- 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