Instructional exposition (textbooks, tutorial papers, etc.)
Research exposition (monographs, survey articles)
General and miscellaneous specific topics
Mathematics for nonmathematicians (engineering, social sciences, etc.)
Dictionaries and other general reference works
Mathematics and visual arts, visualization
Physics. Use more specific entries from Sections 70 through 86 when possible.
Miscellaneous topics in MSC2010 section 00Axx
Conference proceedings and collections of papers
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
None of the above, but in MSC2010 section 00Bxx
General reference works (handbooks, dictionaries, bibliographies, etc.)
History of mathematics and mathematicians
Indigenous European cultures (pre-Greek, etc.)
Collected or selected works; reprintings or translations of classics
Sociology (and profession) of mathematics
Miscellaneous topics in MSC2010 section 01Axx
Explicit machine computation and programs (not the theory of computation or programming)
Philosophical aspects of logic and foundations
None of the above, but in MSC2010 section 03Axx
Subsystems of classical logic (including intuitionistic logic)
Decidability of theories and sets of sentences
Foundations of classical theories (including reverse mathematics)
Mechanization of proofs and logical operations
Logics of knowledge and belief (including belief change)
Modal logic (including the logic of norms)
Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
None of the above, but in MSC2010 section 03Bxx
Basic properties of first-order languages and structures
Quantifier elimination, model completeness and related topics
Categoricity and completeness of theories
Classification theory, stability and related concepts
Abstract elementary classes and related topics
Models with special properties (saturated, rigid, etc.)
Effective and recursion-theoretic model theory
Model theory of ordered structures; o-minimality
Other classical first-order model theory
Logic with extra quantifiers and operators
Nonclassical models (Boolean-valued, sheaf, etc.)
None of the above, but in MSC2010 section 03Cxx
Automata and formal grammars in connection with logical questions
Complexity of computation (including implicit computational complexity)
Recursive functions and relations, subrecursive hierarchies
Recursively (computably) enumerable sets and degrees
Undecidability and degrees of sets of sentences
Theory of numerations, effectively presented structures
Recursive equivalence types of sets and structures, isols
Computability and recursion theory on ordinals, admissible sets, etc.
Abstract and axiomatic computability and recursion theory
Applications of computability and recursion theory
None of the above, but in MSC2010 section 03Dxx
Ordered sets and their cofinalities; pcf theory
Cardinal characteristics of the continuum
Other classical set theory (including functions, relations, and set algebra)
Axiom of choice and related propositions
Axiomatics of classical set theory and its fragments
Other aspects of forcing and Boolean-valued models
Inner models, including constructibility, ordinal definability, and core models
Other notions of set-theoretic definability
Nonclassical and second-order set theories
None of the above, but in MSC2010 section 03Exx
Proof theory and constructive mathematics
Recursive ordinals and ordinal notations
Second- and higher-order arithmetic and fragments
GÃ¶del numberings and issues of incompleteness
Provability logics and related algebras (e.g., diagonalizable algebras)
Linear logic and other substructural logics
None of the above, but in MSC2010 section 03Fxx
Cylindric and polyadic algebras; relation algebras
None of the above, but in MSC2010 section 03Gxx
Other applications of nonstandard models (economics, physics, etc.)
None of the above, but in MSC2010 section 03Hxx
Factorials, binomial coefficients, combinatorial functions
Exact enumeration problems, generating functions
None of the above, but in MSC2010 section 05Axx
Difference sets (number-theoretic, group-theoretic, etc.)
Orthogonal arrays, Latin squares, Room squares
None of the above, but in MSC2010 section 05Bxx
Planar graphs; geometric and topological aspects of graph theory
Graphs and abstract algebra (groups, rings, fields, etc.)
Graphs and linear algebra (matrices, eigenvalues, etc.)
Graph designs and isomomorphic decomposition
Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)
Graph representations (geometric and intersection representations, etc.)
Dominating sets, independent sets, cliques
Factorization, matching, partitioning, covering and packing
Fractional graph theory, fuzzy graph theory
Structural characterization of families of graphs
Graph operations (line graphs, products, etc.)
Graph labelling (graceful graphs, bandwidth, etc.)
None of the above, but in MSC2010 section 05Cxx
None of the above, but in MSC2010 section 05Dxx
Combinatorial aspects of representation theory
Combinatorial aspects of groups and algebras
Group actions on combinatorial structures
Association schemes, strongly regular graphs
Combinatorial aspects of commutative algebra
Combinatorial aspects of simplicial complexes
None of the above, but in MSC2010 section 05Exx
Order, lattices, ordered algebraic structures
None of the above, but in MSC2010 section 06Axx
Free lattices, projective lattices, word problems
Continuous lattices and posets, applications
None of the above, but in MSC2010 section 06Bxx
Complemented lattices, orthocomplemented lattices and posets
Complemented modular lattices, continuous geometries
None of the above, but in MSC2010 section 06Cxx
De Morgan algebras, Łukasiewicz algebras
Fuzzy lattices (soft algebras) and related topics
Other generalizations of distributive lattices
None of the above, but in MSC2010 section 06Dxx
Stone spaces (Boolean spaces) and related structures
Boolean algebras with additional operations (diagonalizable algebras, etc.)
None of the above, but in MSC2010 section 06Exx
Ordered abelian groups, Riesz groups, ordered linear spaces
None of the above, but in MSC2010 section 06Fxx
Applications of universal algebra in computer science
None of the above, but in MSC2010 section 08Axx
Equational logic, Mal'cev (Mal'tsev) conditions
Products, amalgamated products, and other kinds of limits and colimits
Subdirect products and subdirect irreducibility
None of the above, but in MSC2010 section 08Bxx
Natural dualities for classes of algebras
None of the above, but in MSC2010 section 08Cxx
Multiplicative structure; Euclidean algorithm; greatest common divisors
Congruences; primitive roots; residue systems
Arithmetic functions; related numbers; inversion formulas
None of the above, but in MSC2010 section 11Axx
Arithmetic combinatorics; higher degree uniformity
Fibonacci and Lucas numbers and polynomials and generalizations
Farey sequences; the sequences {1k,2k,…})
Bernoulli and Euler numbers and polynomials
None of the above, but in MSC2010 section 11Bxx
None of the above, but in MSC2010 section 11Cxx
Higher degree equations; Fermat's equation
Counting solutions of Diophantine equations
None of the above, but in MSC2010 section 11Dxx
Quadratic forms over local rings and fields
Quadratic forms over global rings and fields
General ternary and quaternary quadratic forms; forms of more than two variables
Sums of squares and representations by other particular quadratic forms
Class numbers of quadratic and Hermitian forms
Analytic theory (Epstein zeta functions; relations with automorphic forms and functions)
K-theory of quadratic and Hermitian forms
Galois cohomology of linear algebraic groups
Algebraic theory of quadratic forms; Witt groups and rings
None of the above, but in MSC2010 section 11Exx
Discontinuous groups and automorphic forms
Structure of modular groups and generalizations; arithmetic groups
Holomorphic modular forms of integral weight
Relationship to Lie algebras and finite simple groups
Relations with algebraic geometry and topology
Hecke-Petersson operators, differential operators (one variable)
Theta series; Weil representation; theta correspondences
Fourier coefficients of automorphic forms
Congruences for modular and p-adic modular forms
Forms of half-integer weight; nonholomorphic modular forms
Automorphic forms on ${\rm GL}(2)$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
Modular forms associated to Drinfel'd modules
Other groups and their modular and automorphic forms (several variables)
Hecke-Petersson operators, differential operators (several variables)
Langlands L-functions; one variable Dirichlet series and functional equations
Special values of automorphic L-series, periods of modular forms, cohomology, modular symbols
Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series
Representation-theoretic methods; automorphic representations over local and global fields
None of the above, but in MSC2010 section 11Fxx
Arithmetic algebraic geometry (Diophantine geometry)
Drinfel'd modules; higher-dimensional motives, etc.
Complex multiplication and moduli of abelian varieties
Arithmetic aspects of modular and Shimura varieties
Curves of arbitrary genus or genus ≠1 over global fields
L-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
Polylogarithms and relations with K-theory
None of the above, but in MSC2010 section 11Gxx
Quadratic forms (reduction theory, extreme forms, etc.)
None of the above, but in MSC2010 section 11Hxx
Diophantine approximation, transcendental number theory
Markov and Lagrange spectra and generalizations
Simultaneous homogeneous approximation, linear forms
Approximation by numbers from a fixed field
Small fractional parts of polynomials and generalizations
Irrationality; linear independence over a field
Measures of irrationality and of transcendence
Linear forms in logarithms; Baker's method
Schmidt Subspace Theorem and applications
Transcendence theory of elliptic and abelian functions
Transcendence theory of other special functions
Transcendence theory of Drinfel'd and t-modules
Analogues of methods in Nevanlinna theory (work of Vojta et al.)
None of the above, but in MSC2010 section 11Jxx
Probabilistic theory: distribution modulo 1; metric theory of algorithms
Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.
Well-distributed sequences and other variations
Continuous, p-adic and abstract analogues
Pseudo-random numbers; Monte Carlo methods
Metric theory of other algorithms and expansions; measure and Hausdorff dimension
Harmonic analysis and almost periodicity
None of the above, but in MSC2010 section 11Kxx
Trigonometric and exponential sums, general
Gauss and Kloosterman sums; generalizations
Jacobsthal and Brewer sums; other complete character sums
None of the above, but in MSC2010 section 11Lxx
Nonreal zeros of ζ(s)) and L(s,χ); Riemann and other hypotheses
Multiple Dirichlet series and zeta functions and multizeta values
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
None of the above, but in MSC2010 section 11Mxx
Distribution of integers with specified multiplicative constraints
Primes represented by polynomials; other multiplicative structure of polynomial values
Asymptotic results on arithmetic functions
Asymptotic results on counting functions for algebraic and topological structures
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
None of the above, but in MSC2010 section 11Nxx
Goldbach-type theorems; other additive questions involving primes
Applications of the Hardy-Littlewood method
Inverse problems of additive number theory, including sumsets
Partitions; congruences and congruential restrictions
Partition identities; identities of Rogers-Ramanujan type
None of the above, but in MSC2010 section 11Pxx
Algebraic numbers; rings of algebraic integers
PV-numbers and generalizations; other special algebraic numbers; Mahler measure
Class numbers, class groups, discriminants
Integral representations related to algebraic numbers; Galois module structure of rings of integers
Langlands-Weil conjectures, nonabelian class field theory
Zeta functions and L-functions of number fields
Quaternion and other division algebras: arithmetic, zeta functions
Other algebras and orders, and their zeta and L-functions
Arithmetic theory of algebraic function fields
Cyclotomic function fields (class groups, Bernoulli objects, etc.)
Class groups and Picard groups of orders
None of the above, but in MSC2010 section 11Rxx
Algebraic number theory: local and p-adic fields
Class field theory; p-adic formal groups
Algebras and orders, and their zeta functions
Other analytic theory (analogues of beta and gamma functions, p-adic integration, etc.)
None of the above, but in MSC2010 section 11Sxx
Finite fields and commutative rings (number-theoretic aspects)
Arithmetic theory of polynomial rings over finite fields
None of the above, but in MSC2010 section 11Txx
None of the above, but in MSC2010 section 11Uxx
Computer solution of Diophantine equations
None of the above, but in MSC2010 section 11Yxx
Miscellaneous applications of number theory
None of the above, but in MSC2010 section 11Zxx
Polynomials: location of zeros (algebraic theorems)
Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
None of the above, but in MSC2010 section 12Dxx
Hilbertian fields; Hilbert's irreducibility theorem
None of the above, but in MSC2010 section 12Exx
None of the above, but in MSC2010 section 12Fxx
None of the above, but in MSC2010 section 12Gxx
None of the above, but in MSC2010 section 12Hxx
None of the above, but in MSC2010 section 12Jxx
None of the above, but in MSC2010 section 12Kxx
None of the above, but in MSC2010 section 12Lxx
Computational aspects of field theory and polynomials
None of the above, but in MSC2010 section 12Yxx
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
Actions of groups on commutative rings; invariant theory
None of the above, but in MSC2010 section 13Axx
Integral dependence; going up, going down
Integral closure of rings and ideals ; integrally closed rings, related rings (Japanese, etc.)
Ãtale and flat extensions; Henselization; Artin approximation
None of the above, but in MSC2010 section 13Bxx
Dimension theory, depth, related rings (catenary, etc.)
Linkage, complete intersections and determinantal ideals
None of the above, but in MSC2010 section 13Cxx
(Co)homology of commutative rings and algebras (e.g., Hochschild, AndrÃ©-Quillen, cyclic, dihedral, etc.)
Homological functors on modules (Tor, Ext, etc.)
Hilbert-Samuel and Hilbert-Kunz functions; PoincarÃ© series
None of the above, but in MSC2010 section 13Dxx
Artinian rings and modules, finite-dimensional algebras
Rings and modules of finite generation or presentation; number of generators
None of the above, but in MSC2010 section 13Exx
Arithmetic rings and other special rings
Dedekind, PrÃ¼fer, Krull and Mori rings and their generalizations
Rings defined by factorization properties (e.g., atomic, factorial, half-factorial)
Polynomial rings and ideals; rings of integer-valued polynomials
Rings with straightening laws, Hodge algebras
Stanley-Reisner face rings; simplicial complexes
None of the above, but in MSC2010 section 13Fxx
None of the above, but in MSC2010 section 13Gxx
Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
None of the above, but in MSC2010 section 13Hxx
None of the above, but in MSC2010 section 13Jxx
Applications of logic to commutative algebra
None of the above, but in MSC2010 section 13Lxx
None of the above, but in MSC2010 section 13Mxx
Rings of differential operators and their modules
None of the above, but in MSC2010 section 13Nxx
GrÃ¶bner bases; other bases for ideals and modules (e.g., Janet and border bases)
Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)
None of the above, but in MSC2010 section 13Pxx
None of the above, but in MSC2010 section 14Axx
Local deformation theory, Artin approximation, etc.
Local structure of morphisms: Ã©tale, flat, etc.
None of the above, but in MSC2010 section 14Bxx
Parametrization (Chow and Hilbert schemes)
(Equivariant) Chow groups and rings; motives
Intersection theory, characteristic classes, intersection multiplicities
Divisors, linear systems, invertible sheaves
Transcendental methods, Hodge theory , Hodge conjecture
Applications of methods of algebraic K-theory
None of the above, but in MSC2010 section 14Cxx
Structure of families (Picard-Lefschetz, monodromy, etc.)
Arithmetic ground fields (finite, local, global)
Algebraic moduli problems, moduli of vector bundles
Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
Geometric Langlands program: algebro-geometric aspects
None of the above, but in MSC2010 section 14Dxx
Birational automorphisms, Cremona group and generalizations
Global theory and resolution of singularities
Minimal model program (Mori theory, extremal rays)
None of the above, but in MSC2010 section 14Exx
Sheaves, derived categories of sheaves and related constructions
Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
Ãtale and other Grothendieck topologies and (co)homologies
Motivic cohomology; motivic homotopy theory
Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
None of the above, but in MSC2010 section 14Fxx
Zeta-functions and related questions  (Birch-Swinnerton-Dyer conjecture)
Other nonalgebraically closed ground fields
Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)
Arithmetic varieties and schemes; Arakelov theory; heights
Applications to coding theory and cryptography
None of the above, but in MSC2010 section 14Gxx
Special divisors (gonality, Brill-Noether theory)
Riemann surfaces; Weierstrass points; gap sequences
Vector bundles on curves and their moduli
None of the above, but in MSC2010 section 14Hxx
Families, moduli, classification: algebraic theory
Moduli, classification: analytic theory; relations with modular forms
Automorphisms of surfaces and higher-dimensional varieties
Vector bundles on surfaces and higher-dimensional varieties, and their moduli
Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)
None of the above, but in MSC2010 section 14Jxx
Analytic theory; abelian integrals and differentials
None of the above, but in MSC2010 section 14Kxx
Affine algebraic groups, hyperalgebra constructions
Group actions on varieties or schemes (quotients)
Other algebraic groups (geometric aspects)
None of the above, but in MSC2010 section 14Lxx
Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
Grassmannians, Schubert varieties, flag manifolds
Compactifications; symmetric and spherical varieties
None of the above, but in MSC2010 section 14Mxx
Configurations and arrangements of linear subspaces
Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants
None of the above, but in MSC2010 section 14Nxx
Real algebraic and real analytic geometry
None of the above, but in MSC2010 section 14Pxx
Computational aspects in algebraic geometry
None of the above, but in MSC2010 section 14Qxx
Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
None of the above, but in MSC2010 section 14Rxx
None of the above, but in MSC2010 section 14Txx
Linear and multilinear algebra; matrix theory
Determinants, permanents, other special matrix functions
Matrix exponential and similar functions of matrices
Eigenvalues, singular values, and eigenvectors
Inequalities involving eigenvalues and eigenvectors
Matrices over function rings in one or more variables
Norms of matrices, numerical range, applications of functional analysis to matrix theory
Quadratic and bilinear forms, inner products
Vector and tensor algebra, theory of invariants
Miscellaneous topics in MSC2010 section 15Axx
Matrices over special rings (quaternions, finite fields, etc.)
Positive matrices and their generalizations; cones of matrices
Hermitian, skew-Hermitian, and related matrices
None of the above, but in MSC2010 section 15Bxx
Category-theoretic methods and results (except as in 16D90)
None of the above, but in MSC2010 section 16Bxx
Infinite-dimensional simple rings (except as in 16Kxx)
Free, projective, and flat modules and ideals
Simple and semisimple modules, primitive rings and ideals
Structure and classification (except as in 16Gxx), direct sum decomposition, cancellation
Module categories ; module theory in a category-theoretic context; Morita equivalence and duality
None of the above, but in MSC2010 section 16Dxx
(Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
Differential graded algebras and applications
von Neumann regular rings and generalizations
Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.
Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
None of the above, but in MSC2010 section 16Exx
Representation theory of rings and algebras
Representations of quivers and partially ordered sets
Representations of orders, lattices, algebras over commutative rings
Representation type (finite, tame, wild, etc.)
Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
None of the above, but in MSC2010 section 16Gxx
Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)
None of the above, but in MSC2010 section 16Hxx
Division rings and semisimple Artin rings
None of the above, but in MSC2010 section 16Kxx
Noncommutative local and semilocal rings, perfect rings
None of the above, but in MSC2010 section 16Lxx
Radicals and radical properties of rings
Nil and nilpotent radicals, sets, ideals, rings
None of the above, but in MSC2010 section 16Nxx
Chain conditions, growth conditions, and other forms of finiteness
Finite rings and finite-dimensional algebras
Chain conditions on annihilators and summands: Goldie-type conditions , Krull dimension
Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence
None of the above, but in MSC2010 section 16Pxx
T-ideals, identities, varieties of rings and algebras
Semiprime p.i. rings, rings embeddable in matrices over commutative rings
Identities other than those of matrices over commutative rings
Other kinds of identities (generalized polynomial, rational, involution)
None of the above, but in MSC2010 section 16Rxx
Rings and algebras arising under various constructions
Rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)
Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)
Universal enveloping algebras of Lie algebras
Twisted and skew group rings, crossed products
Ordinary and skew polynomial rings and semigroup rings
Rings arising from non-commutative algebraic geometry
Rings of functions, subdirect products, sheaves of rings
Torsion theories; radicals on module categories
None of the above, but in MSC2010 section 16Sxx
Hopf algebras, quantum groups and related topics
Ring-theoretic aspects of quantum groups
None of the above, but in MSC2010 section 16Txx
Ore rings, multiplicative sets, Ore localization
None of the above, but in MSC2010 section 16Uxx
Rings and algebras with additional structure
Rings with involution; Lie, Jordan and other nonassociative structures
Actions of groups and semigroups; invariant theory
Valuations, completions, formal power series and related constructions
Filtered rings; filtrational and graded techniques
Topological and ordered rings and modules
None of the above, but in MSC2010 section 16Wxx
None of the above, but in MSC2010 section 16Yxx
Computational aspects of associative rings
None of the above, but in MSC2010 section 16Zxx
Quadratic algebras (but not quadratic Jordan algebras)
None of the above, but in MSC2010 section 17Axx
Quantum groups (quantized enveloping algebras) and related deformations
Homological methods in Lie (super)algebras
Lie (super)algebras associated with other structures (associative, Jordan, etc.)
Lie algebras of vector fields and related (super) algebras
Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
Vertex operators; vertex operator algebras and related structures
None of the above, but in MSC2010 section 17Bxx
Jordan algebras (algebras, triples and pairs)
Jordan structures associated with other structures
Jordan structures on Banach spaces and algebras
None of the above, but in MSC2010 section 17Cxx
None of the above, but in MSC2010 section 17Dxx
General theory of categories and functors
Foundations, relations to logic and deductive systems
Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
Special properties of functors (faithful, full, etc.)
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 MSC2010 section 18Axx
Category of relations, additive relations
Categories of machines, automata, operative categories
Categories of topological spaces and continuous mappings
Preorders, orders and lattices (viewed as categories)
Groupoids, semigroupoids, semigroups, groups (viewed as categories)
None of the above, but in MSC2010 section 18Bxx
Theories (e.g. algebraic theories), structure, and semantics
Triples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples
Algebras and Kleisli categories associated with monads
Accessible and locally presentable categories
Categorical semantics of formal languages
None of the above, but in MSC2010 section 18Cxx
Double categories, 2-categories, bicategories and generalizations
Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories
Closed categories (closed monoidal and Cartesian closed categories, etc.)
Enriched categories (over closed or monoidal categories)
Structured objects in a category (group objects, etc.)
None of the above, but in MSC2010 section 18Dxx
None of the above, but in MSC2010 section 18Exx
None of the above, but in MSC2010 section 18Fxx
Ext and Tor, generalizations, KÃ¼nneth formula
Relative homological algebra, projective classes
Simplicial sets, simplicial objects (in a category)
None of the above, but in MSC2010 section 18Gxx
Frobenius induction, Burnside and representation rings
None of the above, but in MSC2010 section 19Axx
None of the above, but in MSC2010 section 19Bxx
Central extensions and Schur multipliers
Symbols, presentations and stability of K2
None of the above, but in MSC2010 section 19Cxx
Computations of higher K-theory of rings
K-theory and homology; cyclic homology and cohomology
None of the above, but in MSC2010 section 19Dxx
None of the above, but in MSC2010 section 19Exx
Ãtale cohomology, higher regulators, zeta and L-functions
None of the above, but in MSC2010 section 19Fxx
Hermitian K-theory, relations with K-theory of rings
None of the above, but in MSC2010 section 19Gxx
None of the above, but in MSC2010 section 19Jxx
None of the above, but in MSC2010 section 19Kxx
None of the above, but in MSC2010 section 19Lxx
None of the above, but in MSC2010 section 19Mxx
None of the above, but in MSC2010 section 20Axx
Finite automorphism groups of algebraic, geometric, or combinatorial structures
None of the above, but in MSC2010 section 20Bxx
Group rings of finite groups and their modules
Group rings of infinite groups and their modules
Hecke algebras and their representations
Integral representations of finite groups
Integral representations of infinite groups
Representations of finite symmetric groups
Representations of infinite symmetric groups
Representations of finite groups of Lie type
Applications of group representations to physics
None of the above, but in MSC2010 section 20Cxx
Finite simple groups and their classification
Simple groups: alternating groups and groups of Lie type
Solvable groups, theory of formations, Schunck classes, Fitting classes, $\pi$-length, ranks
Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure
Special subgroups (Frattini, Fitting, etc.)
None of the above, but in MSC2010 section 20Dxx
Structure and classification of infinite or finite groups
Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
Chains and lattices of subgroups, subnormal subgroups
Extensions, wreath products, and other compositions
Residual properties and generalizations; residually finite groups
None of the above, but in MSC2010 section 20Exx
Special aspects of infinite or finite groups
Cancellation theory; application of van Kampen diagrams
Word problems, other decision problems, connections with logic and automata
Derived series, central series, and generalizations
Generalizations of solvable and nilpotent groups
Other classes of groups defined by subgroup chains
Representations of groups as automorphism groups of algebraic systems
Fundamental groups and their automorphisms
Other groups related to topology or analysis
Hyperbolic groups and nonpositively curved groups
Algebraic geometry over groups; equations over groups
None of the above, but in MSC2010 section 20Fxx
Linear algebraic groups and related topics
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 adÃ¨les and other rings and schemes
Linear algebraic groups over finite fields
Quantum groups (quantized function algebras) and their representations
None of the above, but in MSC2010 section 20Gxx
Fuchsian groups and their generalizations
Other geometric groups, including crystallographic groups
None of the above, but in MSC2010 section 20Hxx
Connections with homological algebra and category theory
None of the above, but in MSC2010 section 20Jxx
Torsion groups, primary groups and generalized primary groups
None of the above, but in MSC2010 section 20Kxx
Groupoids (i.e. small categories in which all morphisms are isomorphisms)
None of the above, but in MSC2010 section 20Lxx
Free semigroups, generators and relations, word problems
Varieties and pseudovarieties of semigroups
Semigroup rings, multiplicative semigroups of rings
Representation of semigroups; actions of semigroups on sets
Semigroups in automata theory, linguistics, etc.
Connections of semigroups with homological algebra and category theory
None of the above, but in MSC2010 section 20Mxx
Sets with a single binary operation (groupoids)
Ternary systems (heaps, semiheaps, heapoids, etc.)
None of the above, but in MSC2010 section 20Nxx
None of the above, but in MSC2010 section 20Pxx
Topological and differentiable algebraic systems
Topological groupoids (including differentiable and Lie groupoids)
Representations of general topological groups and semigroups
Topological semilattices, lattices and applications
Other topological algebraic systems and their representations
None of the above, but in MSC2010 section 22Axx
Locally compact abelian groups (LCA groups)
General properties and structure of LCA groups
Structure of group algebras of LCA groups
None of the above, but in MSC2010 section 22Bxx
None of the above, but in MSC2010 section 22Cxx
Locally compact groups and their algebras
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
C⁎-algebras and W⁎-algebras in relation to group representations
Automorphism groups of locally compact groups
None of the above, but in MSC2010 section 22Dxx
General properties and structure of complex Lie groups
General properties and structure of real Lie groups
General properties and structure of other Lie groups
Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
Structure and representation of the Lorentz group
Representations of Lie and linear algebraic groups over real fields: analytic methods
Semisimple Lie groups and their representations
Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
Representations of Lie and linear algebraic groups over local fields
Representations of Lie and linear algebraic groups over global fields and adÃ¨le rings
Geometric Langlands program: representation-theoretic aspects
Infinite-dimensional Lie groups and their Lie algebras: general properties
Analysis on and representations of infinite-dimensional Lie groups
Loop groups and related constructions, group-theoretic treatment
Applications of Lie groups to physics; explicit representations
None of the above, but in MSC2010 section 22Exx
General theory of group and pseudogroup actions
Groups as automorphisms of other structures
None of the above, but in MSC2010 section 22Fxx
Foundations: limits and generalizations, elementary topology of the line
Rate of growth of functions, orders of infinity, slowly varying functions
Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)
Classification of real functions; Baire classification of sets and functions
Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems
Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
Singular functions, Cantor functions, functions with other special properties
Denjoy and Perron integrals, other special integrals
Integrals of Riemann, Stieltjes and Lebesgue type
Functions of bounded variation, generalizations
None of the above, but in MSC2010 section 26Axx
Implicit function theorems, Jacobians, transformations with several variables
Integral formulas (Stokes, Gauss, Green, etc.)
Absolutely continuous functions, functions of bounded variation
Special properties of functions of several variables, HÃ¶lder conditions, etc.
Representation and superposition of functions
None of the above, but in MSC2010 section 26Bxx
None of the above, but in MSC2010 section 26Cxx
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
None of the above, but in MSC2010 section 26Dxx
Calculus of functions on infinite-dimensional spaces
Calculus of functions taking values in infinite-dimensional spaces
Real analysis on time scales or measure chains
None of the above, but in MSC2010 section 26Exx
Classes of sets (Borel fields, σ-rings, etc.), measurable sets, Suslin sets, analytic sets
Contents, measures, outer measures, capacities
Abstract differentiation theory, differentiation of set functions
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
Measures and integrals in product spaces
Integration and disintegration of measures
Measures on Boolean rings, measure algebras
Length, area, volume, other geometric measure theory
None of the above, but in MSC2010 section 28Axx
Set functions, measures and integrals with values in abstract spaces
Vector-valued set functions, measures and integrals
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
None of the above, but in MSC2010 section 28Bxx
Set functions and measures on spaces with additional structure
Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
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.)
None of the above, but in MSC2010 section 28Cxx
One-parameter continuous families of measure-preserving transformations
General groups of measure-preserving transformations
None of the above, but in MSC2010 section 28Dxx
Other connections with logic and set theory
None of the above, but in MSC2010 section 28Exx
Monogenic properties of complex functions (including polygenic and areolar monogenic functions)
None of the above, but in MSC2010 section 30Axx
Power series (including lacunary series)
Boundary behavior of power series, over-convergence
Dirichlet series and other series expansions, exponential series
Completeness problems, closure of a system of functions
None of the above, but in MSC2010 section 30Bxx
Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral)
Covering theorems in conformal mapping theory
Numerical methods in conformal mapping theory
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 ${\bf R}^n$, 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, LindelÃ¶f principle, analogues and generalizations; subordination
Capacity and harmonic measure in the complex plane
None of the above, but in MSC2010 section 30Cxx
Entire and meromorphic functions, and related topics
Functional equations in the complex domain, iteration and composition of analytic functions
Representations of entire functions by series and integrals
Special classes of entire functions and growth estimates
Distribution of values, Nevanlinna theory
Cluster sets, prime ends, boundary behavior
Bloch functions, normal functions, normal families
Quasi-analytic and other classes of functions
None of the above, but in MSC2010 section 30Dxx
Miscellaneous topics of analysis in the complex domain
Asymptotic representations in the complex domain
Integration, integrals of Cauchy type, integral representations of analytic functions
None of the above, but in MSC2010 section 30Exx
Compact Riemann surfaces and uniformization
Classification theory of Riemann surfaces
Fuchsian groups and automorphic functions
Conformal metrics (hyperbolic, PoincarÃ©, distance functions)
None of the above, but in MSC2010 section 30Fxx
Finely holomorphic functions and topological function theory
Generalizations of Bers or Vekua type (pseudoanalytic, p-analytic, etc.)
Other generalizations of analytic functions (including abstract-valued functions)
Functions of hypercomplex variables and generalized variables
None of the above, but in MSC2010 section 30Gxx
Spaces and algebras of analytic functions
None of the above, but in MSC2010 section 30Hxx
None of the above, but in MSC2010 section 30Jxx
None of the above, but in MSC2010 section 30Kxx
Quasiconformal mappings in metric spaces
None of the above, but in MSC2010 section 30Lxx
Integral representations, integral operators, integral equations methods
Potentials and capacity, harmonic measure, extremal length
Boundary behavior (theorems of Fatou type, etc.)
Biharmonic, polyharmonic functions and equations, Poisson's equation
None of the above, but in MSC2010 section 31Axx
Potentials and capacities, extremal length
Biharmonic and polyharmonic equations and functions
None of the above, but in MSC2010 section 31Bxx
Potential theory on Riemannian manifolds
Discrete potential theory and numerical methods
Other generalizations (nonlinear potential theory, etc.)
None of the above, but in MSC2010 section 31Cxx
None of the above, but in MSC2010 section 31Dxx
None of the above, but in MSC2010 section 31Exx
Several complex variables and analytic spaces
Holomorphic functions of several complex variables
Special domains (Reinhardt, Hartogs, circular, tube)
Nevanlinna theory (local); growth estimates; other inequalities
Integral representations; canonical kernels (SzegÃ, Bergman, etc.)
Integral representations, constructed kernels (e.g. Cauchy, FantappiÃ¨-type kernels)
Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30)
Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
Boundary behavior of holomorphic functions
Harmonic analysis of several complex variables
None of the above, but in MSC2010 section 32Axx
Analytic algebras and generalizations, preparation theorems
Germs of analytic sets, local parametrization
None of the above, but in MSC2010 section 32Bxx
Real-analytic sets, complex Nash functions
Integration on analytic sets and spaces, currents
Sheaves of differential operators and their modules, D-modules
The Levi problem in complex spaces; generalizations
None of the above, but in MSC2010 section 32Cxx
None of the above, but in MSC2010 section 32Dxx
Holomorphically convex complex spaces, reduction theory
Holomorphic and polynomial approximation, Runge pairs, interpolation
Global boundary behavior of holomorphic functions
None of the above, but in MSC2010 section 32Exx
Topological consequences of geometric convexity
Analytical consequences of geometric convexity (vanishing theorems, etc.)
None of the above, but in MSC2010 section 32Fxx
Deformations of special (e.g. CR) structures
Deformations of submanifolds and subspaces
Moduli of Riemann surfaces, TeichmÃ¼ller theory
Period matrices, variation of Hodge structure; degenerations
Moduli and deformations for ordinary differential equations (e.g. Knizhnik-Zamolodchikov equation)
None of the above, but in MSC2010 section 32Gxx
Holomorphic mappings, (holomorphic) embeddings and related questions
Value distribution theory in higher dimensions
None of the above, but in MSC2010 section 32Hxx
Transcendental methods of algebraic geometry
Compact KÃ¤hler manifolds: generalizations, classification
None of the above, but in MSC2010 section 32Jxx
Generalizations of analytic spaces (should also be assigned at least one other classification number from Section 32 describing the type of problem)
Differentiable functions on analytic spaces, differentiable spaces
None of the above, but in MSC2010 section 32Kxx
Sheaves and cohomology of sections of holomorphic vector bundles, general results
None of the above, but in MSC2010 section 32Lxx
Complex spaces with a group of automorphisms
Complex Lie groups, automorphism groups acting on complex spaces
Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras
Automorphism groups of ${\bf C}^n$ and affine manifolds
None of the above, but in MSC2010 section 32Mxx
General theory of automorphic functions of several complex variables
Automorphic functions in symmetric domains
None of the above, but in MSC2010 section 32Nxx
Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem)
None of the above, but in MSC2010 section 32Pxx
Complex manifolds as subdomains of Euclidean space
Hyperbolic and Kobayashi hyperbolic manifolds
Topological aspects of complex manifolds
None of the above, but in MSC2010 section 32Qxx
Global theory of singularities; cohomological properties
Relations with arrangements of hyperplanes
Deformations of singularities; vanishing cycles
Mixed Hodge theory of singular varieties
Monodromy; relations with differential equations and D-modules
Topological aspects: Lefschetz theorems, topological classification, invariants
Milnor fibration; relations with knot theory
Stratifications; constructible sheaves; intersection cohomology
Singularities of holomorphic vector fields and foliations
None of the above, but in MSC2010 section 32Sxx
Geometric and analytic invariants on weakly pseudoconvex boundaries
None of the above, but in MSC2010 section 32Txx
None of the above, but in MSC2010 section 32Uxx
CR structures, CR operators, and generalizations
Extension of functions and other analytic objects from CR manifolds
None of the above, but in MSC2010 section 32Vxx
Differential operators in several variables
Pseudodifferential operators in several complex variables
Heat kernels in several complex variables
Other partial differential equations of complex analysis
None of the above, but in MSC2010 section 32Wxx
Special functions (33-XX deals with the properties of functions as functions)
Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)
None of the above, but in MSC2010 section 33Bxx
Bessel and Airy functions, cylinder functions, ${}_0F_1$
Confluent hypergeometric functions, Whittaker functions, ${}_1F_1$
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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
Hypergeometric integrals and functions defined by them (E, G, H and I 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
None of the above, but in MSC2010 section 33Cxx
q-gamma functions, q-beta functions and integrals
Basic hypergeometric functions in one variable,  rφs
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
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
None of the above, but in MSC2010 section 33Dxx
LamÃ©, Mathieu, and spheroidal wave 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 MSC2010 section 33Exx
Symbolic computation (Gosper and Zeilberger algorithms, etc.)
None of the above, but in MSC2010 section 33Fxx
Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions
Analytical theory: series, transformations, transforms, operational calculus, etc.
Geometric methods in differential equations
Nonlinear equations and systems, general
Differential equations of infinite order
None of the above, but in MSC2010 section 34Axx
Linear boundary value problems with nonlinear dependence on the spectral parameter
Parameter dependent boundary value problems
Nonlocal and multipoint boundary value problems
Singular nonlinear boundary value problems
Positive solutions of nonlinear boundary value problems
Special equations (Mathieu, Hill, Bessel, etc.)
Boundary value problems on infinite intervals
Boundary value problems on graphs and networks
None of the above, but in MSC2010 section 34Bxx
Location of integral curves, singular points, limit cycles
Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications)
Connections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.)
Oscillation theory, zeros, disconjugacy and comparison theory
Transformation and reduction of equations and systems, normal forms
Almost and pseudo-almost periodic solutions
Qualitative investigation and simulation of models
None of the above, but in MSC2010 section 34Cxx
Structural stability and analogous concepts
None of the above, but in MSC2010 section 34Dxx
Singular perturbations, turning point theory, WKB methods
None of the above, but in MSC2010 section 34Exx
None of the above, but in MSC2010 section 34Fxx
Differential equations in abstract spaces
None of the above, but in MSC2010 section 34Gxx
None of the above, but in MSC2010 section 34Hxx
Spectral theory of functional-differential operators
Growth, boundedness, comparison of solutions
Functional-differential equations with fractional derivatives
None of the above, but in MSC2010 section 34Kxx
Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions
Eigenvalues, 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
Particular operators (Dirac, one-dimensional SchrÃ¶dinger, etc.)
None of the above, but in MSC2010 section 34Lxx
Differential equations in the complex domain
Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical)
Singularities, monodromy, local behavior of solutions, normal forms
Stokes phenomena and connection problems (linear and nonlinear)
Differential equations on complex manifolds
Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.)
PainlevÃ© and other special equations; classification, hierarchies;
Singular perturbation problems in the complex domain (complex WKB, turning points, steepest descent)
None of the above, but in MSC2010 section 34Mxx
Dynamic equations on time scales or measure chains
None of the above, but in MSC2010 section 34Nxx
Existence problems: global existence, local existence, non-existence
Uniqueness problems: global uniqueness, local uniqueness, non-uniqueness
Transform methods (e.g. integral transforms)
Inequalities involving derivatives and differential and integral operators, inequalities for integrals
Methods of ordinary differential equations
Microlocal methods; methods of sheaf theory and homological algebra in PDE
None of the above, but in MSC2010 section 35Axx
Oscillation, zeros of solutions, mean value theorems, etc.
Homogenization; equations in media with periodic structure
Dependence of solutions on initial and boundary data, parameters
Continuation and prolongation of solutions
None of the above, but in MSC2010 section 35Bxx
None of the above, but in MSC2010 section 35Cxx
None of the above, but in MSC2010 section 35Dxx
Equations and systems with constant coefficients
None of the above, but in MSC2010 section 35Exx
General first-order equations and systems
Initial value problems for linear first-order equations
Boundary value problems for linear first-order equations
Initial-boundary value problems for linear first-order equations
Initial value problems for nonlinear first-order equations
Boundary value problems for nonlinear first-order equations
Initial-boundary value problems for nonlinear first-order equations
Initial value problems for linear first-order systems
Boundary value problems for linear first-order systems
Initial-boundary value problems for linear first-order systems
Initial value problems for nonlinear first-order systems
Boundary value problems for nonlinear first-order systems
Initial-boundary value problems for nonlinear first-order systems
None of the above, but in MSC2010 section 35Fxx
General higher-order equations and systems
Initial value problems for linear higher-order equations
Boundary value problems for linear higher-order equations
Initial-boundary value problems for linear higher-order equations
Initial value problems for nonlinear higher-order equations
Boundary value problems for nonlinear higher-order equations
Initial-boundary value problems for nonlinear higher-order equations
Initial value problems for linear higher-order systems
Boundary value problems for linear higher-order systems
Initial-boundary value problems for linear higher-order systems
Initial value problems for nonlinear higher-order systems
Boundary value problems for nonlinear higher-order systems
Initial-boundary value problems for nonlinear higher-order systems
None of the above, but in MSC2010 section 35Gxx
None of the above, but in MSC2010 section 35Hxx
Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
Variational methods for second-order elliptic equations
Boundary value problems for second-order elliptic equations
Variational methods for higher-order elliptic equations
Boundary value problems for higher-order elliptic equations
Variational methods for elliptic systems
Boundary value problems for first-order elliptic systems
Boundary value problems for second-order elliptic systems
Boundary value problems for higher-order elliptic systems
Nonlinear boundary value problems for linear elliptic equations
Nonlinear boundary value problems for nonlinear elliptic equations
Boundary values of solutions to elliptic equations
Linear elliptic unilateral problems and linear elliptic variational inequalities
Nonlinear elliptic unilateral problems and nonlinear elliptic variational inequalities
Systems of elliptic variational inequalities
Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian
Quasilinear elliptic equations with p-Laplacian
Quasilinear elliptic equations with mean curvature operator
None of the above, but in MSC2010 section 35Jxx
Initial value problems for second-order parabolic equations
Initial-boundary value problems for second-order parabolic equations
Initial value problems for higher-order parabolic equations
Initial-boundary value problems for higher-order parabolic equations
Initial value problems for second-order parabolic systems
Initial value problems for higher-order parabolic systems
Initial-boundary value problems for second-order parabolic systems
Initial-boundary value problems for higher-order parabolic systems
Nonlinear initial value problems for linear parabolic equations
Nonlinear initial-boundary value problems for nonlinear parabolic equations
Ultraparabolic equations, pseudoparabolic equations, etc.
Linear parabolic unilateral problems and linear parabolic variational inequalities
Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities
Systems of parabolic variational inequalities
Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian
Quasilinear parabolic equations with p-Laplacian
Quasilinear parabolic equations with mean curvature operator
None of the above, but in MSC2010 section 35Kxx
Initial value problems for first-order hyperbolic equations
Initial-boundary value problems for first-order hyperbolic equations
Initial value problems for second-order hyperbolic equations
Initial-boundary value problems for second-order hyperbolic equations
Initial value problems for higher-order hyperbolic equations
Initial-boundary value problems for higher-order hyperbolic equations
Initial value problems for first-order hyperbolic systems
Initial-boundary value problems for first-order hyperbolic systems
Initial value problems for second-order hyperbolic systems
Initial-boundary value problems for second-order hyperbolic systems
Initial value problems for higher-order hyperbolic systems
Initial-boundary value problems for higher-order hyperbolic systems
Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities
Nonlinear hyperbolic unilateral problems and nonlinear hyperbolic variational inequalities
Unilateral problems and variational inequalities for hyperbolic systems
None of the above, but in MSC2010 section 35Lxx
Equations and systems of special type (mixed, composite, etc.)
Initial value problems for equations of mixed type
Boundary value problems for equations of mixed type
Initial-boundary value problems for equations of mixed type
Initial value problems for systems of mixed type
Boundary value problems for systems of mixed type
Initial-boundary value problems for systems of mixed type
Linear unilateral problems and variational inequalities of mixed type
Nonlinear unilateral problems and nonlinear variational inequalities of mixed type
Systems of variational inequalities of mixed type
None of the above, but in MSC2010 section 35Mxx
Overdetermined systems with constant coefficients
Overdetermined systems with variable coefficients
∂-Neumann problem and generalizations; formal complexes
None of the above, but in MSC2010 section 35Nxx
General topics in linear spectral theory
Completeness of eigenfunctions, eigenfunction expansions
Estimation of eigenvalues, upper and lower bounds
Asymptotic distribution of eigenvalues and eigenfunctions
Nonlinear eigenvalue problems, nonlinear spectral theory
None of the above, but in MSC2010 section 35Pxx
Equations of mathematical physics and other areas of application
PDEs in connection with quantum mechanics
Time-dependent SchrÃ¶dinger equations, Dirac equations
PDEs in connection with optics and electromagnetic theory
PDEs in connection with computer science
PDEs in connection with mechanics of particles and systems
PDEs in connection with mechanics of deformable solids
PDEs in connection with relativity and gravitational theory
PDEs in connection with classical thermodynamics and heat transfer
PDEs in connection with statistical mechanics
PDEs in connection with astronomy and astrophysics
PDEs in connection with mathematical programming
PDEs in connection with game theory, economics, social and behavioral sciences
PDEs in connection with biology and other natural sciences
PDEs in connection with control and optimization
PDEs in connection with information and communication
None of the above, but in MSC2010 section 35Qxx
Partial differential equations on manifolds
Partial differential equations on graphs and networks (ramified or polygonal spaces)
Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc.
Partial differential equations with discontinuous coefficients or data
Partial differential equations with measure
Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in infinitely many variables)
Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for abstract space valued functions)
Partial differential equations of infinite order
Partial differential equations with randomness, stochastic partial differential equations
Partial differential equations with multivalued right-hand sides
None of the above, but in MSC2010 section 35Rxx
Pseudodifferential operators and other generalizations of partial differential operators
Initial value problems for pseudodifferential operators
Initial-boundary value problems for pseudodifferential operators
Boundary value problems for pseudodifferential operators
Topological aspects: intersection cohomology, stratified sets, etc.
None of the above, but in MSC2010 section 35Sxx
Orbit equivalence, cocycles, ergodic equivalence relations
Ergodic theorems, spectral theory, Markov operators
Entropy and other invariants, isomorphism, classification
Nonsingular (and infinite-measure preserving) transformations
Relations with number theory and harmonic analysis
Relations with probability theory and stochastic processes
Relations with the theory of C⁎-algebras
Dynamical systems in statistical mechanics
None of the above, but in MSC2010 section 37Axx
Transformations and group actions with special properties (minimality, distality, proximality, etc.)
Lyapunov functions and stability; attractors, repellers
Gradient-like and recurrent behavior; isolated (locally maximal) invariant sets
Multi-dimensional shifts of finite type, tiling dynamics
None of the above, but in MSC2010 section 37Bxx
Smooth dynamical systems: general theory
Vector fields, flows, ordinary differential equations
Topological and differentiable equivalence, conjugacy, invariants, moduli, classification
Fixed points, periodic points, fixed-point index theory
Periodic orbits of vector fields and flows
Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems
Smooth ergodic theory, invariant measures
Approximate trajectories (pseudotrajectories, shadowing, etc.)
Periodic and quasiperiodic flows and diffeomorphisms
Attractors and repellers, topological structure
Dynamics of group actions other than ${\bf Z}$ and ${\bf R}$, and foliations
None of the above, but in MSC2010 section 37Cxx
Dynamical systems with hyperbolic behavior
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.)
Hyperbolic systems with singularities (billiards, etc.)
None of the above, but in MSC2010 section 37Dxx
Maps of the interval (piecewise continuous, continuous, smooth)
Combinatorial dynamics (types of periodic orbits)
Homeomorphisms and diffeomorphisms of planes and surfaces
None of the above, but in MSC2010 section 37Exx
Polynomials; rational maps; entire and meromorphic functions
Expanding maps; hyperbolicity; structural stability
Quasiconformal methods and TeichmÃ¼ller theory; Fuchsian and Kleinian groups as dynamical systems
Conformal densities and Hausdorff dimension
Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations
Small divisors, rotation domains and linearization; Fatou and Julia sets
Holomorphic foliations and vector fields
None of the above, but in MSC2010 section 37Fxx
Bifurcations of limit cycles and periodic orbits
Hyperbolic singular points with homoclinic trajectories
Bifurcations connected with nontransversal intersection
Infinite nonwandering sets arising in bifurcations
None of the above, but in MSC2010 section 37Gxx
Foundations, general theory of cocycles, algebraic ergodic theory
Generation, random and stochastic difference and differential equations
Multiplicative ergodic theory, Lyapunov exponents
None of the above, but in MSC2010 section 37Hxx
Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
General theory, relations with symplectic geometry and topology
Symmetries, invariants, invariant manifolds, momentum maps, reduction
Obstructions to integrability (nonintegrability criteria)
Completely integrable systems, topological structure of phase space, integration methods
Perturbations, normal forms, small divisors, KAM theory, Arnol'd diffusion
Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
None of the above, but in MSC2010 section 37Jxx
Hamiltonian structures, symmetries, variational principles, conservation laws
Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
Integration of completely integrable systems by inverse spectral and scattering methods
Relations with algebraic geometry, complex analysis, special functions
Relations with infinite-dimensional Lie algebras and other algebraic structures
Soliton theory, asymptotic behavior of solutions
Perturbations, KAM for infinite-dimensional systems
Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics
None of the above, but in MSC2010 section 37Kxx
General theory, nonlinear semigroups, evolution equations
Normal forms, center manifold theory, bifurcation theory
Inertial manifolds and other invariant attracting sets
Attractors and their dimensions, Lyapunov exponents
Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systems
Infinite-dimensional random dynamical systems; stochastic equations
Special approximation methods (nonlinear Galerkin, etc.)
None of the above, but in MSC2010 section 37Lxx
Approximation methods and numerical treatment of dynamical systems
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 MSC2010 section 37Mxx
Dynamical systems in classical and celestial mechanics
Dynamical systems in fluid mechanics, oceanography and meteorology
Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
Dynamical systems in optimization and economics
None of the above, but in MSC2010 section 37Nxx
Arithmetic and non-Archimedean dynamical systems
Height functions; Green functions; invariant measures
Arithmetic properties of periodic points
Arithmetic dynamics on general algebraic varieties
None of the above, but in MSC2010 section 37Pxx
Multiplicative and other generalized difference equations, e.g. of Lyness type
None of the above, but in MSC2010 section 39Axx
Iteration theory, iterative and composite equations
Equations for functions with more general domains and/or ranges
Orthogonal additivity and other conditional equations
Functional inequalities, including subadditivity, convexity, etc.
Systems of functional equations and inequalities
Stability, separation, extension, and related topics
None of the above, but in MSC2010 section 39Bxx
Convergence and divergence of infinite limiting processes
Convergence and divergence of series and sequences
Convergence and divergence of continued fractions
Convergence and divergence of infinite products
Approximation to limiting values (summation of series, etc.)
Convergence and divergence of series and sequences of functions
None of the above, but in MSC2010 section 40Axx
Multiple sequences and series (should also be assigned at least one other classification number in this section)
None of the above, but in MSC2010 section 40Bxx
Function-theoretic methods (including power series methods and semicontinuous methods)
None of the above, but in MSC2010 section 40Cxx
Tauberian constants and oscillation limits
Convergence factors and summability factors
Summability and bounded fields of methods
None of the above, but in MSC2010 section 40Dxx
None of the above, but in MSC2010 section 40Exx
Absolute and strong summability (should also be assigned at least one other classification number in Section 40)
None of the above, but in MSC2010 section 40Fxx
CesÃ¡ro, Euler, NÃ¶rlund and Hausdorff methods
Summability methods using statistical convergence
None of the above, but in MSC2010 section 40Gxx
Functional analytic methods in summability
None of the above, but in MSC2010 section 40Hxx
Summability in abstract structures  (should also be assigned at least one other classification number in this section)
None of the above, but in MSC2010 section 40Jxx
Inequalities in approximation (Bernstein, Jackson, Nikol'skiÄ­-type inequalities)
Rate of convergence, degree of approximation
Approximation by other special function classes
Approximation by operators (in particular, by integral operators)
Approximation by arbitrary linear expressions
Approximation by arbitrary nonlinear expressions; widths and entropy
Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
Multidimensional problems (should also be assigned at least one other classification number in this section)
Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
None of the above, but in MSC2010 section 41Axx
Trigonometric polynomials, inequalities, extremal problems
Fourier coefficients, Fourier series of functions with special properties, special Fourier series
Convergence and absolute convergence of Fourier and trigonometric series
Summability and absolute summability of Fourier and trigonometric series
Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Conjugate functions, conjugate series, singular integrals
Lacunary series of trigonometric and other functions; Riesz products
Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization
Classical almost periodic functions, mean periodic functions
None of the above, but in MSC2010 section 42Axx
Singular and oscillatory integrals (CalderÃ³n-Zygmund, etc.)
Function spaces arising in harmonic analysis
None of the above, but in MSC2010 section 42Bxx
Orthogonal functions and polynomials, general theory
Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
Uniqueness and localization for orthogonal series
None of the above, but in MSC2010 section 42Cxx
Means on groups, semigroups, etc.; amenable groups
Measure algebras on groups, semigroups, etc.
Lp-spaces and other function spaces on groups, semigroups, etc.
Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
Other transforms and operators of Fourier type
Positive definite functions on groups, semigroups, etc.
Spectral synthesis on groups, semigroups, etc.
Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
Convergence of Fourier series and of inverse transforms
Summability methods on groups, semigroups, etc.
Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
Representations of groups, semigroups, etc.
Analysis on specific locally compact and other abelian groups
None of the above, but in MSC2010 section 43Axx
Special transforms (Legendre, Hilbert, etc.)
Calculus of Mikusski and other operational calculi
None of the above, but in MSC2010 section 44Axx
None of the above, but in MSC2010 section 45Axx
None of the above, but in MSC2010 section 45Bxx
None of the above, but in MSC2010 section 45Cxx
None of the above, but in MSC2010 section 45Dxx
Integral equations with kernels of Cauchy type
Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
None of the above, but in MSC2010 section 45Exx
Systems of nonsingular linear integral equations
Dual, triple, etc., integral and series equations
Systems of singular linear integral equations
None of the above, but in MSC2010 section 45Fxx
None of the above, but in MSC2010 section 45Gxx
None of the above, but in MSC2010 section 45Hxx
None of the above, but in MSC2010 section 45Jxx
None of the above, but in MSC2010 section 45Kxx
None of the above, but in MSC2010 section 45Lxx
None of the above, but in MSC2010 section 45Mxx
Abstract integral equations, integral equations in abstract spaces
None of the above, but in MSC2010 section 45Nxx
None of the above, but in MSC2010 section 45Pxx
None of the above, but in MSC2010 section 45Qxx
None of the above, but in MSC2010 section 45Rxx
Topological linear spaces and related structures
Locally convex FrÃ©chet spaces and (DF)-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.)
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.)
Theorems of Hahn-Banach type; extension and lifting of functionals and operators
Open mapping and closed graph theorems; completeness (including B-, Br-completeness)
Spaces of linear operators; topological tensor products; approximation properties
Ordered topological linear spaces, vector lattices
Sequence spaces (including KÃ¶the sequence spaces)
Compactness in topological linear spaces; angelic spaces, etc.
Convex sets in topological linear spaces; Choquet theory
Graded FrÃ©chet spaces and tame operators
Topological invariants ((DN), (Ω), etc.)
Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)
None of the above, but in MSC2010 section 46Axx
Normed linear spaces and Banach spaces; Banach lattices
Isomorphic theory (including renorming) of Banach spaces
Ultraproduct techniques in Banach space theory
Probabilistic methods in Banach space theory
Geometry and structure of normed linear spaces
Radon-Nikom, KreÄ­n-Milman and related properties
Classical Banach spaces in the general theory
Spaces of operators; tensor products; approximation properties
Compactness in Banach (or normed) spaces
Interpolation between normed linear spaces
Nonlinear classification of Banach spaces; nonlinear quotients
Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science
None of the above, but in MSC2010 section 46Bxx
Inner product spaces and their generalizations, Hilbert spaces
Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.)
Spaces with indefinite inner product (KreÄ­n spaces, Pontryagin spaces, etc.)
Generalizations of inner products (semi-inner products, partial inner products, etc.)
None of the above, but in MSC2010 section 46Cxx
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 (=
Rings and algebras of continuous, differentiable or analytic functions
Spaces of measurable functions (Lp-spaces, Orlicz spaces, KÃ¶the 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
None of the above, but in MSC2010 section 46Exx
Distributions, generalized functions, distribution spaces
Topological linear spaces of test functions, distributions and ultradistributions
Integral transforms in distribution spaces
Distributions and ultradistributions as boundary values of analytic functions
Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
None of the above, but in MSC2010 section 46Fxx
Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
Measures and integration on abstract linear spaces
(Spaces of) multilinear mappings, polynomials
None of the above, but in MSC2010 section 46Gxx
Topological algebras, normed rings and algebras, Banach 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
None of the above, but in MSC2010 section 46Hxx
Commutative Banach algebras and commutative topological algebras
General theory of commutative topological algebras
Banach algebras of continuous functions, function algebras
Banach algebras of differentiable or analytic functions, Hp-spaces
Representations of commutative topological algebras
Structure, classification of commutative topological algebras
None of the above, but in MSC2010 section 46Jxx
Topological (rings and) algebras with an involution
General theory of topological algebras with involution
Representations of topological algebras with involution
Nonselfadjoint (sub)algebras in algebras with involution
Nonassociative topological algebras with an involution
None of the above, but in MSC2010 section 46Kxx
Selfadjoint operator algebras (C⁎-algebras, von Neumann (W⁎-) algebras, etc.)
Operator spaces and completely bounded maps
Free probability and free operator algebras
Derivations, dissipations and positive semigroups in C⁎-algebras
Applications of selfadjoint operator algebras to physics
K-theory and operator algebras (including cyclic theory)
Other ``noncommutative'' mathematics based on C⁎-algebra theory
None of the above, but in MSC2010 section 46Lxx
Methods of category theory in functional analysis
Homological methods (exact sequences, right inverses, lifting, etc.)
Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
Abstract interpolation of topological vector spaces
None of the above, but in MSC2010 section 46Mxx
Miscellaneous applications of functional analysis
Applications in optimization, convex analysis, mathematical programming, economics
Applications to differential and integral equations
Applications in probability theory and statistics
Applications in biology and other sciences
None of the above, but in MSC2010 section 46Nxx
Other (nonclassical) types of functional analysis
Functional analysis over fields other than ${\bf R}$ or ${\bf C}$ or the quaternions; non-Archimedean functional analysis
Functional analysis in probabilistic metric linear spaces
Functional analysis on superspaces (supermanifolds) or graded spaces
None of the above, but in MSC2010 section 46Sxx
Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds
Distributions and generalized functions on nonlinear spaces
None of the above, but in MSC2010 section 46Txx
General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
Linear relations (multivalued linear operators)
Several-variable operator theory (spectral, Fredholm, etc.)
Cyclic vectors, hypercyclic and chaotic operators
Norms (inequalities, more than one norm, etc.)
Canonical models for contractions and nonselfadjoint operators
Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.
Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc.
Equations and inequalities involving linear operators, with vector unknowns
(Semi-) Fredholm operators; index theories
Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones)
Operator methods in interpolation, moment and extension problems
Equations involving linear operators, with operator unknowns
Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal operators
Factorization theory (including Wiener-Hopf and spectral factorizations)
(Generalized) eigenfunction expansions; rigged Hilbert spaces
None of the above, but in MSC2010 section 47Axx
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.)
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)
Toeplitz operators, Hankel operators, Wiener-Hopf operators
Jacobi (tridiagonal) operators (matrices) and generalizations
Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
Spectral operators, decomposable operators, well-bounded operators, etc.
Accretive operators, dissipative operators, etc.
Commutators, derivations, elementary operators, etc.
Transformers, preservers (operators on spaces of operators)
Operators on spaces with an indefinite metric
Positive operators and order-bounded operators
None of the above, but in MSC2010 section 47Bxx
Individual linear operators as elements of algebraic systems
Operators in C⁎- or von Neumann algebras
None of the above, but in MSC2010 section 47Cxx
Groups and semigroups of linear operators, their generalizations and applications
Groups and semigroups of linear operators
One-parameter semigroups and linear evolution equations
Markov semigroups and applications to diffusion processes
Operator sine and cosine functions and higher-order Cauchy problems
None of the above, but in MSC2010 section 47Dxx
Ordinary differential operators  (should also be assigned at least one other classification number in section 47)
None of the above, but in MSC2010 section 47Exx
Partial differential operators  (should also be assigned at least one other classification number in section 47)
None of the above, but in MSC2010 section 47Fxx
Integral, integro-differential, and pseudodifferential operators
None of the above, but in MSC2010 section 47Gxx
Nonlinear operators and their properties
Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
Measures of noncompactness and condensing mappings, K-set contractions, etc.
Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.
Particular nonlinear operators (superposition, Hammerstein, NemytskiÄ­, Uryson, etc.)
None of the above, but in MSC2010 section 47Hxx
Equations and inequalities involving nonlinear operators
Equations involving nonlinear operators (general)
Abstract inverse mapping and implicit function theorems
Nonlinear spectral theory, nonlinear eigenvalue problems
Variational and other types of inequalities involving nonlinear operators (general)
Variational and other types of inclusions
None of the above, but in MSC2010 section 47Jxx
Algebras of operators on Banach spaces and other topological linear spaces
Ideals of polynomials and of multilinear mappings
Operator spaces (= matricially normed spaces)
Abstract operator algebras on Hilbert spaces
Limit algebras, subalgebras of C⁎-algebras
Dual algebras; weakly closed singly generated operator algebras
Representations of (nonselfadjoint) operator algebras
Algebras of unbounded operators; partial algebras of operators
Crossed product algebras (analytic crossed products)
Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)
Applications of operator algebras to physics
None of the above, but in MSC2010 section 47Lxx
Miscellaneous applications of operator theory
Applications in chemistry and life sciences
Applications in systems theory, circuits, and control theory
None of the above, but in MSC2010 section 47Nxx
Other (nonclassical) types of operator theory
Operator theory over fields other than ${\bf R}$, ${\bf C}$ or the quaternions; non-Archimedean operator theory
Operator theory in probabilistic metric linear spaces
None of the above, but in MSC2010 section 47Sxx
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 relations other than differential equations
Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
Variational methods including variational inequalities
Methods involving semicontinuity and convergence; relaxation
None of the above, but in MSC2010 section 49Jxx
Problems involving ordinary differential equations
Problems involving partial differential equations
Problems involving relations other than differential equations
Optimal solutions belonging to restricted classes
None of the above, but in MSC2010 section 49Kxx
Hamilton-Jacobi theories, including dynamic programming
None of the above, but in MSC2010 section 49Lxx
None of the above, but in MSC2010 section 49Mxx
Applications of optimal control and differential games
None of the above, but in MSC2010 section 49Nxx
Optimization of shapes other than minimal surfaces
Geometric measure and integration theory, integral and normal currents
Variational problems in a geometric measure-theoretic setting
None of the above, but in MSC2010 section 49Qxx
Variational methods for eigenvalues of operators
Variational methods for eigenvalues of operators  (should also be assigned at least one other classification number in Section 49)
None of the above, but in MSC2010 section 49Rxx
Variational principles of physics (should also be assigned at least one other classification number in section 49)
None of the above, but in MSC2010 section 49Sxx
General theory and projective geometries
Non-Desarguesian affine and projective planes
Incidence structures imbeddable into projective geometries
Polar geometry, symplectic spaces, orthogonal spaces
None of the above, but in MSC2010 section 51Axx
None of the above, but in MSC2010 section 51Bxx
Ring geometry (Hjelmslev, Barbilian, etc.)
None of the above, but in MSC2010 section 51Cxx
Continuous geometries and related topics
None of the above, but in MSC2010 section 51Dxx
Finite geometry and special incidence structures
Finite partial geometries (general), nets, partial spreads
Combinatorial structures in finite projective spaces
None of the above, but in MSC2010 section 51Exx
None of the above, but in MSC2010 section 51Fxx
Ordered geometries (ordered incidence structures, etc.)
None of the above, but in MSC2010 section 51Gxx
Geometries with algebraic manifold structure
None of the above, but in MSC2010 section 51Hxx
Representation by near-fields and near-algebras
None of the above, but in MSC2010 section 51Jxx
None of the above, but in MSC2010 section 51Kxx
Geometry of orders of nondifferentiable curves
None of the above, but in MSC2010 section 51Lxx
Elementary problems in Euclidean geometries
Euclidean geometries (general) and generalizations
Elementary problems in hyperbolic and elliptic geometries
Hyperbolic and elliptic geometries (general) and generalizations
Polyhedra and polytopes; regular figures, division of spaces
Line geometries and their generalizations
Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations)
None of the above, but in MSC2010 section 51Mxx
Analytic geometry with other transformation groups
Questions of classical algebraic geometry
None of the above, but in MSC2010 section 51Nxx
Geometry and physics (should also be assigned at least one other classification number from Sections 70--86)
None of the above, but in MSC2010 section 51Pxx
Convex sets without dimension restrictions
Convex sets in topological vector spaces
Convex sets in 2 dimensions (including convex curves)
Convex sets in 3 dimensions (including convex surfaces)
Convex sets in n dimensions (including convex hypersurfaces)
Finite-dimensional Banach spaces (including special norms, zonoids, etc.)
Random convex sets and integral geometry
Variants of convex sets (star-shaped, (m,n)-convex, etc.)
Helly-type theorems and geometric transversal theory
Other problems of combinatorial convexity
None of the above, but in MSC2010 section 52Axx
Combinatorial properties (number of faces, shortest paths, etc.)
Special polytopes (linear programming, centrally symmetric, etc.)
Lattice polytopes (including relations with commutative algebra and algebraic geometry)
Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.)
Dissections and valuations (Hilbert's third problem, etc.)
Computational aspects related to convexity
None of the above, but in MSC2010 section 52Bxx
Lattices and convex bodies in 2 dimensions
Lattices and convex bodies in n dimensions
ErdÃs problems and related topics of discrete geometry
Circle packings and discrete conformal geometry
Planar arrangements of lines and pseudolines
Arrangements of points, flats, hyperplanes
Combinatorial complexity of geometric structures
None of the above, but in MSC2010 section 52Cxx
Higher-dimensional and -codimensional surfaces in Euclidean n-space
Minimal surfaces, surfaces with prescribed mean curvature
Differential invariants (local theory), geometric objects
None of the above, but in MSC2010 section 53Axx
Finsler spaces and generalizations (areal metrics)
None of the above, but in MSC2010 section 53Bxx
Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills)
Gerbes, differential characters: differential geometric aspects
General geometric structures on manifolds (almost complex, almost product structures, etc.)
Global Riemannian geometry, including pinching
Methods of Riemannian geometry, including PDE methods; curvature restrictions
Global geometric and topological methods (Ã¡ la Gromov); differential geometric analysis on metric spaces
Special Riemannian manifolds (Einstein, Sasakian, etc.)
Hyper-KÃ¤hler and quaternionic KÃ¤hler geometry, ``special'' geometry
Immersions (minimal, prescribed curvature, tight, etc.)
Differential geometric aspects of harmonic maps
Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Global surface theory (convex surfaces Ã¡ la A. D. Aleksandrov)
Lorentz manifolds, manifolds with indefinite metrics
Direct methods (G-spaces of Busemann, etc.)
None of the above, but in MSC2010 section 53Cxx
Almost contact and almost symplectic manifolds
Poisson manifolds; Poisson groupoids and algebroids
Global theory of symplectic and contact manifolds
Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category
Floer homology and cohomology, symplectic aspects
Symplectic field theory; contact homology
Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
None of the above, but in MSC2010 section 53Dxx
None of the above, but in MSC2010 section 53Zxx
Topological spaces and generalizations (closure spaces, etc.)
Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
Cardinality properties (cardinal functions and inequalities, discrete subsets)
None of the above, but in MSC2010 section 54Axx
Adjunction spaces and similar constructions
None of the above, but in MSC2010 section 54Bxx
Maps and general types of spaces defined by maps
Special maps on topological spaces (open, closed, perfect, etc.)
Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)
None of the above, but in MSC2010 section 54Cxx
Connected and locally connected spaces (general aspects)
Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
Noncompact covering properties (paracompact, LindelÃ¶f, etc.)
Extensions of spaces (compactifications, supercompactifications, completions, etc.)
Special constructions of spaces (spaces of ultrafilters, etc.)
None of the above, but in MSC2010 section 54Dxx
Stratifiable spaces, cosmic spaces, etc.
None of the above, but in MSC2010 section 54Exx
Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
Spaces of dimension ≦1; curves, dendrites
Topological characterizations of particular spaces
None of the above, but in MSC2010 section 54Fxx
Extremally disconnected spaces, F-spaces, etc.
None of the above, but in MSC2010 section 54Gxx
Connections with other structures, applications
Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
Topological representations of algebraic systems
None of the above, but in MSC2010 section 54Hxx
None of the above, but in MSC2010 section 54Jxx
Ljusternik-Schnirelman (Lyusternik-Shnirel'man) category of a space
Finite groups of transformations (including Smith theory)
None of the above, but in MSC2010 section 55Mxx
Generalized (extraordinary) homology and cohomology theories
Bordism and cobordism theories, formal group laws
Homology with local coefficients, equivariant cohomology
Axioms for homology theory and uniqueness theorems
None of the above, but in MSC2010 section 55Nxx
Spectra with additional structure (E∞, A∞, ring spectra, etc.)
Relations between equivariant and nonequivariant homotopy theory
None of the above, but in MSC2010 section 55Pxx
Homotopy groups, general; sets of homotopy classes
Homotopy groups of wedges, joins, and simple spaces
None of the above, but in MSC2010 section 55Qxx
Spectral sequences and homology of fiber spaces
Classifying spaces of groups and H-spaces
Homology of classifying spaces, characteristic classes
Homology and homotopy of BO and BU; Bott periodicity
Stable classes of vector space bundles, K-theory
Generalizations of fiber spaces and bundles
None of the above, but in MSC2010 section 55Rxx
Secondary and higher cohomology operations
K-theory operations and generalized cohomology operations
None of the above, but in MSC2010 section 55Sxx
None of the above, but in MSC2010 section 55Txx
Applied homological algebra and category theory
Universal coefficient theorems, Bockstein operator
Topological categories, foundations of homotopy theory
None of the above, but in MSC2010 section 55Uxx
Fundamental group, presentations, free differential calculus
Wild knots and surfaces, etc., wild embeddings
Dehn's lemma, sphere theorem, loop theorem, asphericity
Characterizations of EE and SS (PoincarÃ© conjecture)
Geometric structures on low-dimensional manifolds
None of the above, but in MSC2010 section 57Mxx
Topology of En, n-manifolds (4 &lt; n &lt; ∞)
None of the above, but in MSC2010 section 57Nxx
Local properties of generalized manifolds
None of the above, but in MSC2010 section 57Pxx
Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
Wall finiteness obstruction for CW-complexes
Comparison of PL-structures: classification, Hauptvermutung
None of the above, but in MSC2010 section 57Qxx
Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
Topology of vector bundles and fiber bundles
Controllability of vector fields on C∞ and real-analytic manifolds
Classifying spaces for foliations; Gelfand-Fuks cohomology
Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants
Critical points and critical submanifolds
Complex cobordism (${\rm U}$- and ${\rm SU}$-cobordism)
Equivariant algebraic topology of manifolds
None of the above, but in MSC2010 section 57Rxx
Topological properties of groups of homeomorphisms or diffeomorphisms
Compact Lie groups of differentiable transformations
Noncompact Lie groups of transformations
None of the above, but in MSC2010 section 57Sxx
Homology and homotopy of topological groups and related structures
Homology and cohomology of homogeneous spaces of Lie groups
Homotopy groups of topological groups and homogeneous spaces
Applications of Eilenberg-Moore spectral sequences
None of the above, but in MSC2010 section 57Txx
General theory of differentiable manifolds
Topos-theoretic approach to differentiable manifolds
Exterior differential systems (Cartan theory)
Vector distributions (subbundles of the tangent bundles)
None of the above, but in MSC2010 section 58Axx
Riemannian, Finsler and other geometric structures
Group structures and generalizations on infinite-dimensional manifolds
None of the above, but in MSC2010 section 58Bxx
Calculus on manifolds; nonlinear operators
Set valued and function-space valued mappings
Implicit function theorems; global Newton methods
Differentiation theory (Gateaux, FrÃ©chet, etc.)
Integration on manifolds; measures on manifolds
Analysis on supermanifolds or graded manifolds
None of the above, but in MSC2010 section 58Cxx
Spaces and manifolds of mappings (including nonlinear versions of 46Exx)
Groups of diffeomorphisms and homeomorphisms as manifolds
Groups and semigroups of nonlinear operators
Measures (Gaussian, cylindrical, etc.) on manifolds of maps
Equations in function spaces; evolution equations
Moduli problems for differential geometric structures
Moduli problems for topological structures
Applications (in quantum mechanics (Feynman path integrals), relativity, fluid dynamics, etc.)
None of the above, but in MSC2010 section 58Dxx
Variational problems in infinite-dimensional spaces
Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel'man) theory, etc.)
Applications to the theory of geodesics (problems in one independent variable)
Applications to minimal surfaces (problems in two independent variables)
Application to extremal problems in several variables; Yang-Mills functionals , etc.
Pareto optimality, etc., applications to economics
None of the above, but in MSC2010 section 58Exx
Pseudogroups, differentiable groupoids and general structures on manifolds
Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.)
None of the above, but in MSC2010 section 58Hxx
Partial differential equations on manifolds; differential operators
Elliptic equations on manifolds, general theory
Differential complexes ; elliptic complexes
Index theory and related fixed point theorems
Heat and other parabolic equation methods
Pseudodifferential and Fourier integral operators on manifolds
Noncommutative global analysis, noncommutative residues
Propagation of singularities; initial value problems
Spectral problems; spectral geometry; scattering theory
Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicity
Determinants and determinant bundles, analytic torsion
Relations with special manifold structures (Riemannian, Finsler, etc.)
Diffusion processes and stochastic analysis on manifolds
Correspondences and other transformation methods (e.g. Lie-BÃ¤cklund)
None of the above, but in MSC2010 section 58Jxx
Theory of singularities and catastrophe theory
Critical points of functions and mappings
Algebraic and analytic properties of mappings
Classification; finite determinacy of map germs
Singularities of vector fields, topological aspects
None of the above, but in MSC2010 section 58Kxx
None of the above, but in MSC2010 section 58Zxx
Probability theory and stochastic processes
Computational methods (not classified at a more specific level)
None of the above, but in MSC2010 section 60Axx
Probability theory on algebraic and topological structures
Probability measures on topological spaces
Probability theory on linear topological spaces
Limit theorems for vector-valued random variables (infinite-dimensional case)
Probability measures on groups or semigroups, Fourier transforms, factorization
Random matrices (probabilistic aspects; for algebraic aspects see 15B52)
None of the above, but in MSC2010 section 60Bxx
None of the above, but in MSC2010 section 60Cxx
Geometric probability and stochastic geometry
None of the above, but in MSC2010 section 60Dxx
Infinitely divisible distributions; stable distributions
None of the above, but in MSC2010 section 60Exx
Functional limit theorems; invariance principles
None of the above, but in MSC2010 section 60Fxx
Fractional processes, including fractional Brownian motion
Continuity and singularity of induced measures
Stopping times; optimal stopping problems; gambling theory
Sums of independent random variables; random walks
Processes with independent increments; LÃ©vy processes
Extreme value theory; extremal processes
None of the above, but in MSC2010 section 60Gxx
Stochastic calculus of variations and the Malliavin calculus
Applications of stochastic analysis (to PDE, etc.)
Computational methods for stochastic equations
None of the above, but in MSC2010 section 60Hxx
Discrete-time Markov processes on general state spaces
Markov chains (discrete-time Markov processes on discrete state spaces)
Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Continuous-time Markov processes on general state spaces
Continuous-time Markov processes on discrete state spaces
Applications of continuous-time Markov processes on discrete state spaces
Transition functions, generators and resolvents
Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
Branching processes (Galton-Watson, birth-and-death, etc.)
None of the above, but in MSC2010 section 60Jxx
Applications (reliability, demand theory, etc.)
Markov renewal processes, semi-Markov processes
Applications of Markov renewal processes (reliability, queueing networks, etc.)
Applications (congestion, allocation, storage, traffic, etc.)
Interacting random processes; statistical mechanics type models; percolation theory
Other physical applications of random processes
None of the above, but in MSC2010 section 60Kxx
None of the above, but in MSC2010 section 62Axx
None of the above, but in MSC2010 section 62Bxx
Bayesian problems; characterization of Bayes procedures
Empirical decision procedures; empirical Bayes procedures
None of the above, but in MSC2010 section 62Cxx
None of the above, but in MSC2010 section 62Dxx
Fuzziness in connection with the topics on distributions in this section
None of the above, but in MSC2010 section 62Exx
Bootstrap, jackknife and other resampling methods
None of the above, but in MSC2010 section 62Fxx
Order statistics; empirical distribution functions
Statistics of extreme values; tail inference
None of the above, but in MSC2010 section 62Gxx
Measures of association (correlation, canonical correlation, etc.)
Factor analysis and principal components; correspondence analysis
Classification and discrimination; cluster analysis
None of the above, but in MSC2010 section 62Hxx
Fuzziness, and linear inference and regression
None of the above, but in MSC2010 section 62Jxx
None of the above, but in MSC2010 section 62Kxx
None of the above, but in MSC2010 section 62Lxx
Time series, auto-correlation, regression, etc.
Inference from stochastic processes and fuzziness
None of the above, but in MSC2010 section 62Mxx
Fuzziness, and survival analysis and censored data
None of the above, but in MSC2010 section 62Nxx
Applications to actuarial sciences and financial mathematics
Applications to biology and medical sciences
Applications to environmental and related topics
Applications in engineering and industry
None of the above, but in MSC2010 section 62Pxx
None of the above, but in MSC2010 section 62Qxx
None of the above, but in MSC2010 section 65Axx
Extrapolation to the limit, deferred corrections
None of the above, but in MSC2010 section 65Bxx
Probabilistic methods, simulation and stochastic differential equations
Stochastic differential and integral equations
Other computational problems in probability
None of the above, but in MSC2010 section 65Cxx
Numerical approximation and computational geometry (primarily algorithms)
Computer aided design (modeling of curves and surfaces)
Computer graphics, image analysis, and computational geometry
Computational issues in computer and robotic vision
Computation of special functions, construction of tables
None of the above, but in MSC2010 section 65Dxx
Numerical methods in complex analysis (potential theory, etc.)
None of the above, but in MSC2010 section 65Exx
Direct methods for linear systems and matrix inversion
Matrix exponential and similar matrix functions
None of the above, but in MSC2010 section 65Fxx
Algorithms with automatic result verification
None of the above, but in MSC2010 section 65Gxx
Nonlinear algebraic or transcendental equations
Global methods, including homotopy approaches
None of the above, but in MSC2010 section 65Hxx
None of the above, but in MSC2010 section 65Jxx
Mathematical programming, optimization and variational techniques
Numerical methods for variational inequalities and related problems
None of the above, but in MSC2010 section 65Kxx
Multistep, Runge-Kutta and extrapolation methods
Numerical investigation of stability of solutions
Stability and convergence of numerical methods
Finite elements, Rayleigh-Ritz, Galerkin and collocation methods
None of the above, but in MSC2010 section 65Lxx
Partial differential equations, initial value and time-dependent initial-boundary value problems
Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Spectral, collocation and related methods
Probabilistic methods, particle methods, etc.
Fundamental solutions, Green's function methods, etc.
None of the above, but in MSC2010 section 65Mxx
Partial differential equations, boundary value problems
None of the above, but in MSC2010 section 65Nxx
Hamiltonian systems including symplectic integrators
None of the above, but in MSC2010 section 65Pxx
Difference and functional equations, recurrence relations
None of the above, but in MSC2010 section 65Qxx
None of the above, but in MSC2010 section 65Rxx
None of the above, but in MSC2010 section 65Sxx
None of the above, but in MSC2010 section 65Txx
Computer aspects of numerical algorithms
Algorithms for computer arithmetic, etc.
Algorithms for specific classes of architectures
Complexity and performance of numerical algorithms
None of the above, but in MSC2010 section 65Yxx
None of the above, but in MSC2010 section 65Zxx
Mathematical problems of computer architecture
Reliability, testing and fault tolerance
None of the above, but in MSC2010 section 68Mxx
Functional programming and lambda calculus
Other programming techniques (object-oriented, sequential, concurrent, automatic, etc.)
Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)
None of the above, but in MSC2010 section 68Nxx
Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.)
None of the above, but in MSC2010 section 68Pxx
Models of computation (Turing machines, etc.)
Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)
Complexity classes (hierarchies, relations among complexity classes, etc.)
Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
Descriptive complexity and finite models
Analysis of algorithms and problem complexity
Algorithmic information theory (Kolmogorov complexity, etc.)
Specification and verification (program logics, model checking, etc.)
Abstract data types; algebraic specification
Algebraic theory of languages and automata
Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
Probability in computer science (algorithm analysis, random structures, phase transitions, etc.)
None of the above, but in MSC2010 section 68Qxx
Discrete mathematics in relation to computer science
None of the above, but in MSC2010 section 68Rxx
Theorem proving (deduction, resolution, etc.)
Problem solving (heuristics, search strategies, etc.)
Languages and software systems (knowledge-based systems, expert systems, etc.)
None of the above, but in MSC2010 section 68Txx
Information systems (hypertext navigation, interfaces, decision support, etc.)
None of the above, but in MSC2010 section 68Uxx
Symbolic computation and algebraic computation
None of the above, but in MSC2010 section 68Wxx
None of the above, but in MSC2010 section 70Axx
None of the above, but in MSC2010 section 70Bxx
None of the above, but in MSC2010 section 70Cxx
Dynamics of a rigid body and of multibody systems
Motion of a rigid body with a fixed point
Motion of a rigid body in contact with a solid surface
Perturbation methods for rigid body dynamics
None of the above, but in MSC2010 section 70Exx
Dynamics of a system of particles, including celestial mechanics
Collisions in celestial mechanics, regularization
Collision of rigid or pseudo-rigid bodies
None of the above, but in MSC2010 section 70Fxx
Generalized coordinates; event, impulse-energy, configuration, state, or phase space
Differential-geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.)
Symmetries, Lie-group and Lie-algebra methods
None of the above, but in MSC2010 section 70Gxx
Completely integrable systems and methods of integration
Nearly integrable Hamiltonian systems, KAM theory
Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction
Constrained dynamics, Dirac's theory of constraints
None of the above, but in MSC2010 section 70Hxx
Systems arising from the discretization of structural vibration problems
None of the above, but in MSC2010 section 70Jxx
Quasi-periodic motions and invariant tori
Transition to stochasticity (chaotic behavior)
None of the above, but in MSC2010 section 70Kxx
None of the above, but in MSC2010 section 70Lxx
None of the above, but in MSC2010 section 70Mxx
None of the above, but in MSC2010 section 70Pxx
None of the above, but in MSC2010 section 70Qxx
Lagrangian formalism and Hamiltonian formalism
None of the above, but in MSC2010 section 70Sxx
Generalities, axiomatics, foundations of continuum mechanics of solids
Molecular, statistical, and kinetic theories
Random materials and composite materials
Structured surfaces and interfaces, coexistent phases
None of the above, but in MSC2010 section 74Axx
Equations linearized about a deformed state (small deformations superposed on large)
None of the above, but in MSC2010 section 74Bxx
Plastic materials, materials of stress-rate and internal-variable type
Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials)
Small-strain, rate-dependent theories (including theories of viscoplasticity)
Large-strain, rate-independent theories (including nonlinear plasticity)
None of the above, but in MSC2010 section 74Cxx
Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
None of the above, but in MSC2010 section 74Dxx
Material properties given special treatment
None of the above, but in MSC2010 section 74Exx
Coupling of solid mechanics with other effects
Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
None of the above, but in MSC2010 section 74Fxx
Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.)
Local existence of solutions (near a given solution)
None of the above, but in MSC2010 section 74Gxx
None of the above, but in MSC2010 section 74Hxx
None of the above, but in MSC2010 section 74Jxx
Rods (beams, columns, shafts, arches, rings, etc.)
None of the above, but in MSC2010 section 74Kxx
None of the above, but in MSC2010 section 74Lxx
Control, switches and devices (``smart materials'')
None of the above, but in MSC2010 section 74Mxx
None of the above, but in MSC2010 section 74Nxx
None of the above, but in MSC2010 section 74Pxx
Homogenization, determination of effective properties
Homogenization and oscillations in dynamical problems
None of the above, but in MSC2010 section 74Qxx
None of the above, but in MSC2010 section 74Rxx
None of the above, but in MSC2010 section 74Sxx
None of the above, but in MSC2010 section 76Axx
Existence, uniqueness, and regularity theory
Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
Water waves, gravity waves; dispersion and scattering, nonlinear interaction
Stratification effects in inviscid fluids
None of the above, but in MSC2010 section 76Bxx
Statistical solutions of Navier-Stokes and related equations
Boundary-layer theory, separation and reattachment, higher-order effects
Other free-boundary flows; Hele-Shaw flows
Stratification effects in viscous fluids
None of the above, but in MSC2010 section 76Dxx
Stability and instability of nonparallel flows
Absolute and convective instability and stability
Stability and instability of geophysical and astrophysical flows
Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
None of the above, but in MSC2010 section 76Exx
Dynamical systems approach to turbulence
Renormalization and other field-theoretical methods
Direct numerical and large eddy simulation of turbulence
None of the above, but in MSC2010 section 76Fxx
None of the above, but in MSC2010 section 76Gxx
None of the above, but in MSC2010 section 76Hxx
None of the above, but in MSC2010 section 76Jxx
None of the above, but in MSC2010 section 76Kxx
None of the above, but in MSC2010 section 76Lxx
Particle methods and lattice-gas methods
Symmetry analysis, Lie group and algebra methods
None of the above, but in MSC2010 section 76Mxx
Compressible fluids and gas dynamics, general
None of the above, but in MSC2010 section 76Nxx
None of the above, but in MSC2010 section 76Pxx
None of the above, but in MSC2010 section 76Qxx
None of the above, but in MSC2010 section 76Rxx
Flows in porous media; filtration; seepage
None of the above, but in MSC2010 section 76Sxx
Liquid-gas two-phase flows, bubbly flows
None of the above, but in MSC2010 section 76Txx
None of the above, but in MSC2010 section 76Uxx
None of the above, but in MSC2010 section 76Vxx
None of the above, but in MSC2010 section 76Wxx
Ionized gas flow in electromagnetic fields; plasmic flow
None of the above, but in MSC2010 section 76Xxx
Quantum hydrodynamics and relativistic hydrodynamics
None of the above, but in MSC2010 section 76Yxx
None of the above, but in MSC2010 section 76Zxx
Lasers, masers, optical bistability, nonlinear optics
Mathematically heuristic optics and electromagnetic theory. Must also be assigned at least one other classification number in this section.
Miscellaneous topics in MSC2010 section 78Axx
Finite volume methods, finite integration techniques
None of the above, but in MSC2010 section 78Mxx
None of the above, but in MSC2010 section 80Axx
None of the above, but in MSC2010 section 80Mxx
Logical foundations of quantum mechanics; quantum logic
Quantum state spaces, operational and probabilistic concepts
Stochastic mechanics (including stochastic electrodynamics)
Quantum coherence, entanglement, quantum correlations
Quantum state estimation, approximate cloning
None of the above, but in MSC2010 section 81Pxx
General mathematical topics and methods in quantum theory
Closed and approximate solutions to the SchrÃ¶dinger, Dirac, Klein-Gordon and other equations of quantum mechanics
Selfadjoint operator theory in quantum theory, including spectral analysis
Non-selfadjoint operator theory in quantum theory
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
Quantum mechanics on special spaces: manifolds, fractals, graphs, etc.
Quantum dots, waveguides, ratchets, etc.
Bethe-Salpeter and other integral equations
Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.
Special quantum systems, such as solvable systems
None of the above, but in MSC2010 section 81Qxx
Finite-dimensional groups and algebras motivated by physics and their representations
Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, W-algebras and other current algebras and their representations
Quantum groups and related algebraic methods
None of the above, but in MSC2010 section 81Rxx
General quantum mechanics and problems of quantization
Canonical quantization, commutation relations and statistics
Geometry and quantization, symplectic methods
Open systems, reduced dynamics, master equations, decoherence
Phase-space methods including Wigner distributions, etc.
None of the above, but in MSC2010 section 81Sxx
Quantum field theory; related classical field theories
Axiomatic quantum field theory; operator algebras
Quantum field theory on curved space backgrounds
String and superstring theories; other extended objects (e.g., branes)
Two-dimensional field theories, conformal field theories, etc.
Quantization in field theory; cohomological methods
None of the above, but in MSC2010 section 81Txx
None of the above, but in MSC2010 section 81Uxx
Applications to specific physical systems
Strong interaction, including quantum chromodynamics
None of the above, but in MSC2010 section 81Vxx
Statistical mechanics, structure of matter
Classical equilibrium statistical mechanics (general)
Quantum equilibrium statistical mechanics (general)
Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Continuum models (systems of particles, etc.)
Irreversible thermodynamics, including Onsager-Machlup theory
Random walks, random surfaces, lattice animals, etc.
Disordered systems (random Ising models, random SchrÃ¶dinger operators, etc.)
Numerical methods (Monte Carlo, series resummation, etc.)
None of the above, but in MSC2010 section 82Bxx
Time-dependent statistical mechanics (dynamic and nonequilibrium)
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.)
Dynamic and nonequilibrium phase transitions (general)
Stochastic methods (Fokker-Planck, Langevin, etc.)
Dynamics of random walks, random surfaces, lattice animals, etc.
Dynamics of disordered systems (random Ising systems, etc.)
None of the above, but in MSC2010 section 82Cxx
Applications to specific types of physical systems
Random media, disordered materials (including liquid crystals and spin glasses)
Nuclear reactor theory; neutron transport
None of the above, but in MSC2010 section 82Dxx
None of the above, but in MSC2010 section 83Axx
None of the above, but in MSC2010 section 83Bxx
Einstein's equations (general structure, canonical formalism, Cauchy problems)
Classes of solutions; algebraically special solutions, metrics with symmetries
Lattice gravity, Regge calculus and other discrete methods
Asymptotic procedures (radiation, news functions, H-spaces, etc.)
Gravitational energy and conservation laws; groups of motions
Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
Spinor and twistor methods; Newman-Penrose formalism
Space-time singularities, cosmic censorship, etc.
None of the above, but in MSC2010 section 83Cxx
Relativistic gravitational theories other than Einstein's, including asymmetric field theories
None of the above, but in MSC2010 section 83Dxx
Unified, higher-dimensional and super field theories
Kaluza-Klein and other higher-dimensional theories
None of the above, but in MSC2010 section 83Exx
None of the above, but in MSC2010 section 83Fxx
Miscellaneous topics in MSC2010 section 85Axx
Miscellaneous topics in MSC2010 section 86Axx
Operations research and management science
Management decision making, including multiple objectives
Theory of organizations, manpower planning
None of the above, but in MSC2010 section 90Bxx
Special problems of linear programming (transportation, multi-index, etc.)
Complementarity and equilibrium problems and variational inequalities (finite dimensions)
Programming involving graphs or networks
Markov and semi-Markov decision processes
Methods of successive quadratic programming type
Derivative-free methods and methods using generalized derivatives
Abstract computational complexity for mathematical programming problems
None of the above, but in MSC2010 section 90Cxx
Game theory, economics, social and behavioral sciences
Positional games (pursuit and evasion, etc.)
None of the above, but in MSC2010 section 91Axx
Fundamental topics (basic mathematics, methodology; applicable to economics in general)
Market models (auctions, bargaining, bidding, selling, etc.)
Dynamic stochastic general equilibrium theory
Macro-economic models (monetary models, models of taxation)
Environmental economics (natural resource models, harvesting, pollution, etc.)
Applications of statistical and quantum mechanics to economics (econophysics)
Statistical methods; economic indices and measures
None of the above, but in MSC2010 section 91Bxx
Social and behavioral sciences: general topics
None of the above, but in MSC2010 section 91Cxx
Models of societies, social and urban evolution
None of the above, but in MSC2010 section 91Dxx
None of the above, but in MSC2010 section 91Exx
Other social and behavioral sciences (mathematical treatment)
None of the above, but in MSC2010 section 91Fxx
Numerical methods (including Monte Carlo methods)
Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)
None of the above, but in MSC2010 section 91Gxx
Neural networks, artificial life and related topics
None of the above, but in MSC2010 section 92Bxx
Physiological, cellular and medical topics
Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
Biomedical imaging and signal processing
None of the above, but in MSC2010 section 92Cxx
None of the above, but in MSC2010 section 92Dxx
Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
None of the above, but in MSC2010 section 92Exx
Other natural sciences (should also be assigned at least one other classification number in this section)
Other natural sciences (should also be assigned at least one other classification number in section 92)
None of the above, but in MSC2010 section 92Fxx
Mathematical modeling (models of systems, model-matching, etc.)
None of the above, but in MSC2010 section 93Axx
Controllability, observability, and system structure
Design techniques (robust design, computer-aided design, etc.)
None of the above, but in MSC2010 section 93Bxx
Systems governed by ordinary differential equations
Systems governed by partial differential equations
Systems governed by functional-differential equations
Systems governed by functional relations other than differential equations (such as hybrid and switching systems)
Time-scale analysis and singular perturbations
Control problems involving computers (process control, etc.)
None of the above, but in MSC2010 section 93Cxx
Lyapunov and other classical stabilities (Lagrange, Poisson, $L^p, l^p$, etc.)
Popov-type stability of feedback systems
None of the above, but in MSC2010 section 93Dxx
Stochastic learning and adaptive control
None of the above, but in MSC2010 section 93Exx
Image processing (compression, reconstruction, etc.)
Application of orthogonal and other special functions
Signal theory (characterization, reconstruction, filtering, etc.)
Shift register sequences and sequences over finite alphabets
None of the above, but in MSC2010 section 94Axx
Theory of error-correcting codes and error-detecting codes
Combined modulation schemes (including trellis codes)
Geometric methods (including applications of algebraic geometry)
Applications of the theory of convex sets and geometry of numbers (covering radius, etc.)
None of the above, but in MSC2010 section 94Bxx
Switching theory, application of Boolean algebra; Boolean functions
None of the above, but in MSC2010 section 94Cxx
Fuzzy sets and logic (in connection with questions of Section 94)
None of the above, but in MSC2010 section 94Dxx
History of mathematics and mathematics education
None of the above, but in MSC2010 section 97Axx
None of the above, but in MSC2010 section 97Bxx
Psychology of mathematics education, research in mathematics education
None of the above, but in MSC2010 section 97Cxx
Education and instruction in mathematics
Philosophical and theoretical contributions (maths didactics)
Teaching methods and classroom techniques
Teaching problem solving and heuristic strategies
Student assessment, achievement control and rating
Learning difficulties and student errors
None of the above, but in MSC2010 section 97Dxx
Reasoning and proving in the mathematics classroom
None of the above, but in MSC2010 section 97Exx
Real life mathematics, practical arithmetic
None of the above, but in MSC2010 section 97Fxx
None of the above, but in MSC2010 section 97Gxx
None of the above, but in MSC2010 section 97Hxx
None of the above, but in MSC2010 section 97Ixx
Combinatorics, graph theory, probability theory, statistics
Foundations and methodology of statistics
None of the above, but in MSC2010 section 97Kxx
Mathematical modeling, applications of mathematics
Mathematics in vocational training and career education
None of the above, but in MSC2010 section 97Mxx
None of the above, but in MSC2010 section 97Nxx
None of the above, but in MSC2010 section 97Pxx
Affective aspects in teaching computer science
None of the above, but in MSC2010 section 97Qxx
Comprehensive works, collections of programs
None of the above, but in MSC2010 section 97Rxx
Educational material and media, educational technology
None of the above, but in MSC2010 section 97Uxx
See also the classification number--03 in the other sections.
Must also be assigned at least one classification number from Section 01.
For philosophy of mathematics, see also 00A30.
For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45.
For enumeration in graph theory, see 05C30.
For applications of design theory, see 94C30.
For ordered fields, see 12J15; see also 13J25, 16W80.
For analogues in number fields, see 11R04.
See also 11K50, 30B70, 40A15. For approximation results, see 11J70.
For applications to special functions, see 33-XX.
See also 19Gxx. For quadratic forms in linear algebra, see 15A63.
See also 11R39, 11S37, 14Gxx, 14Kxx, 22E50, 22E55, 30F35, 32Nxx. For relations with quadratic forms, see 11E45.
For applications in coding theory, see 94B75.
For the analytic theory, see 26C10, 30C15.
See mainly 32P05; see also 46S10, 47S10.
For noncommutative rings, see 16Exx; for general categories, see 18Gxx.
For number-theoretic aspects, see 11Txx.
For analytic moduli problems, see 32G13.
For Hilbert modular surfaces, see 14G35.
For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45.
For commutative rings, see 13Dxx; for general categories, see 18Gxx.
For arithmetic aspects, see 11R52, 11R54, 11S45; for representation theory, see 16G30.
For radicals in module categories, see 16S90.
For semisimple, see 16K20; for commutative, see 11Txx, 13Mxx.
See also 13D30, 18E40. For radicals of rings, see 16Nxx.
See also 17A70, 17Bxx, 17C70. For exterior algebras, see 15A75; for Clifford algebras, see 11E88, 15A66.
For commutative rings, see 13Dxx, for associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and 55Uxx for algebraic topology.
See also 13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx.
For arithmetic theory, see 11E57, 11H56; for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47, 22E50, 22E55.
See also 51-XX, especially 51F15, and 82D25.
For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05.
For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX.
For topological rings and fields, see 12Jxx, 13Jxx, 16W80.
For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx; for analysis thereon, see 43A80, 43A85, 43A90.
For the purely algebraic theory, see 20G05.
For the algebraic theory of Lie algebras, see 17Bxx.
For topological properties of spaces with an action, see 57S20.
For general actions on manifolds or preserving geometrical structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40.
For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27.
For maximal function inequalities, see 42B25; for functional inequalities, see 39B72; for probabilistic inequalities, see 60E15.
See also 28B20, 49J53, 54C60. For nonsmooth analysis, see 49J52, 58Cxx, 90Cxx.
For dynamic equations on time scales or measure chains, see 34N05.
For algebraic theory, see 12D10; for real methods, see 26C10.
For probabilistic potential theory, see 60J45.
For infinite-dimensional holomorphy, see 46G20, 58B12.
For functions of several hypercomplex variables, see 30G35.
See also 14H15, 14J15. For algebraic moduli problems, see 14D20, 14D22, 14H10, 14J10.
For function-theoretic properties, see 32A22.
For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic theory, see 14Jxx.
For orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; for representation theory see 22Exx.
For ordinary differential operators, see 34Lxx.
See also 34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx, 58D25.
For real analysis on time scales, see 26E70.
For real analysis on time scales or measure chains, see 26E70.
For numerical analysis, see 65Mxx, 65Nxx.
For equations on manifolds, see 58Jxx; for manifolds of solutions, see 58Bxx; for stochastic PDE, see also 60H15.
See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX.
For operator ergodic theory, see mainly 47A35.
See mainly 22Fxx, and also 57R30, 57Sxx.
See mainly 76-XX, especially 76D05, 76F20, 86A05, 86A10.
For dynamical systems, see 37-XX; for dynamic equations on time scales, see 34N05.
For the Euler-Maclaurin summation formula, see 65B15.
For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx.
For approximation by trigonometric polynomials, see 42A10.
For automorphic theory, see mainly 11F30.
For other analysis on topological and Lie groups, see 22Exx.
For fractional derivatives and integrals, see 26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. For numerical methods, see 65R10.
For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx.
See also 30H05, 32A38, 46F05. For function algebras, see 46J10.
For Banach function algebras, see 46J10, 46J15.
For group algebras, convolution algebras and measure algebras, see 43A10, 43A20.
For nonlinear operators, see 47H20; see also 20M20.
For global and geometric aspects, see 49J53, 58-XX, especially 58Cxx.
See also 46Txx. For global and geometric aspects, see 58-XX.
See also 68Uxx. For computational geometry and algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx.
For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx.
For the topology of manifolds of all dimensions, see 57Nxx.
See also 03Exx. For ultrafilters, see 54D80.
See also 12Jxx. For algebraic aspects, see 13Jxx, 16W80.
For the topology of Euclidean spaces and manifolds, see 57Nxx.
For the low-dimensional case, see 57M25.
For foundational questions of differentiable manifolds, see 58Axx; for infinite-dimensional manifolds, see 58Bxx.
See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx. For geometric integration theory, see 49Q15.
For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX.
For ergodic theory, see 28Dxx and 60Fxx.
See also 90B50, 91B06; for game theory, see 91A35.
For theoretical aspects, see 68U20 and 60H35.
For numerical methods in conformal mapping, see also 30C30.
For papers involving machine computations and programs in a specific mathematical area, see Section--04 in that area.
For numerical algorithms, see 65-XX; for combinatorics and graph theory, see 05C85, 68Rxx.
For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX.
See also 37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX.
For general continuum mechanics, see 74Axx, or other parts of 74-XX.
For thermodynamics of solids, see 74A15.
For crystallographic group theory, see 20H15.