- 74E99: None of the above, but in this section

- 74Fxx: Coupling of solid mechanics with other effects
- 74F05: Thermal effects
- 74F10: Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
- 74F15: Electromagnetic effects
- 74F20: Mixture effects
- 74F25: Chemical and reactive effects
- 74F99: None of the above, but in this section

- 74Gxx: Equilibrium (steady-state) problems
- 74G05: Explicit solutions
- 74G10: Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.)
- 74G15: Numerical approximation of solutions
- 74G20: Local existence of solutions (near a given solution)
- 74G25: Global existence of solutions
- 74G30: Uniqueness of solutions
- 74G35: Multiplicity of solutions
- 74G40: Regularity of solutions
- 74G45: Bounds for solutions
- 74G50: Saint-Venant's principle
- 74G55: Qualitative behavior of solutions
- 74G60: Bifurcation and buckling
- 74G65: Energy minimization
- 74G70: Stress concentrations, singularities
- 74G75: Inverse problems
- 74G99: None of the above, but in this section

- 74Hxx: Dynamical problems
- 74H05: Explicit solutions
- 74H10: Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.)
- 74H15: Numerical approximation of solutions
- 74H20: Existence of solutions
- 74H25: Uniqueness of solutions
- 74H30: Regularity of solutions
- 74H35: Singularities, blowup, stress concentrations
- 74H40: Long-time behavior of solutions
- 74H45: Vibrations
- 74H50: Random vibrations
- 74H55: Stability
- 74H60: Dynamical bifurcation
- 74H65: Chaotic behavior
- 74H99: None of the above, but in this section

- 74Jxx: Waves
- 74J05: Linear waves
- 74J10: Bulk waves
- 74J15: Surface waves
- 74J20: Wave scattering
- 74J25: Inverse problems
- 74J30: Nonlinear waves
- 74J35: Solitary waves
- 74J40: Shocks and related discontinuities
- 74J99: None of the above, but in this section

- 74Kxx: Thin bodies, structures
- 74K05: Strings
- 74K10: Rods (beams, columns, shafts, arches, rings, etc.)
- 74K15: Membranes
- 74K20: Plates
- 74K25: Shells
- 74K30: Junctions
- 74K35: Thin films
- 74K99: None of the above, but in this section

- 74Lxx: Special subfields of solid mechanics
- 74L05: Geophysical solid mechanics
- 74L10: Soil and rock mechanics
- 74L15: Biomechanical solid mechanics
- 74L99: None of the above, but in this section

- 74Mxx: Special kinds of problems
- 74M05: Control, switches and devices (``smart materials'')
- 74M10: Friction
- 74M15: Contact
- 74M20: Impact
- 74M25: Micromechanics
- 74M99: None of the above, but in this section

- 74Nxx: Phase transformations in solids
- 74N05: Crystals
- 74N10: Displacive transformations
- 74N15: Analysis of microstructure
- 74N20: Dynamics of phase boundaries
- 74N25: Transformations involving diffusion
- 74N30: Problems involving hysteresis
- 74N99: None of the above, but in this section

- 74Pxx: Optimization
- 74P05: Compliance or weight optimization
- 74P10: Optimization of other properties
- 74P15: Topological methods
- 74P20: Geometrical methods
- 74P99: None of the above, but in this section

- 74Qxx: Homogenization, determination of effective properties
- 74Q05: Homogenization in equilibrium problems
- 74Q10: Homogenization and oscillations in dynamical problems
- 74Q15: Effective constitutive equations
- 74Q20: Bounds on effective properties
- 74Q99: None of the above, but in this section

- 74Rxx: Fracture and damage
- 74R05: Brittle damage
- 74R10: Brittle fracture
- 74R15: High-velocity fracture
- 74R20: Anelastic fracture and damage
- 74R99: None of the above, but in this section

- 74Sxx: Numerical methods
- 74S05: Finite element methods
- 74S10: Finite volume methods
- 74S15: Boundary element methods
- 74S20: Finite difference methods
- 74S25: Spectral and related methods
- 74S30: Other numerical methods
- 74S99: None of the above, but in this section

- 76-xx: Fluid mechanics
- 76-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
- 76-01: Instructional exposition (textbooks, tutorial papers, etc.)
- 76-02: Research exposition (monographs, survey articles)
- 76-03: Historical (must also be assigned at least one classification number from Section 01)
- 76-04: Explicit machine computation and programs (not the theory of computation or programming)
- 76-05: Experimental work
- 76-06: Proceedings, conferences, collections, etc.
- 76Axx: Foundations, constitutive equations, rheology
- 76A02: Foundations of fluid mechanics
- 76A05: Non-Newtonian fluids
- 76A10: Viscoelastic fluids
- 76A15: Liquid crystals
- 76A20: Thin fluid films
- 76A25: Superfluids (classical aspects)
- 76A99: None of the above, but in this section

- 76Bxx: Incompressible inviscid fluids
- 76B03: Existence, uniqueness, and regularity theory
- 76B07: Free-surface potential flows
- 76B10: Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
- 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction
- 76B20: Ship waves
- 76B25: Solitary waves
- 76B45: Capillarity (surface tension)
- 76B47: Vortex flows
- 76B55: Internal waves
- 76B60: Atmospheric waves
- 76B65: Rossby waves
- 76B70: Stratification effects in inviscid fluids
- 76B75: Flow control and optimization
- 76B99: None of the above, but in this section

- 76Dxx: Incompressible viscous fluids
- 76D03: Existence, uniqueness, and regularity theory
- 76D05: Navier-Stokes equations
- 76D06: Statistical solutions of Navier-Stokes and related equations
- 76D07: Stokes and related (Oseen, etc.) flows
- 76D08: Lubrication theory
- 76D09: Viscous-inviscid interaction
- 76D10: Boundary-layer theory, separation and reattachment, higher-order effects
- 76D17: Viscous vortex flows
- 76D25: Wakes and jets
- 76D27: Other free-boundary flows; Hele-Shaw flows
- 76D33: Waves
- 76D45: Capillarity (surface tension)
- 76D50: Stratification effects in viscous fluids
- 76D55: Flow control and optimization
- 76D99: None of the above, but in this section

- 76Exx: Hydrodynamic stability
- 76E05: Parallel shear flows
- 76E06: Convection
- 76E07: Rotation
- 76E09: Stability and instability of nonparallel flows
- 76E15: Absolute and convective instability and stability
- 76E17: Interfacial stability and instability
- 76E19: Compressibility effects
- 76E20: Stability and instability of geophysical and astrophysical flows
- 76E25: Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
- 76E30: Nonlinear effects
- 76E99: None of the above, but in this section

- 76Fxx: Turbulence
- 76F02: Fundamentals
- 76F05: Isotropic turbulence; homogeneous turbulence
- 76F06: Transition to turbulence
- 76F10: Shear flows
- 76F20: Dynamical systems approach to turbulence
- 76F25: Turbulent transport, mixing
- 76F30: Renormalization and other field-theoretical methods
- 76F35: Convective turbulence
- 76F40: Turbulent boundary layers
- 76F45: Stratification effects
- 76F50: Compressibility effects
- 76F55: Statistical turbulence modeling
- 76F60: $k$-$\varepsilon$ modeling
- 76F65: Direct numerical and large eddy simulation of turbulence
- 76F70: Control of turbulent flows
- 76F99: None of the above, but in this section
- 76G25: General aerodynamics and subsonic flows
- 76H05: Transonic flows
- 76J20: Supersonic flows
- 76K05: Hypersonic flows
- 76L05: Shock waves and blast waves

- 76Mxx: Basic methods in fluid mechanics
- 76M10: Finite element methods
- 76M12: Finite volume methods
- 76M15: Boundary element methods
- 76M20: Finite difference methods
- 76M22: Spectral methods
- 76M23: Vortex methods
- 76M25: Other numerical methods
- 76M27: Visualization algorithms
- 76M28: Particle methods and lattice-gas methods
- 76M30: Variational methods
- 76M35: Stochastic analysis
- 76M40: Complex-variables methods
- 76M45: Asymptotic methods, singular perturbations
- 76M50: Homogenization
- 76M55: Dimensional analysis and similarity
- 76M60: Symmetry analysis, Lie group and algebra methods
- 76M99: None of the above, but in this section

- 76Nxx: Compressible fluids and gas dynamics, general
- 76N10: Existence, uniqueness, and regularity theory
- 76N15: Gas dynamics, general
- 76N17: Viscous-inviscid interaction
- 76N20: Boundary-layer theory
- 76N25: Flow control and optimization
- 76N99: None of the above, but in this section
- 76P05: Rarefied gas flows, Boltzmann equation
- 76Q05: Hydro- and aero-acoustics

- 76Rxx: Diffusion and convection
- 76R05: Forced convection
- 76R10: Free convection
- 76R50: Diffusion
- 76R99: None of the above, but in this section
- 76S05: Flows in porous media; filtration; seepage

- 76Txx: Two-phase and multiphase flows
- 76T10: Liquid-gas two-phase flows, bubbly flows
- 76T15: Dusty-gas two-phase flows
- 76T20: Suspensions
- 76T25: Granular flows
- 76T30: Three or more component flows
- 76T99: None of the above, but in this section
- 76U05: Rotating fluids
- 76V05: Reaction effects in flows
- 76W05: Magnetohydrodynamics and electrohydrodynamics
- 76X05: Ionized gas flow in electromagnetic fields; plasmic flow
- 76Y05: Quantum hydrodynamics and relativistic hydrodynamics

- 76Zxx: Biological fluid mechanics
- 76Z05: Physiological flows
- 76Z10: Biopropulsion in water and in air
- 76Z99: None of the above, but in this section

- 78-xx: Optics, electromagnetic theory
- 78-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
- 78-01: Instructional exposition (textbooks, tutorial papers, etc.)
- 78-02: Research exposition (monographs, survey articles)
- 78-03: Historical (must also be assigned at least one classification number from Section 01)
- 78-04: Explicit machine computation and programs (not the theory of computation or programming)
- 78-05: Experimental work
- 78-06: Proceedings, conferences, collections, etc.
- 78Axx: General
- 78A02: Foundations
- 78A05: Geometric optics
- 78A10: Physical optics
- 78A15: Electron optics
- 78A20: Space charge waves
- 78A25: Electromagnetic theory, general
- 78A30: Electro- and magnetostatics
- 78A35: Motion of charged particles
- 78A40: Waves and radiation
- 78A45: Diffraction, scattering
- 78A46: Inverse scattering problems
- 78A48: Composite media; random media
- 78A50: Antennas, wave-guides
- 78A55: Technical applications
- 78A60: Lasers, masers, optical bistability, nonlinear optics
- 78A70: Biological applications
- 78A97: Mathematically heuristic optics and electromagnetic theory (must also be assigned at least one other classification number in this section)
- 78A99: Miscellaneous topics

- 78Mxx: Basic methods
- 78M05: Method of moments
- 78M10: Finite element methods
- 78M15: Boundary element methods
- 78M20: Finite difference methods
- 78M25: Other numerical methods
- 78M30: Variational methods
- 78M35: Asymptotic analysis
- 78M40: Homogenization
- 78M50: Optimization
- 78M99: None of the above, but in this section

- 80-xx: Classical thermodynamics, heat transfer
- 80-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
- 80-01: Instructional exposition (textbooks, tutorial papers, etc.)
- 80-02: Research exposition (monographs, survey articles)
- 80-03: Historical (must also be assigned at least one classification number from Section 01)
- 80-04: Explicit machine computation and programs (not the theory of computation or programming)
- 80-05: Experimental work
- 80-06: Proceedings, conferences, collections, etc.
- 80Axx: Thermodynamics and heat transfer
- 80A05: Foundations
- 80A10: Classical thermodynamics, including relativistic
- 80A17: Thermodynamics of continua
- 80A20: Heat and mass transfer, heat flow
- 80A22: Stefan problems, phase changes, etc.
- 80A23: Inverse problems
- 80A25: Combustion
- 80A30: Chemical kinetics
- 80A32: Chemically reacting flows
- 80A50: Chemistry (general)
- 80A99: None of the above, but in this section

- 80Mxx: Basic methods
- 80M10: Finite element methods
- 80M15: Boundary element methods
- 80M20: Finite difference methods
- 80M25: Other numerical methods
- 80M30: Variational methods
- 80M35: Asymptotic analysis
- 80M40: Homogenization
- 80M50: Optimization
- 80M99: None of the above, but in this section

- 81-xx: Quantum theory
- 81-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
- 81-01: Instructional exposition (textbooks, tutorial papers, etc.)
- 81-02: Research exposition (monographs, survey articles)
- 81-03: Historical (must also be assigned at least one classification number from Section 01)
- 81-04: Explicit machine computation and programs (not the theory of computation or programming)
- 81-05: Experimental papers
- 81-06: Proceedings, conferences, collections, etc.
- 81-08: Computational methods
- 81Pxx: Axiomatics, foundations, philosophy
- 81P05: General and philosophical
- 81P10: Logical foundations of quantum mechanics; quantum logic
- 81P15: Quantum measurement theory
- 81P20: Stochastic mechanics (including stochastic electrodynamics)
- 81P68: Quantum computation and quantum cryptography
- 81P99: None of the above, but in this section

- 81Qxx: General mathematical topics and methods in quantum theory
- 81Q05: Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations
- 81Q10: Selfadjoint operator theory in quantum theory, including spectral analysis
- 81Q15: Perturbation theories for operators and differential equations
- 81Q20: Semiclassical techniques including WKB and Maslov methods
- 81Q30: Feynman integrals and graphs; applications of algebraic topology and algebraic geometry
- 81Q40: Bethe-Salpeter and other integral equations
- 81Q50: Quantum chaos
- 81Q60: Supersymmetric quantum mechanics
- 81Q70: Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.
- 81Q99: None of the above, but in this section

- 81Rxx: Groups and algebras in quantum theory
- 81R05: Finite-dimensional groups and algebras motivated by physics and their representations
- 81R10: Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $W$-algebras and other current algebras and their representations
- 81R12: Relations with integrable systems
- 81R15: Operator algebra methods
- 81R20: Covariant wave equations
- 81R25: Spinor and twistor methods
- 81R30: Coherent states; squeezed states
- 81R40: Symmetry breaking
- 81R50: Quantum groups and related algebraic methods
- 81R60: Noncommutative geometry
- 81R99: None of the above, but in this section

- 81Sxx: General quantum mechanics and problems of quantization
- 81S05: Commutation relations and statistics
- 81S10: Geometry and quantization, symplectic methods
- 81S20: Stochastic quantization
- 81S25: Quantum stochastic calculus
- 81S30: Phase space methods including Wigner distributions, etc.
- 81S40: Path integrals
- 81S99: None of the above, but in this section

- 81Txx: Quantum field theory; related classical field theories
- 81T05: Axiomatic quantum field theory; operator algebras
- 81T08: Constructive quantum field theory
- 81T10: Model quantum field theories
- 81T13: Yang-Mills and other gauge theories
- 81T15: Perturbative methods of renormalization
- 81T16: Nonperturbative methods of renormalization
- 81T17: Renormalization group methods
- 81T18: Feynman diagrams
- 81T20: Quantum field theory on curved space backgrounds
- 81T25: Quantum field theory on lattices
- 81T27: Continuum limits
- 81T30: String and superstring theories; other extended objects (e.g., branes)
- 81T40: Two-dimensional field theories, conformal field theories, etc.
- 81T45: Topological field theories
- 81T50: Anomalies
- 81T60: Supersymmetric field theories
- 81T70: Quantization in field theory; cohomological methods
- 81T75: Noncommutative geometry methods
- 81T80: Simulation and numerical modeling
- 81T99: None of the above, but in this section

- 81Uxx: Scattering theory
- 81U05: $2$-body potential scattering theory
- 81U10: $n$-body potential scattering theory
- 81U15: Exactly and quasi-solvable systems
- 81U20: $S$-matrix theory, etc.
- 81U30: Dispersion theory, dispersion relations
- 81U40: Inverse scattering problems
- 81U99: None of the above, but in this section

- 81Vxx: Applications to specific physical systems
- 81V05: Strong interaction, including quantum chromodynamics
- 81V10: Electromagnetic interaction; quantum electrodynamics
- 81V15: Weak interaction
- 81V17: Gravitational interaction
- 81V19: Other fundamental interactions
- 81V22: Unified theories
- 81V25: Other elementary particle theory
- 81V35: Nuclear physics
- 81V45: Atomic physics
- 81V55: Molecular physics
- 81V70: Many-body theory; quantum Hall effect
- 81V80: Quantum optics
- 81V99: None of the above, but in this section

- 82-xx: Statistical mechanics, structure of matter
- 82-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
- 82-01: Instructional exposition (textbooks, tutorial papers, etc.)
- 82-02: Research exposition (monographs, survey articles)
- 82-03: Historical (must also be assigned at least one classification number from Section 01)
- 82-04: Explicit machine computation and programs (not the theory of computation or programming)
- 82-05: Experimental papers
- 82-06: Proceedings, conferences, collections, etc.
- 82-08: Computational methods
- 82Bxx: Equilibrium statistical mechanics
- 82B03: Foundations
- 82B05: Classical equilibrium statistical mechanics (general)
- 82B10: Quantum equilibrium statistical mechanics (general)
- 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
- 82B21: Continuum models (systems of particles, etc.)
- 82B23: Exactly solvable models; Bethe ansatz
- 82B24: Interface problems; diffusion-limited aggregation
- 82B26: Phase transitions (general)
- 82B27: Critical phenomena
- 82B28: Renormalization group methods
- 82B30: Statistical thermodynamics
- 82B31: Stochastic methods
- 82B35: Irreversible thermodynamics, including Onsager-Machlup theory
- 82B40: Kinetic theory of gases
- 82B41: Random walks, random surfaces, lattice animals, etc.
- 82B43: Percolation
- 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)
- 82B80: Numerical methods (Monte Carlo, series resummation, etc.)
- 82B99: None of the above, but in this section

- 82Cxx: Time-dependent statistical mechanics (dynamic and nonequilibrium)
- 82C03: Foundations
- 82C05: Classical dynamic and nonequilibrium statistical mechanics (general)
- 82C10: Quantum dynamics and nonequilibrium statistical mechanics (general)
- 82C20: Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs
- 82C21: Dynamic continuum models (systems of particles, etc.)
- 82C22: Interacting particle systems
- 82C23: Exactly solvable dynamic models
- 82C24: Interface problems; diffusion-limited aggregation
- 82C26: Dynamic and nonequilibrium phase transitions (general)
- 82C27: Dynamic critical phenomena
- 82C28: Dynamic renormalization group methods
- 82C31: Stochastic methods (Fokker-Planck, Langevin, etc.)
- 82C32: Neural nets
- 82C35: Irreversible thermodynamics, including Onsager-Machlup theory
- 82C40: Kinetic theory of gases
- 82C41: Dynamics of random walks, random surfaces, lattice animals, etc.
- 82C43: Time-dependent percolation
- 82C44: Dynamics of disordered systems (random Ising systems, etc.)
- 82C70: Transport processes
- 82C80: Numerical methods (Monte Carlo, series resummation, etc.)
- 82C99: None of the above, but in this section

- 82Dxx: Applications to specific types of physical systems
- 82D05: Gases
- 82D10: Plasmas
- 82D15: Liquids
- 82D20: Solids
- 82D25: Crystals
- 82D30: Random media, disordered materials (including liquid crystals and spin glasses)
- 82D35: Metals
- 82D37: Semiconductors
- 82D40: Magnetic materials
- 82D45: Ferroelectrics
- 82D50: Superfluids
- 82D55: Superconductors
- 82D60: Polymers
- 82D75: Nuclear reactor theory; neutron transport
- 82D99: None of the above, but in this section

- 83-xx: Relativity and gravitational theory
- 83-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
- 83-01: Instructional exposition (textbooks, tutorial papers, etc.)
- 83-02: Research exposition (monographs, survey articles)
- 83-03: Historical (must also be assigned at least one classification number from Section 01)
- 83-04: Explicit machine computation and programs (not the theory of computation or programming)
- 83-05: Experimental work
- 83-06: Proceedings, conferences, collections, etc.
- 83-08: Computational methods
- 83A05: Special relativity
- 83B05: Observational and experimental questions

- 83Cxx: General relativity
- 83C05: Einstein's equations (general structure, canonical formalism, Cauchy problems)
- 83C10: Equations of motion
- 83C15: Exact solutions
- 83C20: Classes of solutions; algebraically special solutions, metrics with symmetries
- 83C22: Einstein-Maxwell equations
- 83C25: Approximation procedures, weak fields
- 83C27: Lattice gravity, Regge calculus and other discrete methods
- 83C30: Asymptotic procedures (radiation, news functions, {\scr H]-spaces, etc.)
- 83C35: Gravitational waves
- 83C40: Gravitational energy and conservation laws; groups of motions
- 83C45: Quantization of the gravitational field
- 83C47: Methods of quantum field theory
- 83C50: Electromagnetic fields
- 83C55: Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
- 83C57: Black holes
- 83C60: Spinor and twistor methods; Newman-Penrose formalism
- 83C65: Methods of noncommutative geometry
- 83C75: Space-time singularities, cosmic censorship, etc.
- 83C80: Analogues in lower dimensions
- 83C99: None of the above, but in this section
- 83D05: Relativistic gravitational theories other than Einstein's, including asymmetric field theories

- 83Exx: Unified, higher-dimensional and super field theories
- 83E05: Geometrodynamics
- 83E15: Kaluza-Klein and other higher-dimensional theories
- 83E30: String and superstring theories
- 83E50: Supergravity
- 83E99: None of the above, but in this section
- 83F05: Cosmology

- 85-xx: Astronomy and astrophysics
- 85-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
- 85-01: Instructional exposition (textbooks, tutorial papers, etc.)
- 85-02: Research exposition (monographs, survey articles)
- 85-03: Historical (must also be assigned at least one classification number from Section 01)
- 85-04: Explicit machine computation and programs (not the theory of computation or programming)
- 85-05: Experimental work
- 85-06: Proceedings, conferences, collections, etc.
- 85-08: Computational methods
- 85A04: General
- 85A05: Galactic and stellar dynamics
- 85A15: Galactic and stellar structure
- 85A20: Planetary atmospheres
- 85A25: Radiative transfer
- 85A30: Hydrodynamic and hydromagnetic problems
- 85A35: Statistical astronomy
- 85A40: Cosmology
- 85A99: Miscellaneous topics

- 86-xx: Geophysics
- 86-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
- 86-01: Instructional exposition (textbooks, tutorial papers, etc.)
- 86-02: Research exposition (monographs, survey articles)
- 86-03: Historical (must also be assigned at least one classification number from Section 01)
- 86-04: Explicit machine computation and programs (not the theory of computation or programming)
- 86-05: Experimental work
- 86-06: Proceedings, conferences, collections, etc.
- 86-08: Computational methods
- 86A04: General
- 86A05: Hydrology, hydrography, oceanography
- 86A10: Meteorology and atmospheric physics
- 86A15: Seismology
- 86A17: Global dynamics, earthquake problems
- 86A20: Potentials, prospecting
- 86A22: Inverse problems
- 86A25: Geo-electricity and geomagnetism
- 86A30: Geodesy, mapping problems
- 86A32: Geostatistics
- 86A40: Glaciology
- 86A60: Geological problems
- 86A99: Miscellaneous topics

- 90-xx: Operations research, mathematical programming
- 90-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
- 90-01: Instructional exposition (textbooks, tutorial papers, etc.)
- 90-02: Research exposition (monographs, survey articles)
- 90-03: Historical (must also be assigned at least one classification number from Section 01)
- 90-04: Explicit machine computation and programs (not the theory of computation or programming)
- 90-06: Proceedings, conferences, collections, etc.
- 90-08: Computational methods
- 90Bxx: Operations research and management science
- 90B05: Inventory, storage, reservoirs
- 90B06: Transportation, logistics
- 90B10: Network models, deterministic
- 90B15: Network models, stochastic
- 90B18: Communication networks
- 90B20: Traffic problems
- 90B22: Queues and service
- 90B25: Reliability, availability, maintenance, inspection
- 90B30: Production models
- 90B35: Scheduling theory, deterministic
- 90B36: Scheduling theory, stochastic
- 90B40: Search theory
- 90B50: Management decision making, including multiple objectives
- 90B60: Marketing, advertising
- 90B70: Theory of organizations, manpower planning
- 90B80: Discrete location and assignment
- 90B85: Continuous location
- 90B90: Case-oriented studies
- 90B99: None of the above, but in this section

- 90Cxx: Mathematical programming
- 90C05: Linear programming
- 90C06: Large-scale problems
- 90C08: Special problems of linear programming (transportation, multi-index, etc.)
- 90C09: Boolean programming
- 90C10: Integer programming
- 90C11: Mixed integer programming
- 90C15: Stochastic programming
- 90C20: Quadratic programming
- 90C22: Semidefinite programming
- 90C25: Convex programming
- 90C26: Nonconvex programming
- 90C27: Combinatorial optimization
- 90C29: Multi-objective and goal programming
- 90C30: Nonlinear programming
- 90C31: Sensitivity, stability, parametric optimization
- 90C32: Fractional programming
- 90C33: Complementarity problems
- 90C34: Semi-infinite programming
- 90C35: Programming involving graphs or networks
- 90C39: Dynamic programming
- 90C40: Markov and semi-Markov decision processes
- 90C46: Optimality conditions, duality
- 90C47: Minimax problems
- 90C48: Programming in abstract spaces
- 90C49: Extreme-point and pivoting methods
- 90C51: Interior-point methods
- 90C52: Methods of reduced gradient type
- 90C53: Methods of quasi-Newton type
- 90C55: Methods of successive quadratic programming type
- 90C56: Derivative-free methods
- 90C57: Polyhedral combinatorics, branch-and-bound, branch-and-cut
- 90C59: Approximation methods and heuristics
- 90C60: Abstract computational complexity for mathematical programming problems
- 90C70: Fuzzy programming
- 90C90: Applications of mathematical programming
- 90C99: None of the above, but in this section

- 91-xx: Game theory, economics, social and behavioral sciences
- 91-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
- 91-01: Instructional exposition (textbooks, tutorial papers, etc.)
- 91-02: Research exposition (monographs, survey articles)
- 91-03: Historical (must also be assigned at least one classification number from section 01)
- 91-04: Explicit machine computation and programs (not the theory of computation or programming)
- 91-06: Proceedings, conferences, collections, etc.
- 91-08: Computational methods
- 91Axx: Game theory
- 91A05: 2-person games
- 91A06: $n$-person games, $n>2$
- 91A10: Noncooperative games
- 91A12: Cooperative games
- 91A13: Games with infinitely many players
- 91A15: Stochastic games
- 91A18: Games in extensive form
- 91A20: Multistage and repeated games
- 91A22: Evolutionary games
- 91A23: Differential games
- 91A24: Positional games (pursuit and evasion, etc.)
- 91A25: Dynamic games
- 91A26: Rationality, learning
- 91A28: Signaling, communication
- 91A30: Utility theory for games
- 91A35: Decision theory for games
- 91A40: Game-theoretic models
- 91A43: Games involving graphs
- 91A44: Games involving topology or set theory
- 91A46: Combinatorial games
- 91A50: Discrete-time games
- 91A55: Games of timing
- 91A60: Probabilistic games; gambling
- 91A65: Hierarchical games
- 91A70: Spaces of games
- 91A80: Applications of game theory
- 91A90: Experimental studies
- 91A99: None of the above, but in this section

- 91Bxx: Mathematical economics
- 91B02: Fundamental topics (basic mathematics, methodology; applicable to economics in general)
- 91B06: Decision theory
- 91B08: Individual preferences
- 91B10: Group preferences
- 91B12: Voting theory
- 91B14: Social choice
- 91B16: Utility theory
- 91B18: Public goods
- 91B24: Price theory and market structure
- 91B26: Market models (auctions, bargaining, bidding, selling, etc.)
- 91B28: Finance, portfolios, investment
- 91B30: Risk theory, insurance
- 91B32: Resource and cost allocation
- 91B38: Production theory, theory of the firm
- 91B40: Labor market, contracts
- 91B42: Consumer behavior, demand theory
- 91B44: Informational economics
- 91B50: Equilibrium: general theory
- 91B52: Special types of equilibria
- 91B54: Special types of economies
- 91B60: General economic models, trade models
- 91B62: Dynamic economic models, growth models
- 91B64: Macro-economic models (monetary models, models of taxation)
- 91B66: Multisectoral models
- 91B68: Matching models
- 91B70: Stochastic models
- 91B72: Spatial models
- 91B74: Models of real-world systems
- 91B76: Environmental economics (natural resource models, harvesting, pollution, etc.)
- 91B82: Statistical methods; economic indices and measures
- 91B84: Economic time series analysis
- 91B99: None of the above, but in this section

- 91Cxx: Social and behavioral sciences: general topics
- 91C05: Measurement theory
- 91C15: One- and multidimensional scaling
- 91C20: Clustering
- 91C99: None of the above, but in this section

- 91Dxx: Mathematical sociology (including anthropology)
- 91D10: Models of societies, social and urban evolution
- 91D20: Mathematical geography and demography
- 91D25: Spatial models
- 91D30: Social networks
- 91D35: Manpower systems
- 91D99: None of the above, but in this section

- 91Exx: Mathematical psychology
- 91E10: Cognitive psychology
- 91E30: Psychophysics and psychophysiology; perception
- 91E40: Memory and learning
- 91E45: Measurement and performance
- 91E99: None of the above, but in this section

- 91Fxx: Other social and behavioral sciences (mathematical treatment)
- 91F10: History, political science
- 91F20: Linguistics
- 91F99: None of the above, but in this section

- 92-xx: Biology and other natural sciences
- 92-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
- 92-01: Instructional exposition (textbooks, tutorial papers, etc.)
- 92-02: Research exposition (monographs, survey articles)
- 92-03: Historical (must also be assigned at least one classification number from Section 01)
- 92-04: Explicit machine computation and programs (not the theory of computation or programming)
- 92-06: Proceedings, conferences, collections, etc.
- 92-08: Computational methods
- 92Bxx: Mathematical biology in general
- 92B05: General biology and biomathematics
- 92B10: Taxonomy, statistics
- 92B15: General biostatistics
- 92B20: Neural networks, artificial life and related topics
- 92B99: None of the above, but in this section

- 92Cxx: Physiological, cellular and medical topics
- 92C05: Biophysics
- 92C10: Biomechanics
- 92C15: Developmental biology, pattern formation
- 92C17: Cell movement (chemotaxis, etc.)
- 92C20: Neural biology
- 92C30: Physiology (general)
- 92C35: Physiological flow
- 92C37: Cell biology
- 92C40: Biochemistry, molecular biology
- 92C45: Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
- 92C50: Medical applications (general)
- 92C55: Biomedical imaging and signal processing
- 92C60: Medical epidemiology
- 92C80: Plant biology
- 92C99: None of the above, but in this section

- 92Dxx: Genetics and population dynamics
- 92D10: Genetics
- 92D15: Problems related to evolution
- 92D20: Protein sequences, DNA sequences
- 92D25: Population dynamics (general)
- 92D30: Epidemiology
- 92D40: Ecology
- 92D50: Animal behavior
- 92D99: None of the above, but in this section

- 92Exx: Chemistry
- 92E10: Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
- 92E20: Classical flows, reactions, etc.
- 92E99: None of the above, but in this section
- 92F05: Other natural sciences

- 93-xx: Systems theory; control
- 93-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
- 93-01: Instructional exposition (textbooks, tutorial papers, etc.)
- 93-02: Research exposition (monographs, survey articles)
- 93-03: Historical (must also be assigned at least one classification number from Section 01)
- 93-04: Explicit machine computation and programs (not the theory of computation or programming)
- 93-06: Proceedings, conferences, collections, etc.
- 93Axx: General
- 93A05: Axiomatic system theory
- 93A10: General systems
- 93A13: Hierarchical systems
- 93A14: Decentralized systems
- 93A15: Large scale systems
- 93A30: Mathematical modeling (models of systems, model-matching, etc.)
- 93A99: None of the above, but in this section

- 93Bxx: Controllability, observability, and system structure
- 93B03: Attainable sets
- 93B05: Controllability
- 93B07: Observability
- 93B10: Canonical structure
- 93B11: System structure simplification
- 93B12: Variable structure systems
- 93B15: Realizations from input-output data
- 93B17: Transformations
- 93B18: Linearizations
- 93B20: Minimal systems representations
- 93B25: Algebraic methods
- 93B27: Geometric methods (including algebro-geometric)
- 93B28: Operator-theoretic methods
- 93B29: Differential-geometric methods
- 93B30: System identification
- 93B35: Sensitivity (robustness)
- 93B36: ${H]^\infty$-control
- 93B40: Computational methods
- 93B50: Synthesis problems
- 93B51: Design techniques (robust design, computer-aided design, etc.)
- 93B52: Feedback control
- 93B55: Pole and zero placement problems
- 93B60: Eigenvalue problems
- 93B99: None of the above, but in this section

- 93Cxx: Control systems, guided systems
- 93C05: Linear systems
- 93C10: Nonlinear systems
- 93C15: Systems governed by ordinary differential equations
- 93C20: Systems governed by partial differential equations
- 93C23: Systems governed by functional-differential equations
- 93C25: Systems in abstract spaces
- 93C30: Systems governed by functional relations other than differential equations
- 93C35: Multivariable systems
- 93C40: Adaptive control
- 93C41: Problems with incomplete information
- 93C42: Fuzzy control
- 93C55: Discrete-time systems
- 93C57: Sampled-data systems
- 93C62: Digital systems
- 93C65: Discrete event systems
- 93C70: Time-scale analysis and singular perturbations
- 93C73: Perturbations
- 93C80: Frequency-response methods
- 93C83: Control problems involving computers (process control, etc.)
- 93C85: Automated systems (robots, etc.)
- 93C95: Applications
- 93C99: None of the above, but in this section

- 93Dxx: Stability
- 93D05: Lyapunov and other classical stabilities (Lagrange, Poisson, $L^p, l^p$, etc.)
- 93D09: Robust stability
- 93D10: Popov-type stability of feedback systems
- 93D15: Stabilization of systems by feedback
- 93D20: Asymptotic stability
- 93D21: Adaptive or robust stabilization
- 93D25: Input-output approaches
- 93D30: Scalar and vector Lyapunov functions
- 93D99: None of the above, but in this section

- 93Exx: Stochastic systems and control
- 93E03: Stochastic systems, general
- 93E10: Estimation and detection
- 93E11: Filtering
- 93E12: System identification
- 93E14: Data smoothing
- 93E15: Stochastic stability
- 93E20: Optimal stochastic control
- 93E24: Least squares and related methods
- 93E25: Other computational methods
- 93E35: Stochastic learning and adaptive control
- 93E99: None of the above, but in this section

- 94-xx: Information and communication, circuits
- 94-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
- 94-01: Instructional exposition (textbooks, tutorial papers, etc.)
- 94-02: Research exposition (monographs, survey articles)
- 94-03: Historical (must also be assigned at least one classification number from Section 01)
- 94-04: Explicit machine computation and programs (not the theory of computation or programming)
- 94-06: Proceedings, conferences, collections, etc.
- 94Axx: Communication, information
- 94A05: Communication theory
- 94A08: Image processing (compression, reconstruction, etc.)
- 94A11: Application of orthogonal functions in communication
- 94A12: Signal theory (characterization, reconstruction, etc.)
- 94A13: Detection theory
- 94A14: Modulation and demodulation
- 94A15: Information theory, general
- 94A17: Measures of information, entropy
- 94A20: Sampling theory
- 94A24: Coding theorems (Shannon theory)
- 94A29: Source coding
- 94A34: Rate-distortion theory
- 94A40: Channel models
- 94A45: Prefix, length-variable, comma-free codes
- 94A50: Theory of questionnaires
- 94A55: Shift register sequences and sequences over finite alphabets
- 94A60: Cryptography
- 94A62: Authentication and secret sharing
- 94A99: None of the above, but in this section

- 94Bxx: Theory of error-correcting codes and error-detecting codes
- 94B05: Linear codes, general
- 94B10: Convolutional codes
- 94B12: Combined modulation schemes (including trellis codes)
- 94B15: Cyclic codes
- 94B20: Burst-correcting codes
- 94B25: Combinatorial codes
- 94B27: Geometric methods (including applications of algebraic geometry)
- 94B30: Majority codes
- 94B35: Decoding
- 94B40: Arithmetic codes
- 94B50: Synchronization error-correcting codes
- 94B60: Other types of codes
- 94B65: Bounds on codes
- 94B70: Error probability
- 94B75: Applications of the theory of convex sets and geometry of numbers (covering radius, etc.)
- 94B99: None of the above, but in this section

- 94Cxx: Circuits, networks
- 94C05: Analytic circuit theory
- 94C10: Switching theory, application of Boolean algebra; Boolean functions
- 94C12: Fault detection; testing
- 94C15: Applications of graph theory
- 94C30: Applications of design theory
- 94C99: None of the above, but in this section
- 94D05: Fuzzy sets and logic (in connection with questions of Section 94)

- 97-xx: Mathematics education
- 97-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
- 97-01: Instructional exposition (textbooks, tutorial papers, etc.)
- 97-02: Research exposition (monographs, survey articles)
- 97-03: Historical (must also be assigned at least one classification number from Section 01)
- 97-04: Explicit machine computation and programs (not the theory of computation or programming)
- 97-06: Proceedings, conferences, collections, etc.
- 97Axx: General
- 97A20: Recreational mathematics
- 97A40: Sociological issues
- 97A80: Standards
- 97A90: Fiction and games

- 97Bxx: Educational policy and educational systems
- 97B10: Educational research and planning
- 97B20: General education
- 97B30: Vocational education
- 97B40: Higher education
- 97B50: Teacher education
- 97B60: Out-of-school education. Adult and further education
- 97B70: Syllabuses. Curriculum guides, official documents
- 97B99: None of the above, but in this section

- 97Cxx: Psychology of and research in mathematics education
- 97C20: Affective aspects (motivation, anxiety, persistence, etc.)
- 97C30: Student learning and thinking (misconceptions, cognitive development, problem solving, etc.)
- 97C40: Assessment (large scale assessment, validity, reliability, etc.)
- 97C50: Theoretical perspectives (learning theories, epistemology, philosophies of teaching and learning, etc.)
- 97C60: Sociological aspects of learning (culture, group interactions, equity issues, etc.)
- 97C70: Teachers, and research on teacher education (teacher development, etc.)
- 97C80: Technological tools and other materials in teaching and learning (research on innovations, role in student learning, use of tools by teachers, etc.)
- 97C90: Teaching and curriculum (innovations, teaching practices, studies of curriculum materials, effective teaching, etc. )
- 97C99: None of the above, but in this section

- 97Dxx: Education and instruction in mathematics
- 97D10: Comparative studies on mathematics education
- 97D20: Philosophical and theoretical contributions to mathematical education
- 97D30: Goals of mathematics teaching. Curriculum development
- 97D40: Teaching methods and classroom techniques. Lesson preparation. Educational principles
- 97D50: Teaching problem solving and heuristic strategies
- 97D60: Achievement control and rating
- 97D70: Diagnosis, analysis and remediation of learning difficulties and student errors
- 97D80: Teaching units, draft lessons and master lessons
- 97D99: None of the above, but in this section

- 97Uxx: Educational material and media. Educational technology
- 97U20: Analysis of textbooks, development and evaluation of textbooks. Textbook use in the classroom
- 97U30: Teacher manuals and planning aids
- 97U40: Problem books; student competitions, examination questions
- 97U50: Computer assisted instruction and programmed instruction
- 97U60: Manipulative materials and their use in the classroom
- 97U70: Technological tools (computers, calculators, software, etc.) and their use in the classroom
- 97U80: Audiovisual media and their use in instruction
- 97U99: None of the above, but in this section