General
General mathematics
Mathematics for nonmathematicians (engineering, social sciences, etc.)
Problem books
Recreational mathematics [See also 97A20]
Bibliographies
External book reviews
Dictionaries and other general reference works
Formularies
Philosophy of mathematics [See also 03A05]
Methodology of mathematics, didactics [See also 97Cxx, 97Dxx]
General applied mathematics {For physics, see 00A79 and Sections 70 through 86}
Theory of mathematical modeling
General methods of simulation
Dimensional analysis
Physics (use more specific entries from Sections 70 through 86 when possible)
Miscellaneous topics
Collections of abstracts of lectures
Collections of articles of general interest
Collections of articles of miscellaneous specific content
Proceedings of conferences of general interest
Proceedings of conferences of miscellaneous specific interest
Festschriften
Volumes of selected translations
Miscellaneous volumes of translations
Collections of reprinted articles [See also 01A75]
History and biography [See also the classification number -03
General histories, source books
Ethnomathematics, general
Paleolithic, Neolithic
Indigenous cultures of the Americas
Other indigenous cultures (non-European)
Indigenous European cultures (pre-Greek, etc.)
Egyptian
Babylonian
Greek, Roman
China
Japan
Southeast Asia
Islam (Medieval)
India
Medieval
15th and 16th centuries, Renaissance
17th century
18th century
19th century
20th century
Twenty-first century
Contemporary
Future prospectives
Biographies, obituaries, personalia, bibliographies
Schools of mathematics
Universities
Other institutions and academies
Collected or selected works; reprintings or translations of classics [See also 00B60]
Sociology (and profession) of mathematics
Historiography
Bibliographic studies
Miscellaneous topics
Mathematical logic and foundations
Classical propositional logic
Classical first-order logic
Higher-order logic and type theory
Subsystems of classical logic (including intuitionistic logic)
Abstract deductive systems
Decidability of theories and sets of sentences [See also 11U05, 12L05, 20F10]
Foundations of classical theories (including reverse mathematics) [See also 03F35]
Mechanization of proofs and logical operations [See also 68T15]
Combinatory logic and lambda-calculus [See also 68N18]
Logic of knowledge and belief
Temporal logic
Modal logic {For knowledge and belief see 03B42; for temporal logic see 03B44; for provability logic see also 03F45}
Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52}
Probability and inductive logic [See also 60A05]
Many-valued logic
Fuzzy logic; logic of vagueness [See also 68T27, 68T37, 94D05]
Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.)
Intermediate logics
Other nonclassical logic
Logic of natural languages [See also 68T50, 91F20]
Logic in computer science [See also 68-XX]
Other applications of logic
None of the above, but in this section
Equational classes, universal algebra [See also 08Axx, 08Bxx, 18C05]
Basic properties of first-order languages and structures
Quantifier elimination, model completeness and related topics
Finite structures [See also 68Q15, 68Q19]
Denumerable structures
Ultraproducts and related constructions
Model-theoretic forcing
Other model constructions
Categoricity and completeness of theories
Interpolation, preservation, definability
Classification theory, stability and related concepts
Models with special properties (saturated, rigid, etc.)
Properties of classes of models
Set-theoretic model theory
Effective and recursion-theoretic model theory [See also 03D45]
Model-theoretic algebra [See also 08C10, 12Lxx, 13L05]
Models of arithmetic and set theory [See also 03Hxx]
Model theory of ordered structures; o-minimality
Models of other mathematical theories
Other classical first-order model theory
Logic on admissible sets
Other infinitary logic
Logic with extra quantifiers and operators [See also 03B42, 03B44, 03B45, 03B48]
Second- and higher-order model theory
Nonclassical models (Boolean-valued, sheaf, etc.)
Abstract model theory
Applications of model theory [See also 03C60]
None of the above, but in this section
Thue and Post systems, etc.
Automata and formal grammars in connection with logical questions [See also 68Q45, 68Q70, 68R15]
Turing machines and related notions [See also 68Q05]
Complexity of computation [See also 68Q15, 68Q17]
Recursive functions and relations, subrecursive hierarchies
Recursively (computably) enumerable sets and degrees
Other Turing degree structures
Other degrees and reducibilities
Undecidability and degrees of sets of sentences
Word problems, etc. [See also 06B25, 08A50, 20F10, 68R15]
Theory of numerations, effectively presented structures [See also 03C57; for intuitionistic and similar approaches see 03F55]
Recursive equivalence types of sets and structures, isols
Hierarchies
Computability and recursion theory on ordinals, admissible sets, etc.
Higher-type and set recursion theory
Inductive definability
Abstract and axiomatic computability and recursion theory
Applications of computability and recursion theory
None of the above, but in this section
Proof theory, general
Cut-elimination and normal-form theorems
Structure of proofs
Functionals in proof theory
Recursive ordinals and ordinal notations
Complexity of proofs
Relative consistency and interpretations
First-order arithmetic and fragments
Second- and higher-order arithmetic and fragments [See also 03B30]
Gödel numberings in proof theory
Provability logics and related algebras (e.g., diagonalizable algebras) [See also 03B45, 03G25, 06E25]
Metamathematics of constructive systems
Linear logic and other substructural logics [See also 03B47]
Intuitionistic mathematics
Constructive and recursive analysis [See also 03B30, 03D45, 26E40, 46S30, 47S30]
Other constructive mathematics [See also 03D45]
None of the above, but in this section
Boolean algebras [See also 06Exx]
Lattices and related structures [See also 06Bxx]
Quantum logic [See also 06C15, 81P10]
Cylindric and polyadic algebras; relation algebras
Lukasiewicz and Post algebras [See also 06D25, 06D30]
Other algebras related to logic [See also 03F45, 06D20, 06E25, 06F35]
Categorical logic, topoi [See also 18B25, 18C05, 18C10]
None of the above, but in this section
Nonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05]
Other applications of nonstandard models (economics, physics, etc.)
Nonstandard models of arithmetic [See also 11U10, 12L15, 13L05]
None of the above, but in this section
Combinatorics {For finite fields, see 11Txx}
Block designs [See also 51E05, 62K10]
Triple systems
Difference sets (number-theoretic, group-theoretic, etc.) [See also 11B13]
Orthogonal arrays, Latin squares, Room squares
Matrices (incidence, Hadamard, etc.)
Finite geometries [See also 51D20, 51Exx]
Other designs, configurations [See also 51E30]
Matroids, geometric lattices [See also 52B40, 90C27]
Packing and covering [See also 11H31, 52C15, 52C17]
Tessellation and tiling problems [See also 52C20, 52C22]
Polyominoes
None of the above, but in this section
Trees
Degree sequences
Topological graph theory, imbedding [See also 57M15, 57M25]
Distance in graphs
Coloring of graphs and hypergraphs
Perfect graphs
Directed graphs (digraphs), tournaments
Signed, gain and biased graphs
Graphs and groups [See also 20F65]
Enumeration of graphs and maps
Extremal problems [See also 90C35]
Paths and cycles [See also 90B10]
Connectivity
Eulerian and Hamiltonian graphs
Graphs and matrices
Generalized Ramsey theory
Isomorphism problems (reconstruction conjecture, etc.)
Graph representations (geometric and intersection representations, etc.)
Hypergraphs
Dominating sets, independent sets, cliques
Factorization, matching, covering and packing
Structural characterization of types of graphs
Graph labelling (graceful graphs, bandwidth, etc.)
Random graphs
Graph minors
Graph algorithms [See also 68R10, 68W05]
Applications
None of the above, but in this section
Extremal set theory
Ramsey theory
Transversal (matching) theory
Probabilistic methods
None of the above, but in this section
Symmetric functions
Tableaux, representations of the symmetric group [See also 20C30]
Combinatorial problems concerning the classical groups [See also 22E45, 33C80]
Group actions on designs, geometries and codes
Group actions on posets and homology groups of posets [See also 06A11]
Association schemes, strongly regular graphs
Orthogonal polynomials [See also 33C45, 33C50, 33D45]
None of the above, but in this section
Order, lattices, ordered algebraic structures [See also 18B35]
Total order
Partial order, general
Combinatorics of partially ordered sets
Algebraic aspects of posets [See also 05E25]
Semilattices [See also 20M10; for topological semilattices see 22A26]
Galois correspondences, closure operators
None of the above, but in this section
Structure theory
Ideals, congruence relations
Representation theory
Varieties of lattices
Complete lattices, completions
Free lattices, projective lattices, word problems [See also 03D40, 08A50, 20F10]
Topological lattices, order topologies [See also 06F30, 22A26, 54F05, 54H12]
Continuous lattices and posets, applications [See also 06B30, 06D10, 06F30, 18B35, 22A26, 68Q55]
None of the above, but in this section
Modular lattices, Desarguesian lattices
Semimodular lattices, geometric lattices
Complemented lattices, orthocomplemented lattices and posets [See also 03G12, 81P10]
Complemented modular lattices, continuous geometries
None of the above, but in this section
Structure and representation theory
Complete distributivity
Pseudocomplemented lattices
Heyting algebras [See also 03G25]
Frames, locales {For topological questions see 54-XX}
Post algebras [See also 03G20]
De Morgan algebras, Lukasiewicz algebras [See also 03G20]
MV-algebras
Lattices and duality
Fuzzy lattices (soft algebras) and related topics
None of the above, but in this section
Structure theory
Chain conditions, complete algebras
Stone space and related constructions
Ring-theoretic properties [See also 16E50, 16G30]
Boolean algebras with additional operations (diagonalizable algebras, etc.) [See also 03G25, 03F45]
Boolean functions [See also 94C10]
None of the above, but in this section
Ordered semigroups and monoids [See also 20Mxx]
Quantales
Noether lattices
Ordered groups [See also 20F60]
Ordered abelian groups, Riesz groups, ordered linear spaces [See also 46A40]
Ordered rings, algebras, modules {For ordered fields, see 12J15; see also 13J25, 16W80}
Topological lattices, order topologies [See also 06B30, 22A26, 54F05, 54H12]
BCK-algebras, BCI-algebras [See also 03G25]
None of the above, but in this section
General algebraic systems
Relational systems, laws of composition
Structure theory
Subalgebras, congruence relations
Automorphisms, endomorphisms
Operations, polynomials, primal algebras
Equational compactness
Word problems [See also 03D40, 06B25, 20F10, 68R15]
Partial algebras
Unary algebras
Finitary algebras
Infinitary algebras
Heterogeneous algebras
Applications of universal algebra in computer science
Fuzzy algebraic structures
None of the above, but in this section
Equational logic, Malcev (Maltsev) conditions
Congruence modularity, congruence distributivity
Lattices of varieties
Free algebras
Products, amalgamated products, and other kinds of limits and colimits [See also 18A30]
Subdirect products and subdirect irreducibility
Injectives, projectives
None of the above, but in this section
Categories of algebras [See also 18C05]
Axiomatic model classes [See also 03Cxx, in particular 03C60]
Quasivarieties
None of the above, but in this section
Number theory
Multiplicative structure; Euclidean algorithm; greatest common divisors
Congruences; primitive roots; residue systems
Power residues, reciprocity
Arithmetic functions; related numbers; inversion formulas
Primes
Factorization; primality
Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15]
Radix representation; digital problems {For metric results, see 11K16}
Other representations
None of the above, but in this section
Density, gaps, topology
Additive bases [See also 05B10]
Arithmetic progressions [See also 11N13]
Representation functions
Recurrences {For applications to special functions, see 33-XX}
Fibonacci and Lucas numbers and polynomials and generalizations
Sequences (mod $m$)
Farey sequences; the sequences ${1^k, 2^k, \cdots}$
Binomial coefficients; factorials; $q$-identities [See also 05A10, 05A30]
Bernoulli and Euler numbers and polynomials
Bell and Stirling numbers
Other combinatorial number theory
Special sequences and polynomials
Automata sequences
None of the above, but in this section
Polynomials [See also 13F20]
Matrices, determinants [See also 15A36]
None of the above, but in this section
Linear equations
Quadratic and bilinear equations
Cubic and quartic equations
Higher degree equations; Fermat's equation
Counting solutions of Diophantine equations
Multiplicative and norm form equations
Thue-Mahler equations
Exponential equations
Rational numbers as sums of fractions
Equations in many variables [See also 11P55]
Diophantine inequalities [See also 11J25]
Congruences in many variables
Representation problems [See also 11P55]
$p$-adic and power series fields
None of the above, but in this section
Quadratic forms over general fields
Quadratic forms over local rings and fields
Forms over real fields
Quadratic forms over global rings and fields
General binary quadratic forms
General ternary and quaternary quadratic forms; forms of more than two variables
Sums of squares and representations by other particular quadratic forms
Bilinear and Hermitian forms
Class numbers of quadratic and Hermitian forms
Analytic theory (Epstein zeta functions; relations with automorphic forms and functions)
Classical groups [See also 14Lxx, 20Gxx]
$K$-theory of quadratic and Hermitian forms
Galois cohomology of linear algebraic groups [See also 20G10]
Forms of degree higher than two
Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24]
Quadratic spaces; Clifford algebras [See also 15A63, 15A66]
$p$-adic theory
None of the above, but in this section
Elliptic curves over global fields [See also 14H52]
Elliptic curves over local fields [See also 14G20, 14H52]
Drinfeld modules; higher-dimensional motives, etc. [See also 14L05]
Abelian varieties of dimension $\gtr 1$ [See also 14Kxx]
Complex multiplication and moduli of abelian varieties [See also 14K22]
Elliptic and modular units [See also 11R27]
Arithmetic aspects of modular and Shimura varieties [See also 14G35]
Curves over finite and local fields [See also 14H25]
Varieties over finite and local fields [See also 14G15, 14G20]
Curves of arbitrary genus or genus $\ne 1$ over global fields [See also 14H25]
Varieties over global fields [See also 14G25]
$L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10]
Geometric class field theory [See also 11R37, 14C35, 19F05]
Heights [See also 14G40]
Polylogarithms and relations with $K$-theory
None of the above, but in this section
Lattices and convex bodies [See also 11P21, 52C05, 52C07]
Nonconvex bodies
Lattice packing and covering [See also 05B40, 52C15, 52C17]
Products of linear forms
Minima of forms
Quadratic forms (reduction theory, extreme forms, etc.)
Automorphism groups of lattices
Mean value and transfer theorems
Relations with coding theory
None of the above, but in this section
Homogeneous approximation to one number
Markov and Lagrange spectra and generalizations
Simultaneous homogeneous approximation, linear forms
Approximation by numbers from a fixed field
Inhomogeneous linear forms
Diophantine inequalities [See also 11D75]
Small fractional parts of polynomials and generalizations
Approximation in non-Archimedean valuations
Approximation to algebraic numbers
Continued fractions and generalizations [See also 11A55, 11K50]
Distribution modulo one [See also 11K06]
Irrationality; linear independence over a field
Transcendence (general theory)
Measures of irrationality and of transcendence
Metric theory
Algebraic independence; Gelfond's method
Linear forms in logarithms; Baker's method
Transcendence theory of elliptic and abelian functions
Transcendence theory of other special functions
Transcendence theory of Drinfel'd and $t$-modules
Results involving abelian varieties
Analogues of methods in Nevanlinna theory (work of Vojta et al.)
None of the above, but in this section
Trigonometric and exponential sums, general
Gauss and Kloosterman sums; generalizations
Estimates on exponential sums
Jacobsthal and Brewer sums; other complete character sums
Weyl sums
Sums over primes
Sums over arbitrary intervals
Estimates on character sums
None of the above, but in this section
$\zeta (s)$ and $L(s, \chi)$
Real zeros of $L(s, \chi)$; results on $L(1, \chi)$
Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses
Hurwitz and Lerch zeta functions
Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas
Zeta and $L$-functions in characteristic $p$
Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72}
Tauberian theorems [See also 40E05]
None of the above, but in this section
Distribution of primes
Primes in progressions [See also 11B25]
Distribution of integers with specified multiplicative constraints
Turán theory [See also 30Bxx]
Primes represented by polynomials; other multiplicative structure of polynomial values
Sieves
Applications of sieve methods
Asymptotic results on arithmetic functions
Asymptotic results on counting functions for algebraic and topological structures
Rate of growth of arithmetic functions
Distribution functions associated with additive and positive multiplicative functions
Other results on the distribution of values or the characterization of arithmetic functions
Distribution of integers in special residue classes
Applications of automorphic functions and forms to multiplicative problems [See also 11Fxx]
Generalized primes and integers
None of the above, but in this section
Waring's problem and variants
Lattice points in specified regions
Goldbach-type theorems; other additive questions involving primes
Applications of the Hardy-Littlewood method [See also 11D85]
Inverse problems of additive number theory
Elementary theory of partitions [See also 05A17]
Analytic theory of partitions
Partitions; congruences and congruential restrictions
None of the above, but in this section
Algebraic numbers; rings of algebraic integers
PV-numbers and generalizations; other special algebraic numbers
Polynomials (irreducibility, etc.)
Quadratic extensions
Cubic and quartic extensions
Cyclotomic extensions
Other abelian and metabelian extensions
Other number fields
Iwasawa theory
Units and factorization
Class numbers, class groups, discriminants
Galois theory
Integral representations related to algebraic numbers; Galois module structure of rings of integers [See also 20C10]
Galois cohomology [See also 12Gxx, 16H05, 19A31]
Class field theory
Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55]
Zeta functions and $L$-functions of number fields [See also 11M41, 19F27]
Distribution of prime ideals [See also 11N05]
Density theorems
Other analytic theory [See also 11Nxx]
Quaternion and other division algebras: arithmetic, zeta functions
Other algebras and orders, and their zeta and $L$-functions [See also 11S45, 16H05, 16Kxx]
Adèle rings and groups
Arithmetic theory of algebraic function fields [See also 14-XX]
Cyclotomic function fields (class groups, Bernoulli objects, etc.)
Class groups and Picard groups of orders
$K$-theory of global fields [See also 19Fxx]
Totally real and totally positive fields [See also 12J15]
None of the above, but in this section
Polynomials
Ramification and extension theory
Galois theory
Integral representations
Galois cohomology [See also 12Gxx, 16H05]
Class field theory; $p$-adic formal groups [See also 14L05]
Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50]
Zeta functions and $L$-functions [See also 11M41, 19F27]
Algebras and orders, and their zeta functions [See also 11R52, 11R54, 16H05, 16Kxx]
$K$-theory of local fields [See also 19Fxx]
Other analytic theory (analogues of beta and gamma functions, $p$-adic integration, etc.)
Other nonanalytic theory
Prehomogeneous vector spaces
None of the above, but in this section
Decidability [See also 03B25]
Ultraproducts [See also 03C20]
Model theory [See also 03Cxx]
Nonstandard arithmetic [See also 03H15]
None of the above, but in this section
Factorization
Primality
Algorithms; complexity [See also 68Q25]
Analytic computations
Algebraic number theory computations
Computer solution of Diophantine equations
Calculation of integer sequences
Evaluation of constants
Continued fraction calculations
Values of arithmetic functions; tables
None of the above, but in this section
Field theory and polynomials
Polynomials: factorization
Polynomials: location of zeros (algebraic theorems) {For the analytic theory, see 26C10, 30C15}
Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [See also 11Exx]
None of the above, but in this section
Polynomials (irreducibility, etc.)
Special polynomials
Equations
Skew fields, division rings [See also 11R52, 11R54, 11S45, 16Kxx]
Finite fields (field-theoretic aspects)
Hilbertian fields; Hilbert's irreducibility theorem
Field arithmetic
None of the above, but in this section
Algebraic extensions
Separable extensions, Galois theory
Inverse Galois theory
Inseparable extensions
Transcendental extensions
None of the above, but in this section
Galois cohomology [See also 14F22, 16H05, 16K50]
Cohomological dimension
None of the above, but in this section
Differential algebra [See also 13Nxx]
Difference algebra [See also 39Axx]
Abstract differential equations [See also 34Mxx]
$p$-adic differential equations [See also 11S80, 14G20]
None of the above, but in this section
Normed fields
Valued fields
Formally $p$-adic fields
Ordered fields
Topological semifields
General valuation theory [See also 13A18]
Non-Archimedean valued fields [See also 30G06, 32P05, 46S10, 47S10]
Krasner-Tate algebras [See mainly 32P05; see also 46S10, 47S10]
None of the above, but in this section
Near-fields [See also 16Y30]
Semifields [See also 16Y60]
None of the above, but in this section
Decidability [See also 03B25]
Ultraproducts [See also 03C20]
Model theory [See also 03C60]
Nonstandard arithmetic [See also 03H15]
None of the above, but in this section
Commutative rings and algebras
Graded rings [See also 16W50]
Divisibility
Radical theory
Ideals; multiplicative ideal theory
Valuations and their generalizations [See also 12J20]
Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
Characteristic $p$ methods (Frobenius endomorphism) and reduction to characteristic $p$; tight closure [See also 13B22]
Actions of groups on commutative rings; invariant theory [See also 14L24]
None of the above, but in this section
Extension theory
Galois theory
Morphisms
Integral dependence
Integral closure of rings and ideals [See also 13A35]; integrally closed rings, related rings (Japanese, etc.)
Going up; going down; going between
Polynomials over commutative rings [See also 11C08, 13F20, 13M10]
Quotients and localization
Completion [See also 13J10]
Étale and flat extensions; Henselization; Artin approximation [See also 13J15, 14B12, 14B25]
None of the above, but in this section
Structure, classification theorems
Projective and free modules and ideals [See also 19A13]
Injective and flat modules and ideals
Torsion modules and ideals
Other special types
Cohen-Macaulay modules [See also 13H10]
Dimension theory, depth, related rings (catenary, etc.)
Class groups [See also 11R29]
Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12]
None of the above, but in this section
Noetherian rings and modules
Artinian rings and modules, finite-dimensional algebras
Rings and modules of finite generation or presentation; number of generators
None of the above, but in this section
Dedekind, Prüfer and Krull rings and their generalizations
Euclidean rings and generalizations
Principal ideal rings
Factorial rings, unique factorization domains [See also 14M05]
Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25]
Formal power series rings [See also 13J05]
Valuation rings [See also 13A18]
Excellent rings
Seminormal rings
Rings with straightening laws, Hodge algebras
Face and Stanley-Reisner rings; simplicial complexes [See also 55U10]
None of the above, but in this section
Regular local rings
Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]
Multiplicity theory and related topics [See also 14C17]
None of the above, but in this section
Power series rings [See also 13F25]
Analytical algebras and rings [See also 32B05]
Complete rings, completion [See also 13B35]
Henselian rings [See also 13B40]
Global topological rings
Ordered rings [See also 06F25]
Real algebra [See also 12D15, 14Pxx]
None of the above, but in this section
Structure
Polynomials
None of the above, but in this section
Modules of differentials
Rings of differential operators and their modules [See also 16S32, 32C38]
Derivations
None of the above, but in this section
Polynomials, factorization [See also 12Y05]
Polynomial ideals, Gröbner bases [See also 13F20]
None of the above, but in this section
Algebraic geometry
Relevant commutative algebra [See also 13-XX]
Varieties and morphisms
Schemes and morphisms
Generalizations (algebraic spaces, stacks)
Noncommutative algebraic geometry
Elementary questions
None of the above, but in this section
Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]
Deformations of singularities [See also 14D15, 32S30]
Infinitesimal methods [See also 13D10]
Local deformation theory, Artin approximation, etc. [See also 13B40, 13D10]
Local cohomology [See also 13D45, 32C36]
Formal neighborhoods
Local structure of morphisms: étale, flat, etc. [See also 13B40]
None of the above, but in this section
Parametrization (Chow and Hilbert schemes)
Chow groups and rings
Intersection theory, characteristic classes, intersection multiplicities [See also 13H15]
Divisors, linear systems, invertible sheaves
Pencils, nets, webs [See also 53A60]
Picard groups
Algebraic cycles
Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture
Torelli problem [See also 32G20]
Applications of methods of algebraic $K$-theory [See also 19Exx]
Riemann-Roch theorems [See also 19E20, 19L10]
None of the above, but in this section
Structure of families (Picard-Lefschetz, monodromy, etc.)
Fibrations, degenerations
Variation of Hodge structures [See also 32G20]
Arithmetic ground fields (finite, local, global)
Formal methods; deformations [See also 13D10, 14B07, 32Gxx]
Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}
Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
Fine and coarse moduli spaces
None of the above, but in this section
Rational and birational maps
Birational automorphisms, Cremona group and generalizations
Rationality questions
Global theory and resolution of singularities [See also 14B05, 32S20, 32S45]
Coverings [See also 14H30]
Ramification problems [See also 11S15]
Embeddings
Minimal model program (Mori theory, extremal rays)
None of the above, but in this section
Vector bundles, sheaves, related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
Differentials and other special sheaves [See also 13Nxx, 32C38]
Vanishing theorems [See also 32L20]
Étale and other Grothendieck topologies and cohomologies
Brauer groups of schemes [See also 12G05, 16K50]
Classical real and complex cohomology
$p$-adic cohomology, crystalline cohomology
Homotopy theory; fundamental groups [See also 14H30]
de Rham cohomology [See also 14C30, 32C35, 32L10]
Motivic cohomology
Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
Topological properties
None of the above, but in this section
Rational points
Zeta-functions and related questions [See also 11G40] (Birch-Swinnerton-Dyer conjecture)
Finite ground fields
Local ground fields
Rigid analytic geometry
Global ground fields
Other nonalgebraically closed ground fields
Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)
Modular and Shimura varieties [See also 11F41, 11F46, 11G18]
Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50]
Applications to coding theory and cryptography [See also 94A60, 94B27, 94B40]
None of the above, but in this section
Algebraic functions; function fields [See also 11R58]
Families, moduli (algebraic)
Families, moduli (analytic) [See also 30F10, 32Gxx]
Singularities, local rings [See also 13Hxx, 14B05]
Arithmetic ground fields [See also 11Dxx, 11G05, 14Gxx]
Coverings, fundamental group [See also 14E20, 14F35]
Automorphisms
Jacobians, Prym varieties [See also 32G20]
Theta functions; Schottky problem [See also 14K25, 32G20]
Special curves and curves of low genus
Plane and space curves
Special divisors (gonality, Brill-Noether theory)
Elliptic curves [See also 11G05, 11G07, 14Kxx]
Riemann surfaces; Weierstrass points; gap sequences [See also 30Fxx]
Vector bundles on curves and their moduli [See also 14D20, 14F05]
Relationships with integrable systems
Relationships with physics
None of the above, but in this section
Families, moduli, classification: algebraic theory
Moduli, classification: analytic theory; relations with modular forms [See also 32G13]
Singularities [See also 14B05, 14E15]
Arithmetic ground fields [See also 11Dxx, 11G25, 11G35, 14Gxx]
Special surfaces {For Hilbert modular surfaces, see 14G35}
Rational and ruled surfaces
Elliptic surfaces
$K3$ surfaces and Enriques surfaces
Surfaces of general type
$3$-folds
Calabi-Yau manifolds, mirror symmetry
$4$-folds
$n$-folds ($n>4$)
Fano varieties
Automorphisms of surfaces and higher-dimensional varieties
Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx]
Hypersurfaces
Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)
Relationships with physics
None of the above, but in this section
Isogeny
Algebraic theory
Algebraic moduli, classification [See also 11G15]
Subvarieties
Arithmetic ground fields [See also 11Dxx, 11Fxx, 11Gxx, 14Gxx]
Analytic theory; abelian integrals and differentials
Complex multiplication [See also 11G15]
Theta functions [See also 14H42]
Picard schemes, higher Jacobians [See also 14H40, 32G20]
None of the above, but in this section
Formal groups, $p$-divisible groups [See also 55N22]
Group varieties
Group schemes
Affine algebraic groups, hyperalgebra constructions [See also 17B45, 18D35]
Geometric invariant theory [See also 13A50]
Group actions on varieties or schemes (quotients) [See also 13A50, 14L24]
Classical groups (geometric aspects) [See also 20Gxx, 51N30]
Other algebraic groups (geometric aspects)
None of the above, but in this section
Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also 13F45, 13H10]
Linkage [See also 13C40]
Low codimension problems
Complete intersections [See also 13C40]
Determinantal varieties [See also 13C40]
Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]
Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15]
Rational and unirational varieties
Toric varieties, Newton polyhedra [See also 52B20]
Supervarieties [See also 32C11, 58A50]
None of the above, but in this section
Projective techniques [See also 51N35]
Enumerative problems (combinatorial problems)
Classical problems, Schubert calculus
Configurations of linear subspaces
Varieties of low degree
Adjunction problems
Gromov-Witten invariants, quantum cohomology [See also 53D45]
None of the above, but in this section
Real algebraic sets [See also 12Dxx]
Semialgebraic sets and related spaces
Real analytic and semianalytic sets [See also 32B20, 32C05]
Nash functions and manifolds [See also 32C07, 58A07]
Topology of real algebraic varieties
None of the above, but in this section
Curves
Surfaces, hypersurfaces
Higher-dimensional varieties
Effectivity
None of the above, but in this section
Classification of affine varieties
Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
Jacobian problem
Group actions on affine varieties [See also 13A50, 14L30]
Affine fibrations [See also 14D06]
None of the above, but in this section
Linear and multilinear algebra; matrix theory
Associative rings and algebras {For the commutative case, see 13-XX}
Category-theoretic methods and results (except as in 16D90) [See also 18-XX]
Applications of logic [See also 03Cxx]
None of the above, but in this section
General module theory
Bimodules
Ideals
Infinite-dimensional simple rings (except as in 16Kxx)
Free, projective, and flat modules and ideals [See also 19A13]
Injective modules, self-injective rings [See also 16L60]
Simple and semisimple modules, primitive rings and ideals
Structure and classification (except as in 16Gxx), direct sum decomposition, cancellation
Other classes of modules and ideals [See also 16G50]
Module categories [See also 16Gxx, 16S90]; module theory in a category-theoretic context; Morita equivalence and duality
None of the above, but in this section
Representations of Artinian rings
Representations of quivers and partially ordered sets
Representations of orders, lattices, algebras over commutative rings [See also 16H05]
Cohen-Macaulay modules
Representation type (finite, tame, wild, etc.)
Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
None of the above, but in this section
Finite-dimensional {For crossed products, see 16S35}
Infinite-dimensional and general
Brauer groups [See also 12G05, 14F22]
None of the above, but in this section
Noncommutative local and semilocal rings, perfect rings
Quasi-Frobenius rings [See also 16D50]
None of the above, but in this section
Jacobson radical, quasimultiplication
Nil and nilpotent radicals, sets, ideals, rings
Prime and semiprime rings [See also 16D60, 16U10]
General radicals and rings {For radicals in module categories, see 16S90}
None of the above, but in this section
Finite rings and finite-dimensional algebras {For semisimple, see 16K20; for commutative, see 11Txx, 13Mxx}
Artinian rings and modules
Noetherian rings and modules
Localization and Noetherian rings [See also 16U20]
Chain conditions on annihilators and summands: Goldie-type conditions [See also 16U20], Krull dimension
Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence
Growth rate, Gelfand-Kirillov dimension
None of the above, but in this section
$T$-ideals, identities, varieties of rings and algebras
Semiprime p.i. rings, rings embeddable in matrices over commutative rings
Trace rings and invariant theory
Identities other than those of matrices over commutative rings
Other kinds of identities (generalized polynomial, rational, involution)
None of the above, but in this section
Rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)
Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)
Centralizing and normalizing extensions
Universal enveloping algebras of Lie algebras [See mainly 17B35]
Rings of differential operators [See also 13N10, 32C38]
Group rings [See also 20C05, 20C07], Laurent polynomial rings
Twisted and skew group rings, crossed products
Ordinary and skew polynomial rings and semigroup rings [See also 20M25]
Quadratic and Koszul algebras
Rings arising from non-commutative algebraic geometry
Smash products of general Hopf actions [See also 16W30]
Endomorphism rings; matrix rings [See also 15-XX]
Rings of functions, subdirect products, sheaves of rings
Extensions of rings by ideals
Deformations of rings [See also 13D10, 14D15]
Maximal ring of quotients, torsion theories, radicals on module categories [See also 13D30, 18E40] {For radicals of rings, see 16Nxx}
None of the above, but in this section
Integral domains
Ore rings, multiplicative sets, Ore localization
Divisibility, noncommutative UFDs
Units, groups of units
Center, normalizer (invariant elements)
Generalizations of commutativity
None of the above, but in this section
Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx]
Automorphisms and endomorphisms
Actions of groups and semigroups; invariant theory
Derivations, actions of Lie algebras
Coalgebras, bialgebras, Hopf algebras [See also 16S40, 57T05]; rings, modules, etc. on which these act
Ring-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50]
Graded rings and modules
``Super'' (or ``skew'') structure [See also 17A70, 17Bxx, 17C70] {For exterior algebras, see 15A75; for Clifford algebras, see 11E88, 15A66}
Valuations, completions, formal power series and related constructions [See also 13Jxx]
Filtered rings; filtrational and graded techniques
Topological and ordered rings and modules [See also 06F25, 13Jxx]
None of the above, but in this section
Near-rings [See also 12K05]
Semirings [See also 12K10]
None of the above, but in this section
Nonassociative rings and algebras
General theory
Power-associative rings
Noncommutative Jordan algebras
Flexible algebras
Algebras satisfying other identities
Leibniz algebras
Division algebras
Automorphisms, derivations, other operators
Ternary compositions
Other $n$-ary compositions $(n \ge 3)$
Quadratic algebras (but not quadratic Jordan algebras)
Free algebras
Structure theory
Radical theory
Superalgebras
Composition algebras
Valued algebras
None of the above, but in this section
Identities, free Lie (super)algebras
Structure theory
Representations, algebraic theory (weights)
Representations, analytic theory
Simple, semisimple, reductive (super)algebras (roots)
Exceptional (super)algebras
Solvable, nilpotent (super)algebras
Universal enveloping (super)algebras [See also 16S30]
Quantum groups (quantized enveloping algebras) and related deformations [See also 16W35, 20G42, 81R50, 82B23]
Automorphisms, derivations, other operators
Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx]
Modular Lie (super)algebras
Homological methods in Lie (super)algebras
Cohomology of Lie (super)algebras
Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50]
Lie bialgebras
Poisson algebras
Infinite-dimensional Lie (super)algebras [See also 22E65]
Lie algebras of vector fields and related (super) algebras
Kac-Moody (super)algebras (structure and representation theory)
Virasoro and related algebras
Vertex operators; vertex operator algebras and related structures
Graded Lie (super)algebras
Color Lie (super)algebras
Applications to integrable systems
Applications to physics
None of the above, but in this section
Identities and free Jordan structures
Structure theory
Radicals
Simple, semisimple algebras
Idempotents, Peirce decompositions
Associated groups, automorphisms
Associated manifolds
Associated geometries
Exceptional Jordan structures
Jordan structures associated with other structures [See also 16W10]
Finite-dimensional structures
Division algebras
Jordan structures on Banach spaces and algebras [See also 46H70, 46L70]
Super structures
Applications to physics
None of the above, but in this section
Alternative rings
Malcev (Maltsev) rings and algebras
Right alternative rings
$(\gamma, \delta)$-rings, including $(1,-1)$-rings
Lie-admissible algebras
Genetic algebras
None of the above, but in this section
Category theory; homological algebra {For commutative rings
Definitions, generalizations
Graphs, diagram schemes, precategories [See especially 20L05]
Foundations, relations to logic and deductive systems [See also 03-XX]
Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
Special properties of functors (faithful, full, etc.)
Natural morphisms, dinatural morphisms
Functor categories, comma categories
Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
Factorization of morphisms, substructures, quotient structures, congruences, amalgams
Categories admitting limits (complete categories), functors preserving limits, completions
Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
None of the above, but in this section
Equational categories [See also 03C05, 08C05]
Theories (e.g. algebraic theories), structure, and semantics [See also 03G30]
Triples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples [See also 18Gxx]
Algebras and Kleisli categories associated with monads
Sketches and generalizations
Accessible and locally presentable categories
Categorical semantics of formal languages [See also 68Q55, 68Q65]
None of the above, but in this section
Double categories, $2$-categories, bicategories and generalizations
Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23]
Closed categories (closed monoidal and Cartesian closed categories, etc.)
Enriched categories (over closed or monoidal categories)
Strong functors, strong adjunctions
Fibered categories
Structured objects in a category (group objects, etc.)
Operads [See also 55P48]
None of the above, but in this section
Preadditive, additive categories
Exact categories, abelian categories
Grothendieck categories
Embedding theorems [See also 18B15]
Derived functors and satellites
Derived categories, triangulated categories
Localization of categories
Torsion theories, radicals [See also 13D30, 16S90]
None of the above, but in this section
Projectives and injectives [See also 13C10, 13C11, 16D40, 16D50]
Resolutions; derived functors [See also 13D02, 16E05, 18E25]
Ext and Tor, generalizations, Künneth formula [See also 55U25]
Homological dimension [See also 13D05, 16E10]
Relative homological algebra, projective classes
Simplicial sets, simplicial objects (in a category) [See also 55U10]
Chain complexes [See also 18E30, 55U15]
Spectral sequences, hypercohomology [See also 55Txx]
Nonabelian homological algebra
Homotopical algebra
Other (co)homology theories [See also 19D55, 46L80, 58J20, 58J22]
None of the above, but in this section
$K$-theory [See also 16E20, 18F25]
Stability for projective modules [See also 13C10]
Efficient generation
Frobenius induction, Burnside and representation rings
$K_0$ of group rings and orders
$K_0$ of other rings
None of the above, but in this section
Stable range conditions
Stability for linear groups
$K_1$ of group rings and orders [See also 57Q10]
Congruence subgroup problems [See also 20H05]
None of the above, but in this section
Central extensions and Schur multipliers
Symbols, presentations and stability of $K_2$
$K_2$ and the Brauer group
Excision for $K_2$
None of the above, but in this section
$Q$- and plus-constructions
Algebraic $K$-theory of spaces
Symmetric monoidal categories [See also 18D10]
Karoubi-Villamayor-Gersten $K$-theory
Negative $K$-theory, NK and Nil
Higher symbols, Milnor $K$-theory
Computations of higher $K$-theory of rings [See also 13D15, 16E20]
$K$-theory and homology; cyclic homology and cohomology [See also 18G60]
None of the above, but in this section
$K$-theory of schemes [See also 14C35]
Algebraic cycles and motivic cohomology [See also 14C25, 14C35]
Relations with cohomology theories [See also 14Fxx]
None of the above, but in this section
Generalized class field theory [See also 11G45]
Symbols and arithmetic [See also 11R37]
Étale cohomology, higher regulators, zeta and $L$-functions [See also 11G40, 11R42, 11S40, 14F20, 14G10]
None of the above, but in this section
Stability for quadratic modules
Witt groups of rings [See also 11E81]
$L$-theory of group rings [See also 11E81]
Hermitian $K$-theory, relations with $K$-theory of rings
None of the above, but in this section
Finiteness and other obstructions in $K_0$
Whitehead (and related) torsion
Surgery obstructions [See also 57R67]
Obstructions to group actions
None of the above, but in this section
$K_0$ as an ordered group, traces
EXT and $K$-homology [See also 55N22]
Kasparov theory ($KK$-theory) [See also 58J22]
Index theory [See also 58J20, 58J22]
None of the above, but in this section
Riemann-Roch theorems, Chern characters
$J$-homomorphism, Adams operations [See also 55Q50]
Connective $K$-theory, cobordism [See also 55N22]
Equivariant $K$-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91]
Computations, geometric applications
None of the above, but in this section
Group theory and generalizations
Axiomatics and elementary properties
Metamathematical considerations {For word problems, see 20F10}
Applications of logic to group theory
None of the above, but in this section
General theory for finite groups
General theory for infinite groups
Characterization theorems
Primitive groups
Multiply transitive finite groups
Multiply transitive infinite groups
Finite automorphism groups of algebraic, geometric, or combinatorial structures [See also 05Bxx, 12F10, 20G40, 20H30, 51-XX]
Infinite automorphism groups [See also 12F10]
Symmetric groups
Subgroups of symmetric groups
Computational methods
None of the above, but in this section
Group rings of finite groups and their modules [See also 16S34]
Group rings of infinite groups and their modules [See also 16S34]
Hecke algebras and their representations
Integral representations of finite groups
$p$-adic representations of finite groups
Integral representations of infinite groups
Ordinary representations and characters
Modular representations and characters
Projective representations and multipliers
Representations of finite symmetric groups
Representations of infinite symmetric groups
Representations of finite groups of Lie type
Representations of sporadic groups
Applications of group representations to physics
Computational methods
None of the above, but in this section
Classification of simple and nonsolvable groups
Simple groups: alternating groups and groups of Lie type [See also 20Gxx]
Simple groups: sporadic groups
Solvable groups, theory of formations, Schunck classes, Fitting classes, $\pi$-length, ranks [See also 20F17]
Nilpotent groups, $p$-groups
Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure
Special subgroups (Frattini, Fitting, etc.)
Series and lattices of subgroups
Subnormal subgroups
Products of subgroups
Automorphisms
Arithmetic and combinatorial problems
None of the above, but in this section
Free nonabelian groups
Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
Subgroup theorems; subgroup growth
Groups acting on trees [See also 20F65]
Quasivarieties and varieties of groups
Chains and lattices of subgroups, subnormal subgroups [See also 20F22]
Limits, profinite groups
Extensions, wreath products, and other compositions [See also 20J05]
Local properties
Residual properties and generalizations
Maximal subgroups
Simple groups [See also 20D05]
General structure theorems
General theorems concerning automorphisms of groups
Groups with a $BN$-pair; buildings [See also 51E24]
Conjugacy classes
None of the above, but in this section
Generators, relations, and presentations
Cancellation theory; application of van Kampen diagrams [See also 57M05]
Word problems, other decision problems, connections with logic and automata [See also 03B25, 03D05, 03D40, 06B25, 08A50, 68Q70]
Commutator calculus
Derived series, central series, and generalizations
Solvable groups, supersolvable groups [See also 20D10]
Formations of groups, Fitting classes [See also 20D10]
Nilpotent groups [See also 20D15]
Generalizations of solvable and nilpotent groups
Other classes of groups defined by subgroup chains
FC-groups and their generalizations
Automorphism groups of groups [See also 20E36]
Representations of groups as automorphism groups of algebraic systems
Fundamental groups and their automorphisms [See also 57M05, 57Sxx]
Braid groups; Artin groups
Other groups related to topology or analysis
Associated Lie structures
Engel conditions
Periodic groups; locally finite groups
Reflection and Coxeter groups [See also 22E40, 51F15]
Ordered groups [See mainly 06F15]
Geometric group theory [See also 05C25, 20E08, 57Mxx]
Hyperbolic groups and nonpositively curved groups
Asymptotic properties of groups
None of the above, but in this section
Representation theory
Cohomology theory
Linear algebraic groups over arbitrary fields
Linear algebraic groups over the reals, the complexes, the quaternions
Linear algebraic groups over local fields and their integers
Linear algebraic groups over global fields and their integers
Linear algebraic groups over adèles and other rings and schemes
Linear algebraic groups over finite fields
Quantum groups (quantized function algebras) and their representations [See also 16W35, 17B37, 81R50]
Applications to physics
None of the above, but in this section
Unimodular groups, congruence subgroups [See also 11F06, 19B37, 22E40, 51F20]
Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx]
Other geometric groups, including crystallographic groups [See also 51-XX, especially 51F15, and 82D25]
Other matrix groups over fields
Other matrix groups over rings
Other matrix groups over finite fields
None of the above, but in this section
Finite abelian groups
Torsion groups, primary groups and generalized primary groups
Torsion-free groups, finite rank
Torsion-free groups, infinite rank
Mixed groups
Direct sums, direct products, etc.
Subgroups
Automorphisms, homomorphisms, endomorphisms, etc.
Extensions
Homological and categorical methods
Topological methods [See also 22A05, 22B05]
None of the above, but in this section
Free semigroups, generators and relations, word problems
Varieties of semigroups
General structure theory
Radical theory
Ideal theory
Commutative semigroups
Mappings of semigroups
Regular semigroups
Inverse semigroups
Orthodox semigroups
Semigroups of transformations, etc. [See also 47D03, 47H20, 54H15]
Semigroup rings, multiplicative semigroups of rings [See also 16S36, 16Y60]
Representation of semigroups; actions of semigroups on sets
Semigroups in automata theory, linguistics, etc. [See also 03D05, 68Q70, 68T50]
Connections of semigroups with homological algebra and category theory
None of the above, but in this section
Sets with a single binary operation (groupoids)
Loops, quasigroups [See also 05Bxx]
Ternary systems (heaps, semiheaps, heapoids, etc.)
$n$-ary systems $(n\ge 3)$
Hypergroups
Fuzzy groups [See also 03E72]
None of the above, but in this section
Topological groups, Lie groups {For transformation groups, see
Structure of general topological groups
Analysis on general topological groups
Structure of topological semigroups
Analysis on topological semigroups
Topological groupoids (including differentiable and Lie groupoids) [See also 58H05]
Representations of general topological groups and semigroups
Topological semilattices, lattices and applications [See also 06B30, 06B35, 06F30]
Other topological algebraic systems and their representations
None of the above, but in this section
General properties and structure of LCA groups
Structure of group algebras of LCA groups
None of the above, but in this section
General properties and structure of locally compact groups
Unitary representations of locally compact groups
Other representations of locally compact groups
Group algebras of locally compact groups
Representations of group algebras
$C^*$-algebras and $W$*-algebras in relation to group representations [See also 46Lxx]
Induced representations
Duality theorems
Ergodic theory on groups [See also 28Dxx]
Automorphism groups of locally compact groups
None of the above, but in this section
General theory of group and pseudogroup actions {For topological properties of spaces with an action, see 57S20}
Measurable group actions [See also 22D40, 28Dxx, 37Axx]
Homogeneous spaces {For general actions on manifolds or preserving geometrical structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups see especially 22E40}
Groups as automorphisms of other structures
Real functions [See also 54C30]
Continuity and differentiation questions
Implicit function theorems, Jacobians, transformations with several variables
Calculus of vector functions
Integration: length, area, volume [See also 28A75, 51M25]
Integral formulas (Stokes, Gauss, Green, etc.)
Convexity, generalizations
Absolutely continuous functions, functions of bounded variation
Special properties of functions of several variables, Hölder conditions, etc.
Representation and superposition of functions
None of the above, but in this section
Polynomials: analytic properties, etc. [See also 12Dxx, 12Exx]
Polynomials: location of zeros [See also 12D10, 30C15, 65H05]
Rational functions [See also 14Pxx]
None of the above, but in this section
Inequalities for trigonometric functions and polynomials
Inequalities involving other types of functions
Inequalities involving derivatives and differential and integral operators
Inequalities for sums, series and integrals
Other analytical inequalities
None of the above, but in this section
Real-analytic functions [See also 32B05, 32C05]
$C^\infty$-functions, quasi-analytic functions [See also 58C25]
Calculus of functions on infinite-dimensional spaces [See also 46G05, 58Cxx]
Calculus of functions taking values in infinite-dimensional spaces [See also 46E40, 46G10, 58Cxx]
Set-valued functions [See also 28B20, 54C60] {For nonsmooth analysis, see 49J52, 58Cxx, 90Cxx}
Non-Archimedean analysis [See also 12J25]
Nonstandard analysis [See also 03H05, 28E05, 54J05]
Constructive real analysis [See also 03F60]
Fuzzy real analysis [See also 03E72, 28E10]
Means [See also 47A64]
None of the above, but in this section
Measure and integration {For analysis on manifolds, see 58-XX}
Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]
Real- or complex-valued set functions
Contents, measures, outer measures, capacities
Abstract differentiation theory, differentiation of set functions [See also 26A24]
Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
Integration with respect to measures and other set functions
Spaces of measures, convergence of measures [See also 46E27, 60Bxx]
Measures and integrals in product spaces
Integration and disintegration of measures
Lifting theory [See also 46G15]
Measures on Boolean rings, measure algebras [See also 54H10]
Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]
Hausdorff and packing measures
Fractals [See also 37Fxx]
None of the above, but in this section
Vector-valued set functions, measures and integrals [See also 46G10]
Group- or semigroup-valued set functions, measures and integrals
Set functions, measures and integrals with values in ordered spaces
Set-valued set functions and measures; integration of set-valued functions; measurable selections [See also 26E25, 54C60, 54C65, 91B14]
None of the above, but in this section
Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
Set functions and measures on topological groups, Haar measures, invariant measures [See also 22Axx, 43A05]
Set functions and measures on topological spaces (regularity of measures, etc.)
Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11]
None of the above, but in this section
Nonstandard measure theory [See also 03H05, 26E35]
Fuzzy measure theory [See also 03E72, 26E50, 94D05]
Other connections with logic and set theory
None of the above, but in this section
Functions of a complex variable {For analysis on manifolds, see
Monogenic properties of complex functions (including polygenic and areolar monogenic functions)
Inequalities in the complex domain
None of the above, but in this section
Power series (including lacunary series)
Random power series
Boundary behavior of power series, over-convergence
Analytic continuation
Dirichlet series and other series expansions, exponential series [See also 11M41, 42-XX]
Completeness problems, closure of a system of functions
Continued fractions [See also 11A55, 40A15]
None of the above, but in this section
Polynomials
Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral) {For algebraic theory, see 12D10; for real methods, see 26C10}
Conformal mappings of special domains
Covering theorems in conformal mapping theory
Numerical methods in conformal mapping theory [See also 65E05]
General theory of conformal mappings
Kernel functions and applications
Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Coefficient problems for univalent and multivalent functions
General theory of univalent and multivalent functions
Quasiconformal mappings in the plane
Quasiconformal mappings in $R^n$, other generalizations
Extremal problems for conformal and quasiconformal mappings, variational methods
Extremal problems for conformal and quasiconformal mappings, other methods
Maximum principle; Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination
Capacity and harmonic measure in the complex plane [See also 31A15]
None of the above, but in this section
Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX]
Representations of entire functions by series and integrals
Special classes of entire functions and growth estimates
Entire functions, general theory
Meromorphic functions, general theory
Distribution of values, Nevanlinna theory
Cluster sets, prime ends, boundary behavior
Bloch functions, normal functions, normal families
Blaschke products, bounded mean oscillation, bounded characteristic, bounded functions, functions with positive real part
${H}^p$-classes
Quasi-analytic and other classes of functions
None of the above, but in this section
Compact Riemann surfaces and uniformization [See also 14H15, 32G15]
Harmonic functions on Riemann surfaces
Classification theory of Riemann surfaces
Ideal boundary theory
Differentials on Riemann surfaces
Fuchsian groups and automorphic functions [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx]
Kleinian groups [See also 20H10]
Conformal metrics (hyperbolic, Poincaré, distance functions)
Klein surfaces
Teichmüller theory [See also 32G15]
None of the above, but in this section
Non-Archimedean function theory [See also 12J25]; nonstandard function theory [See also 03H05]
Finely holomorphic functions and topological function theory
Generalizations of Bers or Vekua type (pseudoanalytic, $p$-analytic, etc.)
Discrete analytic functions
Other generalizations of analytic functions (including abstract-valued functions)
Functions of hypercomplex variables and generalized variables
None of the above, but in this section
Potential theory {For probabilistic potential theory, see 60J45}
Harmonic, subharmonic, superharmonic functions
Integral representations, integral operators, integral equations methods
Potentials and capacity, harmonic measure, extremal length [See also 30C85]
Boundary behavior (theorems of Fatou type, etc.)
Boundary value and inverse problems
Biharmonic, polyharmonic functions and equations, Poisson's equation
Connections with differential equations
None of the above, but in this section
Harmonic, subharmonic, superharmonic functions
Integral representations, integral operators, integral equations methods
Potentials and capacities, extremal length
Boundary value and inverse problems
Boundary behavior
Biharmonic and polyharmonic equations and functions
Connections with differential equations
None of the above, but in this section
Harmonic, subharmonic, superharmonic functions
Pluriharmonic and plurisubharmonic functions [See also 32U05]
Potential theory on Riemannian manifolds [See also 53C20; for Hodge theory, see 58A14]
Potentials and capacities
Discrete potential theory and numerical methods
Dirichlet spaces
Martin boundary theory [See also 60J50]
Fine potential theory
Other generalizations (nonlinear potential theory, etc.)
None of the above, but in this section
Several complex variables and analytic spaces {For infinite-
Power series, series of functions
Special domains (Reinhardt, Hartogs, circular, tube)
Holomorphic functions
Multifunctions
Entire functions
Special families of functions
Bloch functions, normal functions
Normal families of functions, mappings
Meromorphic functions
Nevanlinna theory (local); growth estimates; other inequalities {For geometric theory, see 32H25, 32H30}
Integral representations; canonical kernels (Szegó, Bergman, etc.)
Integral representations, constructed kernels (e.g. Cauchy, Fantappiè-type kernels)
Local theory of residues [See also 32C30]
Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30) {For functions of several hypercomplex variables, see 30G35}
${H}^p$-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15]
Bergman spaces
Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx]
Algebras of holomorphic functions [See also 30H05, 46J10, 46J15]
Boundary behavior of holomorphic functions
Hyperfunctions [See also 46F15]
Harmonic analysis of several complex variables [See mainly 43-XX]
Singular integrals
Zero sets of holomorphic functions
Banach algebra techniques [See mainly 46Jxx]
Functional analysis techniques [See mainly 46Exx]
None of the above, but in this section
Analytic algebras and generalizations, preparation theorems
Germs of analytic sets, local parametrization
Analytic subsets of affine space
Semi-analytic sets and subanalytic sets [See also 14P15]
Triangulation and related questions
None of the above, but in this section
Deformations of complex structures [See also 13D10, 16S80, 58H10, 58H15]
Deformations of special (e.g. CR) structures
Deformations of fiber bundles
Deformations of submanifolds and subspaces
Analytic moduli problems {For algebraic moduli problems, see 14D20, 14D22, 14H10, 14J10} [See also 14H15, 14J15]
Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]
Period matrices, variation of Hodge structure; degenerations [See also 14D05, 14D07, 14K30]
Moduli and deformations for ordinary differential equations (e.g. Khnizhnik-Zamolodchikov equation) [See also 34Mxx]
Applications to physics
None of the above, but in this section
Holomorphic mappings, (holomorphic) embeddings and related questions
Meromorphic mappings
Boundary uniqueness of mappings
Picard-type theorems and generalizations {For function-theoretic properties, see 32A22}
Value distribution theory in higher dimensions {For function-theoretic properties, see 32A22}
Proper mappings, finiteness theorems
Boundary regularity of mappings
Iteration problems
None of the above, but in this section
Compactification of analytic spaces
Algebraic dependence theorems
Compact surfaces
Compact $3$-folds
Compact $n$-folds
Transcendental methods of algebraic geometry [See also 14C30]
Compact Kähler manifolds: generalizations, classification
Applications to physics
None of the above, but in this section
Banach analytic spaces [See also 58Bxx]
Formal and graded complex spaces [See also 58C50]
Differentiable functions on analytic spaces, differentiable spaces [See also 58C25]
None of the above, but in this section
Holomorphic bundles and generalizations
Sheaves and cohomology of sections of holomorphic vector bundles, general results [See also 14F05, 18F20, 55N30]
Bundle convexity [See also 32F10]
Vanishing theorems
Twistor theory, double fibrations [See also 53C28]
Applications to physics
None of the above, but in this section
Complex Lie groups, automorphism groups acting on complex spaces [See also 22E10]
Homogeneous complex manifolds [See also 14M17, 57T15]
Almost homogeneous manifolds and spaces [See also 14M17]
Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15]
Automorphism groups of ${\bf C}^n$ and affine manifolds
Complex vector fields
None of the above, but in this section
General theory of automorphic functions of several complex variables
Automorphic forms
Automorphic functions in symmetric domains
None of the above, but in this section
Local dynamics around a fixed point
Bifurcation theory
Iterations of polynomial automorphism
Dynamics of holomorphic and meromorphic maps
Hyperbolic maps
Classification of Fatou components
Invariant currents and measures, ergodic theory
Holomorphic vector fields
Holomorphic foliations and laminations
Computer graphs
None of the above, but in this section
Local singularities [See also 14J17]
Invariants of analytic local rings
Equisingularity (topological and analytic) [See also 14E15]
Global theory of singularities; cohomological properties [See also 14E15]
Relations with arrangements of hyperplanes [See also 52C35]
Surface and hypersurface singularities [See also 14J17]
Deformations of singularities; vanishing cycles [See also 14B07]
Mixed Hodge theory of singular varieties [See also 14C30, 14D07]
Monodromy; relations with differential equations and $D$-modules
Modifications; resolution of singularities [See also 14E15]
Topological aspects: Lefschetz theorems, topological classification, invariants
Milnor fibration; relations with knot theory [See also 57M25, 57Q45]
Stratifications; constructible sheaves; intersection cohomology [See also 58Kxx]
Singularities of holomorphic vector fields and foliations
Other operations on singularities
None of the above, but in this section
Domains of holomorphy
Strongly pseudoconvex domains
Worm domains
Finite type domains
Geometric and analytic invariants on weakly pseudoconvex boundaries
Exhaustion functions
Peak functions
None of the above, but in this section
Plurisubharmonic functions and generalizations [See also 31C10]
Plurisubharmonic exhaustion functions
General pluripotential theory
Capacity theory and generalizations
Lelong numbers
Removable sets
Pluricomplex Green functions
Currents
None of the above, but in this section
CR structures, CR operators, and generalizations
CR functions
CR manifolds as boundaries of domains
Analysis on CR manifolds
Extension of functions and other analytic objects from CR manifolds
Embeddings of CR manifolds
Finite type conditions on CR manifolds
Real submanifolds in complex manifolds
None of the above, but in this section
Special functions (33-XX deals with the properties of functions
Exponential and trigonometric functions
Gamma, beta and polygamma functions
Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)
Higher logarithm functions
None of the above, but in this section
Classical hypergeometric functions, $_2F_1$
Bessel and Airy functions, cylinder functions, $_0F_1$
Confluent hypergeometric functions, Whittaker functions, $_1F_1$
Generalized hypergeometric series, $_pF_q$
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions]
Other special orthogonal polynomials and functions
Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable
Orthogonal polynomials and functions associated with root systems
Spherical harmonics
Hypergeometric integrals and functions defined by them ($E$, $G$ and ${H}$ functions)
Appell, Horn and Lauricella functions
Hypergeometric functions associated with root systems
Other hypergeometric functions and integrals in several variables
Elliptic integrals as hypergeometric functions
Connections with groups and algebras, and related topics
Applications
None of the above, but in this section
$q$-gamma functions, $q$-beta functions and integrals
Basic hypergeometric functions in one variable, ${}_r\phi_s$
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable
Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)
Basic hypergeometric integrals and functions defined by them
Bibasic functions and multiple bases
Basic hypergeometric functions associated with root systems
Other basic hypergeometric functions and integrals in several variables
Connections with quantum groups, Chevalley groups, $p$-adic groups, Hecke algebras, and related topics
Applications
None of the above, but in this section
Elliptic functions and integrals
Lamé, Mathieu, and spheroidal wave functions
Mittag-Leffler functions and generalizations
Other wave functions
Painlevé-type functions
Other functions defined by series and integrals
Other functions coming from differential, difference and integral equations
Special functions in characteristic $p$ (gamma functions, etc.)
None of the above, but in this section
Numerical approximation [See also 65D20]
Symbolic computation (Gosper and Zeilberger algorithms, etc.) [See also 68W30]
None of the above, but in this section
Ordinary differential equations
Explicit solutions and reductions
Implicit equations, differential-algebraic equations [See also 65L80]
Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions
Analytical theory: series, transformations, transforms, operational calculus, etc. [See also 44-XX]
Geometric methods in differential equations
Linear equations and systems, general
Nonlinear equations and systems, general
Differential equations of infinite order
Discontinuous equations
Differential equations with impulses
Differential inequalities [See also 26D20]
Theoretical approximation of solutions {For numerical analysis, see 65Lxx}
Inverse problems
Differential inclusions [See also 49J24, 49K24]
None of the above, but in this section
Linear boundary value problems
Linear boundary value problems with nonlinear dependence on the spectral parameter
Multi-parameter boundary value problems
Boundary value problems with an indefinite weight
Multipoint boundary value problems
Nonlinear boundary value problems
Singular nonlinear boundary value problems
Positive solutions of nonlinear boundary value problems
Weyl theory and its generalizations
Sturm-Liouville theory [See also 34Lxx]
Green functions
Special equations (Mathieu, Hill, Bessel, etc.)
Boundary value problems with impulses
Boundary value problems on infinite intervals
Boundary value problems on graphs and networks
Applications
None of the above, but in this section
Asymptotic expansions
Perturbations, asymptotics
Multiple scale methods
Singular perturbations, general theory
Methods of nonstandard analysis
Singular perturbations, turning point theory, WKB methods
None of the above, but in this section
General spectral theory
Eigenfunction expansions, completeness of eigenfunctions
Estimation of eigenvalues, upper and lower bounds
Numerical approximation of eigenvalues and of other parts of the spectrum
Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions
Scattering theory
Nonlinear ordinary differential operators
Particular operators (Dirac, one-dimensional Schrödinger, etc.)
None of the above, but in this section
Entire and meromorphic solutions
Oscillation, growth of solutions
Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical)
Nonanalytic aspects
Formal solutions, transform techniques
Asymptotics, summation methods
Singularities, monodromy, local behavior of solutions, normal forms
Resurgence phenomena
Stokes phenomena and connection problems (linear and nonlinear)
Differential equations on complex manifolds
Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.)
Painlevé and other special equations; classification, hierarchies; isomonodromic deformations
Singular perturbation problems in the complex domain (complex WKB, turning points, steepest descent) [See also 34E20]
None of the above, but in this section
Partial differential equations
PDE with discontinuous coefficients or data
Partial functional-differential or differential-difference equations, with or without deviating arguments
Impulsive partial differential equations
Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in infinitely many variables) [See also 46Gxx, 58D25]
Partial operator-differential equations (i.e. PDE on finite-dimensional spaces for abstract space valued functions) [See also 34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx]
Improperly posed problems for PDE
Inverse problems (undetermined coefficients, etc.) for PDE
Free boundary problems for PDE
Partial differential inequalities
Partial differential equations of infinite order
Partial differential equations with randomness [See also 60H15]
PDE with multivalued right-hand sides
None of the above, but in this section
Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx,
Measure-preserving transformations
One-parameter continuous families of measure-preserving transformations
General groups of measure-preserving transformations [See mainly 22Fxx]
Homogeneous flows [See also 22Fxx]
Orbit equivalence, cocycles, ergodic equivalence relations
Ergodicity, mixing, rates of mixing
Ergodic theorems, spectral theory, Markov operators {For operator ergodic theory, see mainly 47A35}
Entropy and other invariants, isomorphism, classification
Nonsingular (and infinite-measure preserving) transformations
Relations with number theory and harmonic analysis [See also 11Kxx]
Relations with probability theory and stochastic processes [See also 60Fxx and 60G10]
Relations with the theory of $C^*$-algebras [See mainly 46L55]
Dynamical systems in statistical mechanics [See also 82Cxx]
None of the above, but in this section
Transformations and group actions with special properties (minimality, distality, proximality, etc.)
Symbolic dynamics [See also 37Cxx, 37Dxx]
Cellular automata
Notions of recurrence
Lyapunov functions and stability; attractors, repellers
Index theory, Morse-Conley indices
Gradient-like and recurrent behavior; isolated (locally-maximal) invariant sets
Topological entropy
Continua theory in dynamics
Multi-dimensional shifts of finite type, tiling dynamics
Nonautonomous dynamical systems
None of the above, but in this section
Smooth mappings and diffeomorphisms
Vector fields, flows, ordinary differential equations
Topological and differentiable equivalence, conjugacy, invariants, moduli, classification
Generic properties, structural stability
Fixed points, periodic points, fixed-point index theory
Periodic orbits of vector fields and flows
Homoclinic and heteroclinic orbits
Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems
Orbit growth
Smooth ergodic theory, invariant measures [See also 37Dxx]
Dimension theory of dynamical systems
Approximate trajectories (pseudotrajectories, shadowing, etc.)
Periodic and quasiperiodic flows and diffeomorphisms
Nonautonomous smooth dynamical systems [See also 37B55]
Monotone flows
Attractors and repellers, topological structure
Stability theory
Symmetries, equivariant dynamical systems
Dynamics of group actions other than Z and R, and foliations [See mainly 22Fxx, and also 57R30, 57Sxx]
None of the above, but in this section
Hyperbolic orbits and sets
Invariant manifold theory
Morse-Smale systems
Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
Partially hyperbolic systems and dominated splittings
Thermodynamic formalism, variational principles, equilibrium states
Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
Strange attractors, chaotic dynamics
Hyperbolic systems with singularities (billiards, etc.)
None of the above, but in this section
Maps of the interval (piecewise continuous, continuous, smooth)
Maps of the circle
Combinatorial dynamics (types of periodic orbits)
Universality, renormalization [See also 37F25]
Maps of trees and graphs
Homeomorphisms and diffeomorphisms of planes and surfaces
Flows on surfaces
Twist maps
Rotation numbers and vectors
None of the above, but in this section
Relations and correspondences
Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04]
Expanding maps; hyperbolicity; structural stability
Combinatorics and topology
Renormalization
Quasiconformal methods and Teichmüller theory; Fuchsian and Kleinian groups as dynamical systems
Conformal densities and Hausdorff dimension
Geometric limits
Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations
Small divisors, rotation domains and linearization; Fatou and Julia sets
Holomorphic foliations and vector fields [See also 32M25, 32S65, 34Mxx]
None of the above, but in this section
Normal forms
Bifurcations of singular points
Bifurcations of limit cycles and periodic orbits
Hyperbolic singular points with homoclinic trajectories
Bifurcations connected with nontransversal intersection
Infinite nonwandering sets arising in bifurcations
Attractors and their bifurcations
Symmetries, equivariant bifurcation theory
None of the above, but in this section
Foundations, general theory of cocycles, algebraic ergodic theory [See also 37Axx]
Generation, random and stochastic difference and differential equations [See also 34F05, 34K50, 60H10, 60H15]
Multiplicative ergodic theory, Lyapunov exponents [See also 34D08, 37Axx, 37Cxx, 37Dxx]
Bifurcation theory [See also 37Gxx]
None of the above, but in this section
General theory, relations with symplectic geometry and topology
Symplectic mappings, fixed points
Symmetries, invariants, invariant manifolds, momentum maps, reduction [See also 53D20]
Bifurcation problems
Stability problems
Obstructions to integrability (nonintegrability criteria)
Completely integrable systems, topological structure of phase space, integration methods
Perturbations, normal forms, small divisors, KAM theory, Arnold diffusion
Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
Action-minimizing orbits and measures
Contact systems [See also 53D10]
Nonholonomic dynamical systems [See also 70F25]
None of the above, but in this section
General theory, nonlinear semigroups, evolution equations
Normal forms, center manifold theory, bifurcation theory
Stability problems
Symmetries
Inertial manifolds and other invariant attracting sets
Attractors and their dimensions, Lyapunov exponents
Invariant measures
Hyperbolicity; Lyapunov functions
Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systems
Infinite-dimensional random dynamical systems; stochastic equations [See also 35R60, 60H10, 60H15]
Lattice dynamics [See also 37K60]
Special approximation methods (nonlinear Galerkin, etc.)
None of the above, but in this section
Simulation
Time series analysis
Symplectic integrators
Computational methods for bifurcation problems
Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy)
None of the above, but in this section
Dynamical systems in classical and celestial mechanics [See mainly 70Fxx, 70Hxx, 70Kxx]
Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly 76-XX, especially 76D05, 76F20, 86A05, 86A10]
Dynamical systems in solid mechanics [See mainly 74Hxx]
Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
Dynamical systems in biology [See mainly 92-XX, but also 91-XX]
Dynamical systems in numerical analysis
Dynamical systems in control
Dynamical systems in optimization and economics
None of the above, but in this section
Difference and functional equations
General
Difference equations, additive
Stability and asymptotics of difference equations; oscillatory and periodic solutions, etc.
Discrete version of topics in analysis
Difference equations, scaling ($q$-differences) [See also 33Dxx]
Multiplicative and other generalized difference equations, e.g. of Lyness type
Difference operators [See also 47B39]
None of the above, but in this section
General
Iteration theory, iterative and composite equations [See also 26A18, 30D05, 37-XX]
Equations for real functions [See also 26A51, 26B25]
Equations for complex functions [See also 30D05]
Matrix and operator equations [See also 47Jxx]
Equations for functions with more general domains and/or ranges
Orthogonal additivity and other conditional equations
Functional inequalities, including subadditivity, convexity, etc. [See also 26A51, 26B25, 26Dxx]
Systems of functional equations and inequalities
Stability, separation, extension, and related topics [See also 46A22]
None of the above, but in this section
Sequences, series, summability
Convergence and divergence of series and sequences
Convergence and divergence of integrals
Convergence and divergence of continued fractions [See also 30B70]
Convergence and divergence of infinite products
Approximation to limiting values (summation of series, etc.) {For the Euler-Maclaurin summation formula, see 65B15}
Convergence and divergence of series and sequences of functions
None of the above, but in this section
Matrix methods
Integral methods
Function-theoretic methods (including power series methods and semicontinuous methods)
None of the above, but in this section
General theorems
Structure of summability fields
Tauberian constants and oscillation limits
Convergence factors and summability factors
Summability and bounded fields of methods
Inclusion and equivalence theorems
None of the above, but in this section
Tauberian theorems, general
Growth estimates
Lacunary inversion theorems
Tauberian constants
None of the above, but in this section
Cesàro, Euler, Nörlund and Hausdorff methods
Abel, Borel and power series methods
None of the above, but in this section
Approximations and expansions {For all approximation theory in the
Fourier analysis
Abstract harmonic analysis {For other analysis on topological and
Integral transforms, operational calculus {For fractional
Integral equations
Functional analysis {For manifolds modeled on topological linear
General theory of locally convex spaces
Locally convex Fréchet spaces and (DF)-spaces
Barrelled spaces, bornological spaces
Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
Spaces defined by inductive or projective limits (LB, LF, etc.) [See also 46M40]
Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
Bornologies and related structures; Mackey convergence, etc.
Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than ${\bf R}$, etc.)
Duality theory
Theorems of Hahn-Banach type; extension and lifting of functionals and operators [See also 46M10]
Reflexivity and semi-reflexivity [See also 46B10]
Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness)
Spaces of linear operators; topological tensor products; approximation properties [See also 46B28, 46M05, 47L05, 47L20]
Summability and bases [See also 46B15]
Ordered topological linear spaces, vector lattices [See also 06F20, 46B40, 46B42]
Sequence spaces (including Köthe sequence spaces) [See also 46B45]
Compactness in topological linear spaces; angelic spaces, etc.
Convex sets in topological linear spaces; Choquet theory [See also 52A07]
Graded Fréchet spaces and tame operators
Topological invariants ((DN), ($\Omega$), etc.)
Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)
Modular spaces
None of the above, but in this section
Isomorphic theory (including renorming) of Banach spaces
Isometric theory of Banach spaces
Local theory of Banach spaces
Ultraproduct techniques in Banach space theory [See also 46M07]
Probabilistic methods in Banach space theory [See also 60Bxx]
Duality and reflexivity [See also 46A25]
Summability and bases [See also 46A35]
Geometry and structure of normed linear spaces
Radon-Nikodym, Krein-Milman and related properties [See also 46G10]
Classical Banach spaces in the general theory
Nonseparable Banach spaces
Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]
Ordered normed spaces [See also 46A40, 46B42]
Banach lattices [See also 46A40, 46B40]
Banach sequence spaces [See also 46A45]
Compactness in Banach (or normed) spaces
Interpolation between normed linear spaces [See also 46M35]
None of the above, but in this section
Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) [See also 46B70, 46M35]
Characterizations of Hilbert spaces
Spaces with indefinite inner product (Krein spaces, Pontryagin spaces, etc.) [See also 47B50]
Generalizations of inner products (semi-inner products, partial inner products, etc.)
None of the above, but in this section
Lattices of continuous, differentiable or analytic functions
Topological linear spaces of continuous, differentiable or analytic functions
Banach spaces of continuous, differentiable or analytic functions
Hilbert spaces of continuous, differentiable or analytic functions
Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32]
Rings and algebras of continuous, differentiable or analytic functions {For Banach function algebras, see 46J10, 46J15}
Spaces of measures [See also 28A33, 46Gxx]
Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
Sobolev (and similar kinds of) spaces of functions of discrete variables
Spaces of vector- and operator-valued functions
Spaces of differentiable or holomorphic functions on infinite-dimensional spaces [See also 46G20, 46G25, 47H60]
None of the above, but in this section
General theory of topological algebras
Ideals and subalgebras
Representations of topological algebras
Structure, classification of topological algebras
Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
Functional calculus in topological algebras [See also 47A60]
Topological algebras of operators [See mainly 47Lxx]
Automatic continuity
Nonassociative topological algebras [See also 46K70, 46L70]
None of the above, but in this section
General theory of commutative topological algebras
Banach algebras of continuous functions, function algebras [See also 46E25]
Banach algebras of differentiable or analytic functions, ${H}^p$-spaces [See also 30D55, 30H05, 32A35, 32A37, 32A38, 42B30]
Ideals, maximal ideals, boundaries
Representations of commutative topological algebras
Subalgebras
Structure, classification of commutative topological algebras
Radical Banach algebras
None of the above, but in this section
General theory of topological algebras with involution
Representations of topological algebras with involution
Hilbert algebras
Nonselfadjoint (sub)algebras in algebras with involution
Nonassociative topological algebras with an involution [See also 46H70, 46L70]
None of the above, but in this section
Tensor products [See also 46A32, 46B28, 47A80]
Ultraproducts [See also 46B08, 46S20]
Projective and injective objects [See also 46A22]
Categories, functors {For $K$-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M20}
Homological methods (exact sequences, right inverses, lifting, etc.)
Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.) [See also 14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx]
Abstract interpolation of topological vector spaces [See also 46B70]
Inductive and projective limits [See also 46A13]
None of the above, but in this section
Applications in optimization, convex analysis, mathematical programming, economics
Applications to differential and integral equations
Applications in probability theory and statistics
Applications in numerical analysis [See also 65Jxx]
Applications in quantum physics
Applications in statistical physics
Applications in biology and other sciences
None of the above, but in this section
Functional analysis over fields other than R or C or the quaternions; non-Archimedean functional analysis [See also 12J25, 32P05]
Nonstandard functional analysis [See also 03H05]
Constructive functional analysis [See also 03F60]
Fuzzy functional analysis [See also 03E72]
Functional analysis in probabilistic metric linear spaces
Functional analysis on superspaces (supermanifolds) or graded spaces [See also 58A50 and 58C50]
None of the above, but in this section
Operator theory
Riesz operators; eigenvalue distributions; approximation numbers, $s$-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
Operators defined by compactness properties
Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20]
Hermitian and normal operators (spectral measures, functional calculus, etc.)
Subnormal operators, hyponormal operators, etc.
Symmetric and selfadjoint operators (unbounded)
Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) [See also 46E22]
Composition operators
Kernel operators
Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
Jacobi (tridiagonal) operators (matrices) and generalizations
Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
Operators on function spaces (general)
Difference operators [See also 39A70]
Spectral operators, decomposable operators, well-bounded operators, etc.
Accretive operators, dissipative operators, etc.
Commutators, derivations, elementary operators, etc.
Operators on Banach algebras
Transformers (= operators on spaces of operators)
Operators on spaces with an indefinite metric [See also 46C50]
Operators on ordered spaces
Positive operators and order-bounded operators
Random operators [See also 60H25]
None of the above, but in this section
Operators in algebras
Operators in $^*$-algebras
Operators in $C^*$- or von Neumann algebras
None of the above, but in this section
Integral operators [See also 45P05]
Integro-differential operators [See also 34K30, 35R10, 45J05, 45K05]
Pseudodifferential operators [See also 35Sxx, 58Jxx]
None of the above, but in this section
Equations involving nonlinear operators (general)
Nonlinear ill-posed problems
Abstract inverse mapping and implicit function theorems [See also 46T20 and 58C15]
Nonlinear eigenvalue problems
Abstract bifurcation theory [See also 58E07, 58E09]
Variational and other types of inequalities involving nonlinear operators (general)
Methods for solving nonlinear operator equations (general)
Variational methods [See also 58Exx]
Nonlinear evolution equations [See also 34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx, 37Lxx, 58D25]
Equations with hysteresis operators
None of the above, but in this section
Applications in optimization, convex analysis, mathematical programming, economics
Applications to differential and integral equations
Applications in probability theory and statistics
Applications in numerical analysis [See also 65Jxx]
Applications in quantum physics
Applications in statistical physics
Applications in biology and other sciences
Applications in systems theory, circuits, etc.
None of the above, but in this section
Operator theory over fields other than R, C or the quaternions; non-Archimedean operator theory
Nonstandard operator theory [See also 03H05]
Constructive operator theory [See also 03F60]
Fuzzy operator theory [See also 03E72]
Operator theory in probabilistic metric linear spaces
None of the above, but in this section
Calculus of variations and optimal control; optimization
Free problems in one independent variable
Free problems in two or more independent variables
Optimal control problems involving ordinary differential equations
Optimal control problems involving partial differential equations
Optimal control problems involving integral equations
Optimal control problems involving differential inclusions [See also 34A60]
Optimal control problems involving equations with retarded arguments [See also 34K35]
Problems in abstract spaces [See also 90C48, 93C25]
Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
Minimax problems
Variational methods including variational inequalities [See also 47J20]
Methods involving semicontinuity and convergence; relaxation
Fréchet and Gateaux differentiability [See also 46G05, 58C20]
Nonsmooth analysis [See also 46G05, 58C50]
Set-valued and variational analysis [See also 28B20, 47H04, 54C60, 58C06]
Problems involving randomness [See also 93E20]
None of the above, but in this section
Free problems in one independent variable
Free problems in two or more independent variables
Problems involving ordinary differential equations
Problems involving partial differential equations
Problems involving integral equations
Problems involving differential inclusions [See also 34A60]
Problems involving equations with retarded arguments [See also 34K35]
Problems in abstract spaces [See also 90C48, 93C25]
Optimal solutions belonging to restricted classes
Minimax problems
Sensitivity, stability, well-posedness [See also 90C31]
Problems involving randomness [See also 93E20]
None of the above, but in this section
Dynamic programming method
Viscosity solutions
None of the above, but in this section
Methods based on necessary conditions
Methods of Newton-Raphson, Galerkin and Ritz types
Methods of relaxation type
Discrete approximations
Decomposition methods
Methods involving duality
Other methods, not based on necessary conditions (penalty function, etc.)
Methods of nonlinear programming type [See also 90C30, 65Kxx]
None of the above, but in this section
Linear optimal control problems [See also 93C05]
Linear-quadratic problems
Duality theory
Periodic optimization
Impulsive optimal control problems
Problems with incomplete information [See also 93C41]
Optimal feedback synthesis [See also 93B52]
Inverse problems
Regularity of solutions
Differential games
Pursuit and evasion games
Applications of optimal control and differential games [See also 90C90, 93C95]
None of the above, but in this section
Geometry {For algebraic geometry, see 14-XX}
General theory and projective geometries
Homomorphism, automorphism and dualities
Structures with parallelism
Configuration theorems
Algebraization [See also 12Kxx, 20N05]
Desarguesian and Pappian geometries
Non-Desarguesian affine and projective planes
Translation planes and spreads
Incidence structures imbeddable into projective geometries
Polar geometry, symplectic spaces, orthogonal spaces
None of the above, but in this section
General theory
Möbius geometries
Laguerre geometries
Minkowski geometries
Lie geometries
None of the above, but in this section
Abstract (Maeda) geometries
Abstract geometries with exchange axiom
Abstract geometries with parallelism
Combinatorial geometries [See also 05B25, 05B35]
Lattices of subspaces [See also 05B35]
Continuous geometries and related topics [See also 06Cxx]
None of the above, but in this section
General block designs [See also 05B05]
Steiner systems
Generalized quadrangles, generalized polygons
Finite partial geometries (general), nets, partial spreads
Affine and projective planes
Combinatorial structures in finite projective spaces [See also 05Bxx]
Blocking sets, ovals, $k$-arcs
Linear codes and caps in Galois spaces [See also 94B05]
Spreads and packing problems
Buildings and the geometry of diagrams
Other finite nonlinear geometries
Other finite linear geometries
Other finite incidence structures [See also 05B30]
None of the above, but in this section
Absolute planes
Absolute spaces
Reflection groups, reflection geometries [See also 20H10, 20H15; for Coxeter groups, see 20F55]
Congruence and orthogonality [See also 20H05]
Orthogonal and unitary groups [See also 20H05]
None of the above, but in this section
General theory
Topological linear incidence structures
Topological nonlinear incidence structures
Topological geometries on manifolds [See also 57-XX]
Geometries with differentiable structure [See also 53Cxx, 53C70]
Geometries with algebraic manifold structure [See also 14-XX]
None of the above, but in this section
General theory
Projective incidence groups
Kinematic spaces
Representation by near-fields and near-algebras [See also 12K05, 16Y30]
None of the above, but in this section
General theory
Synthetic differential geometry
None of the above, but in this section
Geometry of orders of nondifferentiable curves
Directly differentiable curves
$n$-vertex theorems via direct methods
Geometry of orders of surfaces
None of the above, but in this section
Elementary problems in Euclidean geometries
Euclidean geometries (general) and generalizations
Elementary problems in hyperbolic and elliptic geometries
Hyperbolic and elliptic geometries (general) and generalizations
Geometric constructions
Inequalities and extremum problems {For convex problems, see 52A40}
Polyhedra and polytopes; regular figures, division of spaces [See also 51F15]
Length, area and volume [See also 26B15]
Line geometries and their generalizations [See also 53A25]
Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) [See also 14M15]
None of the above, but in this section
Descriptive geometry [See also 65D17, 68U07]
Affine analytic geometry
Projective analytic geometry
Euclidean analytic geometry
Analytic geometry with other transformation groups
Geometry of classical groups [See also 20Gxx, 14L35]
Questions of classical algebraic geometry [See also 14Nxx]
None of the above, but in this section
Convex and discrete geometry
Axiomatic and generalized convexity
Convex sets without dimension restrictions
Convex sets in topological vector spaces [See also 46A55]
Convex sets in $2$ dimensions (including convex curves) [See also 53A04]
Convex sets in $3$ dimensions (including convex surfaces) [See also 53A05, 53C45]
Convex sets in $n$ dimensions (including convex hypersurfaces) [See also 53A07, 53C45]
Finite-dimensional Banach spaces (including special norms, zonoids, etc.) [See also 46Bxx]
Random convex sets and integral geometry [See also 53C65, 60D05]
Approximation by convex sets
Variants of convex sets (star-shaped, ($m, n$)-convex, etc.)
Helly-type theorems and geometric transversal theory
Other problems of combinatorial convexity
Length, area, volume [See also 26B15, 28A75, 49Q20]
Mixed volumes and related topics
Inequalities and extremum problems
Convex functions and convex programs [See also 26B25, 90C25]
Spherical and hyperbolic convexity
None of the above, but in this section
Combinatorial properties (number of faces, shortest paths, etc.) [See also 05Cxx]
Three-dimensional polytopes
$n$-dimensional polytopes
Special polytopes (linear programming, centrally symmetric, etc.)
Symmetry properties of polytopes
Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx]
Shellability
Gale and other diagrams
Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) [See also 05B35, 52Cxx]
Dissections and valuations (Hilbert's third problem, etc.)
Computational aspects related to convexity {For computational geometry and algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx} [See also 68Uxx]
Isoperimetric problems for polytopes
Polyhedral manifolds
None of the above, but in this section
Lattices and convex bodies in $2$ dimensions [See also 11H06, 11H31, 11P21]
Lattices and convex bodies in $n$ dimensions [See also 11H06, 11H31, 11P21]
Erdös problems and related topics of discrete geometry [See also 11Hxx]
Packing and covering in $2$ dimensions [See also 05B40, 11H31]
Packing and covering in $n$ dimensions [See also 05B40, 11H31]
Tilings in $2$ dimensions [See also 05B45, 51M20]
Tilings in $n$ dimensions [See also 05B45, 51M20]
Quasicrystals, aperiodic tilings
Rigidity and flexibility of structures [See also 70B15]
Circle packings and discrete conformal geometry
Planar arrangements of lines and pseudolines
Arrangements of points, flats, hyperplanes [See also 32S22]
Oriented matroids
Combinatorial complexity of geometric structures [See also 68U05]
None of the above, but in this section
Differential geometry {For differential topology, see 57Rxx. For
Curves in Euclidean space
Surfaces in Euclidean space
Higher-dimensional and -codimensional surfaces in Euclidean $n$-space
Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Affine differential geometry
Kinematics
Projective differential geometry
Differential line geometry
Conformal differential geometry
Non-Euclidean differential geometry
Other special differential geometries
Vector and tensor analysis
Differential invariants (local theory), geometric objects
Geometry of webs [See also 14C21, 20N05]
None of the above, but in this section
Linear and affine connections
Projective connections
Other connections
Local Riemannian geometry
Methods of Riemannian geometry
Local submanifolds [See also 53C40]
Lorentz metrics, indefinite metrics
Hermitian and Kählerian structures [See also 32Cxx]
Finsler spaces and generalizations (areal metrics)
Applications to physics
None of the above, but in this section
Symplectic manifolds, general
Contact manifolds, general
Lagrangian submanifolds; Maslov index
Almost contact and almost symplectic manifolds
Poisson manifolds
Momentum maps; symplectic reduction
Canonical transformations
Geodesic flows
Symplectic structures of moduli spaces
Global theory of symplectic and contact manifolds [See also 57Rxx]
Floer homology and cohomology, symplectic aspects
Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]
Geometric quantization
Deformation quantization, star products
None of the above, but in this section
General topology {For the topology of manifolds of all dimensions,
Connected and locally connected spaces (general aspects)
Lower separation axioms ($T_0$--$T_3$, etc.)
Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
Noncompact covering properties (paracompact, Lindelöf, etc.)
``$P$-minimal'' and ``$P$-closed'' spaces
Compactness
Extensions of spaces (compactifications, supercompactifications, completions, etc.)
Remainders
Local compactness, $\sigma$-compactness
$k$-spaces
Sequential spaces
Realcompactness and realcompactification
Separability
Base properties
Special constructions of spaces (spaces of ultrafilters, etc.)
None of the above, but in this section
Proximity structures and generalizations
Uniform structures and generalizations
Nearness spaces
$p$-spaces, $M$-spaces, $\sigma$-spaces, etc.
Stratifiable spaces, cosmic spaces, etc.
Semimetric spaces
Moore spaces
Metric spaces, metrizability
Special maps on metric spaces
Compact (locally compact) metric spaces
Complete metric spaces
Baire category, Baire spaces
Bitopologies
Probabilistic metric spaces
None of the above, but in this section
Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces [See also 06B30, 06F30]
Continua and generalizations
Higher-dimensional local connectedness [See also 55Mxx, 55Nxx]
Dimension theory [See also 55M10]
Spaces of dimension $\leq 1$; curves, dendrites [See also 26A03]
Unicoherence, multicoherence
Topological characterizations of particular spaces
None of the above, but in this section
Extremally disconnected spaces, $F$-spaces, etc.
$P$-spaces
Scattered spaces
Pathological spaces
Counterexamples
None of the above, but in this section
Algebraic topology
Duality
Dimension theory [See also 54F45]
Absolute neighborhood retracts [See also 54C55]
Fixed points and coincidences [See also 54H25]
Degree, winding number
Ljusternik-Schnirelman (Lyusternik-Shnirelman) category of a space
Finite groups of transformations (including Smith theory) [See also 57S17]
None of the above, but in this section
Homotopy extension properties, cofibrations
Homotopy equivalences
Classification of homotopy type
Eilenberg-Mac Lane spaces
Spanier-Whitehead duality
Eckmann-Hilton duality
Loop spaces
Suspensions
Stable homotopy theory, spectra
Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.)
${H}$-spaces and duals
Infinite loop spaces
Loop space machines, operads [See also 18D50]
Shape theory [See also 54C56, 55Q07]
Proper homotopy theory
Localization and completion
Rational homotopy theory
Homotopy functors
Equivariant homotopy theory [See also 19L47]
Relations between equivariant and nonequivariant homotopy theory
None of the above, but in this section
Homotopy groups, general; sets of homotopy classes
Shape groups
Stable homotopy groups
Whitehead products and generalizations
Homotopy groups of wedges, joins, and simple spaces
Hopf invariants
Operations in homotopy groups
Homotopy groups of spheres
Stable homotopy of spheres
$J$-morphism [See also 19L20]
$v_n$-periodicity
Homotopy groups of special spaces
Cohomotopy groups
Homotopy groups of special types [See also 55N05, 55N07]
Equivariant homotopy groups [See also 19L47]
None of the above, but in this section
Fiber spaces
Fiber bundles
Transfer
Classification
Spectral sequences and homology of fiber spaces [See also 55Txx]
Sphere bundles and vector bundles
Classifying spaces of groups and ${H}$-spaces
Maps between classifying spaces
Homology of classifying spaces, characteristic classes [See also 57Txx, 57R20]
Homology and homotopy of $B{\rm O}$ and $B{\rm U}$; Bott periodicity
Stable classes of vector space bundles, $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19-XX}
Fiberings with singularities
Microbundles and block bundles [See also 57N55, 57Q50]
Generalizations of fiber spaces and bundles
Fibrewise topology
Discriminantal varieties, configuration spaces
Equivariant fiber spaces and bundles [See also 19L47]
None of the above, but in this section
Primary cohomology operations
Steenrod algebra
Dyer-Lashof operations
Symmetric products, cyclic products
Secondary and higher cohomology operations
$K$-theory operations and generalized cohomology operations [See also 19D55, 19Lxx]
Massey products
Obstruction theory
Extension and compression of mappings
Classification of mappings
Sectioning fiber spaces and bundles
Postnikov systems, $k$-invariants
Equivariant operations and obstructions [See also 19L47]
None of the above, but in this section
General
Serre spectral sequences
Adams spectral sequences
Eilenberg-Moore spectral sequences [See also 57T35]
Generalized cohomology
None of the above, but in this section
Manifolds and cell complexes {For complex manifolds, see 32Qxx}
Fundamental group, presentations, free differential calculus
Topological methods in group theory
Covering spaces
Special coverings, e.g. branched
Relations with graph theory [See also 05Cxx]
Two-dimensional complexes
Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Invariants of knots and 3-manifolds
Wild knots and surfaces, etc., wild embeddings
Dehn's lemma, sphere theorem, loop theorem, asphericity
Characterizations of $E^3$ and $S^3$ (Poincaré conjecture) [See also 57N12]
Geometric structures on low-dimensional manifolds
Group actions in low dimensions
None of the above, but in this section
Local properties of generalized manifolds
Poincaré duality spaces
None of the above, but in this section
General topology of complexes
Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28]
Wall finiteness obstruction for CW-complexes
Triangulating manifolds
Cobordism
Comparison of PL-structures: classification, Hauptvermutung
Engulfing
Embeddings and immersions
Isotopy
Regular neighborhoods
Knots and links (in high dimensions) {For the low-dimensional case, see 57M25}
Microbundles and block bundles [See also 55R60, 57N55]
Approximations
Cobordism and concordance
General position and transversality
Equivariant PL-topology
None of the above, but in this section
Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx,
Pseudogroups and differentiable groupoids [See also 22A22, 22E65]
Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) [See also 57R32]
Deformations of structures [See also 32Gxx, 58J10]
None of the above, but in this section
Critical points of functions and mappings
Monodromy
Topological properties of mappings
Algebraic and analytic properties of mappings
Stability
Global theory
Catastrophe theory
Classification; finite determinacy of map germs
Singularities of vector fields, topological aspects
Normal forms
Asymptotic behavior
Deformation of singularities
Topological invariants
Symmetries, equivariance
None of the above, but in this section
Probability theory and stochastic processes {For additional
Axioms; other general questions
Probabilistic measure theory {For ergodic theory, see 28Dxx and 60Fxx}
None of the above, but in this section
Probability measures on topological spaces
Convergence of probability measures
Probability theory on linear topological spaces [See also 28C20]
Limit theorems for vector-valued random variables (infinite-dimensional case)
Probability measures on groups, Fourier transforms, factorization
None of the above, but in this section
Distributions: general theory
Infinitely divisible distributions; stable distributions
Characteristic functions; other transforms
Inequalities; stochastic orderings
None of the above, but in this section
Central limit and other weak theorems
Large deviations
Strong theorems
Functional limit theorems; invariance principles
Zero-one laws
$L^p$-limit theorems
None of the above, but in this section
Foundations of stochastic processes
General theory of processes
Exchangeability
Stationary processes
General second-order processes
Gaussian processes
Sample path properties
Self-similar processes
Generalized stochastic processes
Prediction theory [See also 62M20]
Continuity and singularity of induced measures
Applications (signal detection, filtering, etc.) [See also 62M20, 93E10, 93E11, 94Axx]
Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Martingales with discrete parameter
Martingales with continuous parameter
Martingales and classical analysis
Generalizations of martingales
Sums of independent random variables; random walks
Processes with independent increments
Stable processes
Point processes
Random measures
Random fields
Extreme value theory; extremal processes
None of the above, but in this section
Statistics
Sufficient statistics and fields
Information-theoretic topics [See also 94A17]
Theory of statistical experiments
None of the above, but in this section
General considerations
Complete class results
Bayesian problems; characterization of Bayes procedures
Empirical decision procedures; empirical Bayes procedures
Admissibility
Minimax procedures
Compound decision problems
None of the above, but in this section
Characterization and structure theory
Exact distribution theory
Approximations to distributions (nonasymptotic)
Asymptotic distribution theory
None of the above, but in this section
Hypothesis testing
Asymptotic properties of tests
Ranking and selection
Point estimation
Asymptotic properties of estimators
Bayesian inference
Tolerance and confidence regions
Inference under constraints
Robustness and adaptive procedures
Bootstrap, jackknife and other resampling methods
None of the above, but in this section
Estimation
Density estimation
Nonparametric regression
Resampling methods
Hypothesis testing
Tolerance and confidence regions
Asymptotic properties
Order statistics; empirical distribution functions
Statistics of extreme values; tail inference
Robustness
None of the above, but in this section
Characterization and structure theory
Distribution of statistics
Directional data; spatial statistics
Estimation
Hypothesis testing
Contingency tables
Measures of association (correlation, canonical correlation, etc.)
Factor analysis and principal components; correspondence analysis
Classification and discrimination; cluster analysis [See also 68T10]
Image analysis
None of the above, but in this section
General nonlinear regression
Linear regression
Ridge regression; shrinkage estimators
Analysis of variance and covariance
Generalized linear models
Paired and multiple comparisons
Diagnostics
None of the above, but in this section
Optimal designs
Block designs
Factorial designs
Response surface designs
Robust parameter designs
None of the above, but in this section
Sequential design
Sequential analysis
Sequential estimation
Optimal stopping [See also 60G40, 91A60]
Stochastic approximation
None of the above, but in this section
Markov processes: hypothesis testing
Markov processes: estimation
Non-Markovian processes: hypothesis testing
Non-Markovian processes: estimation
Time series, auto-correlation, regression, etc. [See also 91B84]
Spectral analysis
Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]
Spatial processes
Random fields; image analysis
Neural nets and related approaches
None of the above, but in this section
Censored data models
Estimation
Testing
Reliability and life testing [See also 90B25]
None of the above, but in this section
Applications to actuarial sciences and financial mathematics
Applications to biology and medical sciences
Applications to environmental and related topics
Applications to psychology
Applications to economics [See also 91Bxx]
Applications to social sciences
Applications in engineering and industry
Applications to physics
None of the above, but in this section
Numerical analysis
Extrapolation to the limit, deferred corrections
Summation of series
Euler-Maclaurin formula
None of the above, but in this section
Monte Carlo methods
Random number generation
Models, numerical methods [See also 68U20]
Stochastic differential and integral equations
Stochastic particle methods [See also 82C80]
Computational Markov chains
Other computational problems in probability
Computational problems in statistics
None of the above, but in this section
Direct methods for linear systems and matrix inversion
Iterative methods for linear systems [See also 65N22]
Eigenvalues, eigenvectors
Inverse eigenvalue problems
Overdetermined systems, pseudoinverses
Ill-posedness, regularization
Orthogonalization
Other matrix algorithms
Matrix norms, conditioning, scaling [See also 15A12, 15A60]
Determinants
Sparse matrices
None of the above, but in this section
Algorithms with automatic result verification
Interval and finite arithmetic
General methods in interval analysis
Roundoff error
None of the above, but in this section
Single equations
Systems of equations
Eigenvalues, eigenvectors [See also 47Hxx, 47Jxx, 58C40, 58E07, 90C30]
Global methods, including homotopy approaches [See also 58C30, 90C30]
None of the above, but in this section
General theory
Equations with linear operators (do not use 65Fxx)
Equations with nonlinear operators (do not use 65Hxx)
Improperly posed problems; regularization
Inverse problems
None of the above, but in this section
Initial value problems
Multistep, Runge-Kutta and extrapolation methods
Numerical investigation of stability of solutions
Improperly posed problems
Inverse problems
Boundary value problems
Finite difference methods
Eigenvalue problems
Stability and convergence of numerical methods
Mesh generation and refinement
Finite elements, Rayleigh-Ritz, Galerkin and collocation methods
Error bounds
Methods for differential-algebraic equations
None of the above, but in this section
Finite difference methods
Stability and convergence of numerical methods
Error bounds
Method of lines
Method of characteristics
Improperly posed problems
Inverse problems
Mesh generation and refinement
Multigrid methods; domain decomposition
Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Spectral, collocation and related methods
None of the above, but in this section
Finite difference methods
Stability and convergence of numerical methods
Error bounds
Inverse problems
Solution of discretized equations [See also 65Fxx, 65Hxx]
Eigenvalue problems
Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Spectral, collocation and related methods
Boundary element methods
Method of lines
Method of contraction of the boundary
Mesh generation and refinement
Multigrid methods; domain decomposition
None of the above, but in this section
Hamiltonian systems including symplectic integrators
Numerical chaos
Bifurcation problems
Nonlinear stabilities
None of the above, but in this section
Trigonometric approximation and interpolation
Discrete and fast Fourier transforms
Wavelets
None of the above, but in this section
Parallel computation
Algorithms for specific classes of architectures
Packaged methods
Complexity and performance of numerical algorithms [See also 68Q25]
None of the above, but in this section
Computer science {For papers involving machine computations and
General
Mathematical problems of computer architecture
Network design and communication [See also 68R10, 90B18]
Network protocols
Distributed systems
Reliability, testing and fault tolerance [See also 94C12]
Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]
None of the above, but in this section
General
Programming languages
Logic programming
Functional programming and lambda calculus [See also 03B40]
Other programming techniques (object-oriented, sequential, concurrent, automatic, etc.)
Compilers and interpreters
Operating systems
Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)
None of the above, but in this section
General
Data structures
Searching and sorting
Database theory
Information storage and retrieval
Data encryption [See also 94A60, 81P68]
Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) [See also 94Axx]
None of the above, but in this section
General
Models of computation (Turing machines, etc.) [See also 03D10, 81P68]
Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.) [See also 68Q85]
Complexity classes (hierarchies, relations among complexity classes, etc.) [See also 03D15, 68Q17, 68Q19]
Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) [See also 68Q15]
Descriptive complexity and finite models [See also 03C13]
Analysis of algorithms and problem complexity [See also 68W40]
Algorithmic information theory (Kolmogorov complexity, etc.)
Computational learning theory [See also 68T05]
Grammars and rewriting systems
Formal languages and automata [See also 03D05, 68Q70, 94A45]
Semantics [See also 03B70, 06B35, 18C50]
Specification and verification (program logics, model checking, etc.) [See also 03B70]
Abstract data types; algebraic specification [See also 18C50]
Algebraic theory of languages and automata [See also 18B20, 20M35]
Cellular automata [See also 37B15]
Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
None of the above, but in this section
General
Combinatorics
Graph theory [See also 05Cxx, 90B10, 90B35, 90C35]
Combinatorics on words
None of the above, but in this section
General
Learning and adaptive systems [See also 68Q32, 91E40]
Pattern recognition, speech recognition {For cluster analysis, see 62H30}
Theorem proving (deduction, resolution, etc.) [See also 03B35]
Problem solving (heuristics, search strategies, etc.)
Logic in artificial intelligence
Knowledge representation
Languages and software systems (knowledge-based systems, expert systems, etc.)
Reasoning under uncertainty
Robotics [See also 93C85]
Machine vision and scene understanding
Natural language processing [See also 03B65]
None of the above, but in this section
General
Computer graphics; computational geometry [See also 65D18]
Computer-aided design [See also 65D17]
Image processing
Text processing; mathematical typography
Simulation [See also 65Cxx]
Information systems (hypertext navigation, interfaces, decision support, etc.)
None of the above, but in this section
General
Nonnumerical algorithms
Parallel algorithms
Distributed algorithms
Randomized algorithms
Approximation algorithms
Symbolic computation and algebraic computation [See also 11Yxx, 12Y05, 13Pxx, 14Qxx, 16Z05, 17-08, 33F10]
VLSI algorithms
Analysis of algorithms [See also 68Q25]
None of the above, but in this section
Mechanics of particles and systems {For relativistic mechanics,
Kinematics of a particle
Kinematics of a rigid body
Mechanisms, robots [See also 68T40, 70Q05, 93C85]
None of the above, but in this section
Motion of the gyroscope
Free motion of a rigid body [See also 70M20]
Motion of a rigid body with a fixed point
Motion of a rigid body in contact with a solid surface [See also 70F25]
Perturbation methods for rigid body dynamics
Integrable cases of motion
Higher-dimensional generalizations
Stability problems
Dynamics of multibody systems
Robot dynamics and control [See also 68T40, 70Q05, 93C85]
None of the above, but in this section
Mechanics of deformable solids
Explicit solutions
Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.)
Numerical approximation of solutions
Existence of solutions
Uniqueness of solutions
Regularity of solutions
Singularities, blowup, stress concentrations
Long-time behavior of solutions
Vibrations
Random vibrations
Stability
Dynamical bifurcation
Chaotic behavior
None of the above, but in this section
Linear waves
Bulk waves
Surface waves
Wave scattering
Inverse problems
Nonlinear waves
Solitary waves
Shocks and related discontinuities
None of the above, but in this section
Strings
Rods (beams, columns, shafts, arches, rings, etc.)
Membranes
Plates
Shells
Junctions
Thin films
None of the above, but in this section
Geophysical solid mechanics [See also 86-XX]
Soil and rock mechanics
Biomechanical solid mechanics [See also 92C10]
None of the above, but in this section
Crystals
Displacive transformations
Analysis of microstructure
Dynamics of phase boundaries
Transformations involving diffusion
Problems involving hysteresis
None of the above, but in this section
Fluid mechanics {For general continuum mechanics, see 74Axx, or
Optics, electromagnetic theory {For quantum optics, see 81V80}
Classical thermodynamics, heat transfer {For thermodynamics of
Foundations
Classical thermodynamics, including relativistic
Thermodynamics of continua [See also 74A15]
Heat and mass transfer, heat flow
Stefan problems, phase changes, etc. [See also 74Nxx]
Inverse problems
Combustion
Chemical kinetics [See also 76V05, 92C45, 92E20]
Chemically reacting flows [See also 92C45, 92E20]
Chemistry (general) [See mainly 92Exx]
None of the above, but in this section
Quantum theory
General and philosophical
Logical foundations of quantum mechanics; quantum logic [See also 03G12, 06C15]
Quantum measurement theory
Stochastic mechanics (including stochastic electrodynamics)
Quantum computation and quantum cryptography [See also 68Q05, 94A60]
None of the above, but in this section
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations
Selfadjoint operator theory in quantum theory, including spectral analysis
Perturbation theories for operators and differential equations
Semiclassical techniques including WKB and Maslov methods
Feynman integrals and graphs; applications of algebraic topology and algebraic geometry [See also 14D05, 32S40]
Bethe-Salpeter and other integral equations
Quantum chaos [See also 37Dxx]
Supersymmetric quantum mechanics
Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.
None of the above, but in this section
Finite-dimensional groups and algebras motivated by physics and their representations [See also 20C35, 22E70]
Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $W$-algebras and other current algebras and their representations [See also 17B65, 17B67, 22E65, 22E67, 22E70]
Relations with integrable systems [See also 17Bxx, 37J35]
Operator algebra methods [See also 46Lxx, 81T05]
Covariant wave equations
Spinor and twistor methods [See also 32L25]
Coherent states [See also 22E45]; squeezed states [See also 81V80]
Symmetry breaking
Quantum groups and related algebraic methods [See also 16W35, 17B37]
Noncommutative geometry
None of the above, but in this section
Commutation relations and statistics
Geometry and quantization, symplectic methods [See also 53D50]
Stochastic quantization
Quantum stochastic calculus
Phase space methods including Wigner distributions, etc.
Path integrals [See also 58D30]
None of the above, but in this section
Axiomatic quantum field theory; operator algebras
Constructive quantum field theory
Model quantum field theories
Yang-Mills and other gauge theories [See also 53C07, 58E15]
Perturbative methods of renormalization
Nonperturbative methods of renormalization
Renormalization group methods
Feynman diagrams
Quantum field theory on curved space backgrounds
Quantum field theory on lattices
Continuum limits
String and superstring theories; other extended objects (e.g., branes) [See also 83E30]
Two-dimensional field theories, conformal field theories, etc.
Topological field theories [See also 57R56, 58Dxx]
Anomalies
Supersymmetric field theories
Quantization in field theory; cohomological methods [See also 58D29]
Noncommutative geometry methods [See also 46L85, 46L87, 58B34]
Simulation and numerical modeling
None of the above, but in this section
Statistical mechanics, structure of matter
Foundations
Classical dynamic and nonequilibrium statistical mechanics (general)
Quantum dynamics and nonequilibrium statistical mechanics (general)
Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs
Dynamic continuum models (systems of particles, etc.)
Interacting particle systems [See also 60K35]
Exactly solvable dynamic models [See also 37K60]
Interface problems; diffusion-limited aggregation
Dynamic and nonequilibrium phase transitions (general)
Dynamic critical phenomena
Dynamic renormalization group methods [See also 81T17]
Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]
Neural nets [See also 68T05, 91E40, 92B20]
Irreversible thermodynamics, including Onsager-Machlup theory
Kinetic theory of gases
Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50]
Time-dependent percolation [See also 60K35]
Dynamics of disordered systems (random Ising systems, etc.)
Transport processes
Numerical methods (Monte Carlo, series resummation, etc.)
None of the above, but in this section
Relativity and gravitational theory
Astronomy and astrophysics {For celestial mechanics, see 70F15}
General reference works (handbooks, dictionaries, bibliographies, etc.)
Instructional exposition (textbooks, tutorial papers, etc.)
Research exposition (monographs, survey articles)
Historical (must also be assigned at least one classification number from Section 01)
Explicit machine computation and programs (not the theory of computation or programming)
Experimental work
Proceedings, conferences, collections, etc.
Computational methods
Geophysics [See also 76U05, 76V05]
Operations research, mathematical programming
Inventory, storage, reservoirs
Transportation, logistics
Network models, deterministic
Network models, stochastic
Communication networks [See also 68M10, 94A05]
Traffic problems
Queues and service [See also 60K25, 68M20]
Reliability, availability, maintenance, inspection [See also 60K10, 62N05]
Production models
Scheduling theory, deterministic [See also 68M20]
Scheduling theory, stochastic [See also 68M20]
Search theory
Management decision making, including multiple objectives [See also 90C31, 91A35, 91B06]
Marketing, advertising [See also 91B60]
Theory of organizations, manpower planning [See also 91D35]
Discrete location and assignment [See also 90C10]
Continuous location
Case-oriented studies
None of the above, but in this section
Game theory, economics, social and behavioral sciences
2-person games
$n$-person games, $n>2$
Noncooperative games
Cooperative games
Games with infinitely many players
Stochastic games
Games in extensive form
Multistage and repeated games
Evolutionary games
Differential games [See also 49N70]
Positional games (pursuit and evasion, etc.) [See also 49N75]
Dynamic games
Rationality, learning
Signaling, communication
Utility theory for games [See also 91B16]
Decision theory for games [See also 62Cxx, 91B06, 90B50]
Game-theoretic models
Games involving graphs
Games involving topology or set theory
Combinatorial games
Discrete-time games
Games of timing
Probabilistic games; gambling
Hierarchical games
Spaces of games
Applications of game theory
Experimental studies
None of the above, but in this section
Fundamental topics (basic mathematics, methodology; applicable to economics in general)
Decision theory [See also 62Cxx, 90B50, 91A35]
Individual preferences
Group preferences
Voting theory
Social choice
Utility theory
Public goods
Price theory and market structure
Market models (auctions, bargaining, bidding, selling, etc.)
Finance, portfolios, investment
Risk theory, insurance
Resource and cost allocation
Production theory, theory of the firm
Labor market, contracts
Consumer behavior, demand theory
Informational economics
Equilibrium: general theory
Special types of equilibria
Special types of economies
General economic models, trade models
Dynamic economic models, growth models
Macro-economic models (monetary models, models of taxation)
Multisectoral models
Matching models
Stochastic models
Spatial models
Models of real-world systems
Environmental economics (natural resource models, harvesting, pollution, etc.)
Statistical methods; economic indices and measures
Economic time series analysis [See also 62M10]
None of the above, but in this section
Measurement theory
One- and multidimensional scaling
Clustering [See also 62D05]
None of the above, but in this section
Models of societies, social and urban evolution
Mathematical geography and demography
Spatial models [See also 91B72]
Social networks
Manpower systems [See also 91B40, 90B70]
None of the above, but in this section
Cognitive psychology
Psychophysics and psychophysiology; perception
Memory and learning [See also 68T05]
Measurement and performance
None of the above, but in this section
History, political science
Linguistics [See also 03B65, 68T50]
None of the above, but in this section
Biology and other natural sciences
Biophysics
Biomechanics [See also 74L15]
Developmental biology, pattern formation
Cell movement (chemotaxis, etc.)
Neural biology
Physiology (general)
Physiological flow [See also 76Z05]
Cell biology
Biochemistry, molecular biology
Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) [See also 80A30]
Medical applications (general)
Biomedical imaging and signal processing [See also 44A12, 65R10]
Medical epidemiology
Plant biology
None of the above, but in this section
Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
Classical flows, reactions, etc. [See also 80A30, 80A32]
None of the above, but in this section
Systems theory; control {For optimal control, see 49-XX}
Axiomatic system theory
General systems
Hierarchical systems
Decentralized systems
Large scale systems
Mathematical modeling (models of systems, model-matching, etc.)
None of the above, but in this section
Attainable sets
Controllability
Observability
Canonical structure
System structure simplification
Variable structure systems
Realizations from input-output data
Transformations
Linearizations
Minimal systems representations
Algebraic methods
Geometric methods (including algebro-geometric)
Operator-theoretic methods [See also 47A48, 47A57, 47B35, 47N70]
Differential-geometric methods
System identification
Sensitivity (robustness)
${H}^\infty$-control
Computational methods
Synthesis problems
Design techniques (robust design, computer-aided design, etc.)
Feedback control
Pole and zero placement problems
Eigenvalue problems
None of the above, but in this section
Linear systems
Nonlinear systems
Systems governed by ordinary differential equations [See also 34H05]
Systems governed by partial differential equations [See also 35B37]
Systems governed by functional-differential equations [See also 34K35]
Systems in abstract spaces
Systems governed by functional relations other than differential equations
Multivariable systems
Adaptive control
Problems with incomplete information
Fuzzy control
Discrete-time systems
Sampled-data systems
Digital systems
Discrete event systems
Time-scale analysis and singular perturbations
Perturbations
Frequency-response methods
Control problems involving computers (process control, etc.)
Automated systems (robots, etc.) [See also 68T40, 70B15, 70Q05]
Applications
None of the above, but in this section
Lyapunov and other classical stabilities (Lagrange, Poisson, $L^p, l^p$, etc.)
Robust stability
Popov-type stability of feedback systems
Stabilization of systems by feedback
Asymptotic stability
Adaptive or robust stabilization
Input-output approaches
Scalar and vector Lyapunov functions
None of the above, but in this section
Stochastic systems, general
Estimation and detection [See also 60G35]
Filtering [See also 60G35]
System identification
Data smoothing
Stochastic stability
Optimal stochastic control
Least squares and related methods
Other computational methods
Stochastic learning and adaptive control
None of the above, but in this section
Information and communication, circuits
Communication theory [See also 60G35, 90B18]
Image processing (compression, reconstruction, etc.) [See also 68U10]
Application of orthogonal functions in communication
Signal theory (characterization, reconstruction, etc.)
Detection theory
Modulation and demodulation
Information theory, general [See also 62B10]
Measures of information, entropy
Sampling theory
Coding theorems (Shannon theory)
Source coding [See also 68P30]
Rate-distortion theory
Channel models
Prefix, length-variable, comma-free codes [See also 20M35, 68Q45]
Theory of questionnaires
Shift register sequences and sequences over finite alphabets
Cryptography [See also 11T71, 14G50, 68P25]
Authentication and secret sharing
None of the above, but in this section
Linear codes, general
Convolutional codes
Combined modulation schemes (including trellis codes)
Cyclic codes
Burst-correcting codes
Combinatorial codes
Geometric methods (including applications of algebraic geometry) [See also 11T71, 14G50]
Majority codes
Decoding
Arithmetic codes [See also 11T71, 14G50]
Synchronization error-correcting codes
Other types of codes
Bounds on codes
Error probability
Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) [See also 11H31]
None of the above, but in this section
Analytic circuit theory
Switching theory, application of Boolean algebra; Boolean functions [See also 06E30]
Fault detection; testing
Applications of graph theory [See also 05Cxx, 68R10]
Applications of design theory [See also 05Bxx]
None of the above, but in this section
General reference works (handbooks, dictionaries, bibliographies, etc.)
Instructional exposition (textbooks, tutorial papers, etc.)
Research exposition (monographs, survey articles)
Historical (must also be assigned at least one classification number from Section 01)
Explicit machine computation and programs (not the theory of computation or programming)
Proceedings, conferences, collections, etc.
Mathematics education
Recreational mathematics [See also 00A08]
Sociological issues [See also 97C60]
Standards [See also 97B70]
Fiction and games
General
Educational research and planning
General education
Vocational education
Higher education
Teacher education {For research aspects see 97C70}
Out-of-school education. Adult and further education
Syllabuses. Curriculum guides, official documents [See also 97A80]
None of the above, but in this section
Educational policy and educational systems
Affective aspects (motivation, anxiety, persistence, etc.)
Student learning and thinking (misconceptions, cognitive development, problem solving, etc.)
Assessment (large scale assessment, validity, reliability, etc.) [See also 97D10]
Theoretical perspectives (learning theories, epistemology, philosophies of teaching and learning, etc.) [See also 97D20]
Sociological aspects of learning (culture, group interactions, equity issues, etc.)
Teachers, and research on teacher education (teacher development, etc.) [See also 97B50]
Technological tools and other materials in teaching and learning (research on innovations, role in student learning, use of tools by teachers, etc.)
Teaching and curriculum (innovations, teaching practices, studies of curriculum materials, effective teaching, etc. )
None of the above, but in this section
Psychology of and research in mathematics education
Comparative studies on mathematics education [See also 97C40]
Philosophical and theoretical contributions to mathematical education [See also 97C50]
Goals of mathematics teaching. Curriculum development
Teaching methods and classroom techniques. Lesson preparation. Educational principles {For research aspects see 97Cxx}
Teaching problem solving and heuristic strategies {For research aspects see 97Cxx}
Achievement control and rating
Diagnosis, analysis and remediation of learning difficulties and student errors
Teaching units, draft lessons and master lessons
None of the above, but in this section
Education and instruction in mathematics
Analysis of textbooks, development and evaluation of textbooks. Textbook use in the classroom
Teacher manuals and planning aids
Problem books; student competitions, examination questions
Computer assisted instruction and programmed instruction
Manipulative materials and their use in the classroom {For research aspects see 97C80}
Technological tools (computers, calculators, software, etc.) and their use in the classroom
Audiovisual media and their use in instruction
None of the above, but in this section
Educational material and media. Educational technology