
General


General and miscellaneous specific topics


Conference proceedings and collections of papers


History and biography
[See also the classification number 03 in the other sections]


History of mathematics and mathematicians


Mathematical logic and foundations


General logic


Model theory


Computability and recursion theory
/:> Computability and 

Set theory
/:< [See also 

Proof theory and constructive mathematics


Algebraic logic


Nonstandard models
[See also


Set theory [See also 

Combinatorics
{For finite fields, see


Classical combinatorial problems


Designs and configurations
{For applications of design theory, see


Graph theory
{For applications of graphs, see
/:< 

Extremal combinatorics


Algebraic combinatorics


Order, lattices, ordered algebraic structures
[See also


Ordered sets


Lattices
[See also


Modular lattices, complemented lattices


Distributive lattices


Boolean algebras (Boolean rings)
[See also


Ordered structures


General algebraic systems


Algebraic structures
[See also


Varieties


Other classes of algebras


Number theory


Elementary number theory
{For analogues in number fields, see


Sequences and sets


Polynomials and matrices


Diophantine equations
[See also


Forms and linear algebraic groups
[See also


Discontinuous groups and automorphic forms
[See also


Arithmetic algebraic geometry (Diophantine geometry)
[See also


Geometry of numbers
{For applications in coding theory, see


Diophantine approximation, transcendental number theory
[See also


Probabilistic theory: distribution modulo $1$; metric theory of algorithms


Exponential sums and character sums
{For finite fields, see


Zeta and $L$functions: analytic theory


Multiplicative number theory


Additive number theory; partitions


Algebraic number theory: global fields
{For complex multiplication, see


Algebraic number theory: local and $p$adic fields


Finite fields and commutative rings (numbertheoretic aspects)


Connections with logic


Computational number theory
[See also


Field theory and polynomials


Real and complex fields


General field theory


Field extensions


Homological methods (field theory)


Differential and difference algebra


Topological fields


Generalizations of fields


Connections with logic


Commutative rings and algebras


General commutative ring theory


Ring extensions and related topics


Theory of modules and ideals


Homological methods
{For noncommutative rings, see
(Co)homological methods 

Chain conditions, finiteness conditions


Arithmetic rings and other special rings
/:< [See also 

Local rings and semilocal rings


Topological rings and modules
[See also


Finite commutative rings
{For numbertheoretic aspects, see


Differential algebra
[See also


Computational aspects of commutative algebra
[See also
// 

Algebraic geometry


Foundations


Local theory
/:< [See also 

Cycles and subschemes


Families, fibrations


Birational geometry
Mappings and correspondences 

(Co)homology theory
[See also


Arithmetic problems. Diophantine geometry
[See also


Curves


Surfaces and higherdimensional varieties
{For analytic theory, see


Abelian varieties and schemes


Algebraic groups
{For linear algebraic groups, see
// Algebraic groups ~ group schemes 

Special varieties


Projective and enumerative geometry
[See also
Classical methods and problems [See also 

Real algebraic and real analytic geometry


Computational aspects in algebraic geometry
[See also
// 

Affine geometry


Linear and multilinear algebra; matrix theory
/:< (Finite and infinite) 

Associative rings and algebras
{For the commutative case, see


General and miscellaneous


Modules, bimodules and ideals


Homological methods
{For commutative rings, see
Homological methods and results [See also 

Representation theory of rings and algebras


Division rings and semisimple Artin rings
[See also


Local rings and generalizations


Radicals and radical properties of rings


Chain conditions, growth conditions, and other forms of finiteness


Rings with polynomial identity


Rings and algebras arising under various constructions


Conditions on elements
/:< (Including elements of matrix rings, etc.) 

Rings and algebras with additional structure


Generalizations
{For nonassociative rings, see


Nonassociative rings and algebras


General nonassociative rings


Lie algebras and Lie superalgebras
{For Lie groups, see
/:> And Lie superalgebras 

Jordan algebras (algebras, triples and pairs)


Other nonassociative rings and algebras


Category theory; abstract homological algebra
{See
Category theory, homological algebra 

General theory of categories and functors


Special categories


Categories and theories
Categories and algebraic theories 

Categories with structure


Abelian categories


Categories and geometry


Abstract homological algebra
[See also
/:> Abstract /:> 

$K$theory
[See also


Grothendieck groups and $K_0$
[See also


Whitehead groups and $K_1$


Steinberg groups and $K_2$


Higher algebraic $K$theory


$K$theory in geometry


$K$theory in number theory
[See also


$K$theory of forms
[See also


Obstructions from topology


$K$theory and operator algebras
[See mainly


Topological $K$theory
[See also


Group theory and generalizations


Foundations


Permutation groups


Representation theory of groups
{For representation rings and Burnside rings, see also


Abstract finite groups


Structure and classification of infinite or finite groups


Special aspects of infinite or finite groups


Linear algebraic groups (classical groups)
{For arithmetic theory, see
// 

Other groups of matrices
[See also


Connections with homological algebra and category theory


Abelian groups


Groupoids (i.e. Small categories in which all morphisms are isomorphisms) {For sets with a single binary operation, see 

Semigroups


Other generalizations of groups


Topological groups, Lie groups
{For transformation groups, see


Topological and differentiable algebraic systems
{For topological rings and fields, see
/:< ; For dual spaces of operator algebras and topological groups, see 

Locally compact Abelian groups (LCA groups)


Locally compact groups and their algebras


Lie groups
{For the topology of Lie groups and homogeneous spaces, see


Noncompact transformation groups


Real functions
[See also


Functions of one variable


Functions of several variables


Polynomials, rational functions


Inequalities
{For maximal function inequalities, see


Miscellaneous topics
[See also


Measure and integration
{For analysis on manifolds, see


Classical measure theory


Set functions, measures and integrals with values in abstract spaces


Set functions and measures on spaces with additional structure
[See also


Measuretheoretic ergodic theory
[See also
// 

Miscellaneous topics in measure theory


Functions of a complex variable
{For analysis on manifolds, see


General properties


Series expansions


Geometric function theory


Entire and meromorphic functions, and related topics


Miscellaneous topics of analysis in the complex domain


Riemann surfaces


Generalized function theory


Potential theory
{For probabilistic potential theory, see


Twodimensional theory


Higherdimensional theory


Other generalizations


Several complex variables and analytic spaces
{For infinitedimensional holomorphy, see also


Holomorphic functions of several complex variables


Local analytic geometry
[See also


Analytic spaces
General theory of analytic spasec 

Analytic continuation


Holomorphic convexity


Geometric convexity
/:< Partial differential operators 

Deformations of analytic structures


Holomorphic mappings and correspondences


Compact analytic spaces
{For Riemann surfaces, see


Generalizations of analytic spaces {!should also be assigned at least one other classification number from section 32 describing the type of problem}
// From section 32 describing the type of problem ~ in this section 

Holomorphic fiber spaces
[See also


Complex spaces with a group of automorphisms


Automorphic functions
[See also


Complex manifolds


Singularities


Pseudoconvex domains


Pluripotential theory


$CR$ manifolds


Differential operators in several variables


Special functions {!


Elementary classical functions


Hypergeometric functions


Basic hypergeometric functions


Other special functions


Computational aspects


Ordinary differential equations


General theory


Boundary value problems
{For ordinary differential operators, see


Qualitative theory
[See also
// 

Stability theory
[See also
// 

Asymptotic theory


Differential equations in abstract spaces
[See also
/:> 

Functionaldifferential and differentialdifference equations
[See also
/:< , With or without deviating arguments /:> [See also 

Ordinary differential operators
[See also


Differential equations in the complex domain
[See also


Partial differential equations


General theory


Qualitative properties of solutions


Representations of solutions


Generalized solutions of partial differential equations


Equations and systems with constant coefficients
[See also


General firstorder equations and systems


General higherorder equations and systems


Closetoelliptic equations


Partial differential equations of elliptic type
[See also
// 

Parabolic equations and systems
[See also
// 

Partial differential equations of hyperbolic type
[See also
// 

Partial differential equations of special type (mixed, composite, etc.)
{For degenerate types, see


Overdetermined systems
[See also
// 

Spectral theory and eigenvalue problems for partial differential operators
[See also


Equations of mathematical physics and other areas of application
[See also


Miscellaneous topics involving partial differential equations
{For equations on manifolds, see
// 

Pseudodifferential operators and other generalizations of partial differential operators
[See also
// 

Dynamical systems and ergodic theory
[See also


Ergodic theory


Topological dynamics
[See also


Smooth dynamical systems: general theory
[See also


Dynamical systems with hyperbolic behavior


Lowdimensional dynamical systems


Complex dynamical systems
[See also


Local and global bifurcation theory


Random dynamical systems


Finitedimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
[See also


Infinitedimensional Hamiltonian systems
[See also


Infinitedimensional dissipative dynamical systems
[See also


Approximation methods and numerical treatment of dynamical systems
[See also


Applications


Difference and functional equations
// Difference ~ finite differences 

Difference equations
{For dynamical systems, see
// 

Functional equations and inequalities
[See also
/:> And inequalities 

Sequences, series, summability


Convergence and divergence of infinite limiting processes


General summability methods


Direct theorems on summability


Inversion theorems


Special methods of summability


Approximations and expansions
{For all approximation theory in the complex domain, see
/:> 

Fourier analysis


Fourier analysis in one variable


Fourier analysis in several variables
{For automorphic theory, see mainly


Nontrigonometric Fourier analysis


Abstract harmonic analysis
{For other analysis on topological and Lie groups, see


Integral transforms, operational calculus
{For fractional derivatives and integrals, see


Integral equations


Singular integral equations
[See also
/:> 

Systems of linear integral equations


Nonlinear integral equations
[See also
// 

Approximation of solutions 

Qualitative behavior


Functional analysis
{For manifolds modeled on topological linear spaces, see


Topological linear spaces and related structures
{For function spaces, see


Normed linear spaces and Banach spaces; Banach lattices
{For function spaces, see


Inner product spaces and their generalizations, Hilbert spaces
{For function spaces, see


Linear function spaces and their duals
[See also
// 

Distributions, generalized functions, distribution spaces
[See also
// [See also 

Measures, integration, derivative, holomorphy (all involving infinitedimensional spaces)
[See also
/:< {For nonlinear functional anlysis, see 

Topological algebras, normed rings and algebras, Banach algebras
{For group algebras, convolution algebras and measure algebras, see


Commutative Banach algebras and commutative topological algebras
[See also


Topological (rings and) algebras with an involution
[See also


Selfadjoint operator algebras ($C^*$algebras, von_Neumann ($W^*$) algebras, etc.)
[See also


Methods of category theory in functional analysis
[See also


Miscellaneous applications of functional analysis
[See also


Other (nonclassical) types of functional analysis
[See also


Nonlinear functional analysis
[See also


Operator theory


General theory of linear operators


Special classes of linear operators


Individual linear operators as elements of algebraic systems


Groups and semigroups of linear operators, their generalizations and applications
Algebraic systems of linear operators [See also 

Integral, integrodifferential, and pseudodifferential operators
[See also
/:> [See also 

Nonlinear operators and their properties
{For global and geometric aspects, see
/:> And their properties 

Equations and inequalities involving linear operators


Linear spaces and algebras of operators
[See also


Miscellaneous applications of operator theory
[See also


Other (nonclassical) types of operator theory
[See also


Calculus of variations and optimal control; optimization
[See also
/:> 

Existence theories


Necessary conditions and sufficient conditions for optimality


HamiltonJacobi theories, including dynamic programming
Carath\'eodory, HamiltonJacobi theories, including dynamic programming 

Methods of successive approximations
[See also
// [See also 

Miscellaneous topics


Manifolds
[See also
// 

Variational methods {For eigenvalues of operators, see 

Geometry
{For algebraic geometry, see


Linear incidence geometry


Nonlinear incidence geometry


Geometric closure systems


Finite geometry and special incidence structures


Metric geometry


Topological geometry


Incidence groups


Distance geometry


Geometric order structures
[See also


Real and complex geometry


Analytic and descriptive geometry


Convex and discrete geometry


General convexity


Polytopes and polyhedra


Discrete geometry


Differential geometry
{For differential topology, see


Classical differential geometry


Local differential geometry


Global differential geometry
[See also


Symplectic geometry, contact geometry
[See also


General topology
{For the topology of manifolds of all dimensions, see


Generalities


Basic constructions


Maps and general types of spaces defined by maps


Fairly general properties


Spaces with richer structures


Special properties


Peculiar spaces


Connections with other structures, applications


Algebraic topology


Classical topics
{For the topology of Euclidean spaces and manifolds, see


Homology and cohomology theories
[See also


Homotopy theory
{For simple homotopy type, see


Homotopy groups


Fiber spaces and bundles
[See also


Operations and obstructions


Spectral sequences
[See also


Applied homological algebra and category theory
[See also


Manifolds and cell complexes
{For complex manifolds, see
// 

Lowdimensional topology


Topological manifolds


Generalized manifolds
[See also


PLtopology


Differential topology
{For foundational questions of differentiable manifolds, see


Topological transformation groups
[See also


Homology and homotopy of topological groups and related structures


Global analysis, analysis on manifolds
[See also


General theory of differentiable manifolds


Infinitedimensional manifolds


Calculus on manifolds; nonlinear operators
[See also
/:> 

Spaces and manifolds of mappings {!including nonlinear versions of


Variational problems in infinitedimensional spaces


Ordinary differential equations on manifolds; dynamical systems [See also 

Partial differential equations on manifolds; differential operators [See also 

Pseudogroups, differentiable groupoids and general structures on manifolds


Partial differential equations on manifolds
[See also


Theory of singularities and catastrophe theory
[See also


Probability theory and stochastic processes
{For additional applications, see
// 

Foundations of probability theory


Probability theory on algebraic and topological structures


Distribution theory
[See also


Limit theorems
[See also


Stochastic processes


Stochastic analysis
[See also
// 

Markov processes


Special processes


Statistics
/:< {For numerical methods, see 

Foundations 

Sufficiency and information


Decision theory
[See also
// 

Distribution theory
[See also


Parametric inference


Nonparametric inference


Multivariate analysis
[See also


Linear inference, regression


Design of experiments
[See also
// Design of experiment ~ experimental design 

Sequential methods


Inference from stochastic processes


Survival analysis and censored data
Engineering statistics 

Applications
[See also
/:> 

Numerical analysis


Acceleration of convergence


Probabilistic methods, simulation and stochastic differential equations
{For theoretical aspects, see
Numerical simulation {For theoretical aspects, see 

Numerical approximation and computational geometry (primarily algorithms)
{For theory, see
/:> And computational geometry /:> and 

Numerical linear algebra


Error analysis and interval analysis
/:> And interval analysis 

Nonlinear algebraic or transcendental equations


Numerical analysis in abstract spaces


Mathematical programming, optimization and variational techniques


Ordinary differential equations


Partial differential equations, initial value and timedependent initialboundary value problems


Partial differential equations, boundary value problems


Numerical problems in dynamical systems
[See also


Integral equations, integral transforms
/:< [See also 

Numerical methods in Fourier analysis


Computer aspects of numerical algorithms


Computer science
{For papers involving machine computations and programs in a specific mathematical area, see section 04 in that area}


Computer system organization


Software


Theory of data


Theory of computing


Discrete mathematics in relation to computer science


Artificial intelligence
/:< [See also 

Computing methodologies and applications
/:> And applications 

Algorithms
{For numerical algorithms, see


Mechanics of particles and systems
{For relativistic mechanics, see
// See 

Kinematics
[See also


Dynamics of a particle [See also 

Dynamics of a rigid body and of multibody systems
/:> And of multibody systems 

Dynamics of a system of particles, including celestial mechanics


General models, approaches, and methods
[See also
General representations of dynamical systems [See also 

Hamiltonian and Lagrangian mechanics
[See also
// 

Linear vibration theory
/:< [See also 

Nonlinear dynamics
[See also
Nonlinear motions [See also 

Classical field theories
[See also


Mechanics of solids 

Continuum mechanics of solids (constitutive description and properties) 

Elasticity {For the biharmonic equation, see 

Wave propagation in and vibrations of solids 

Plasticity 

Viscoelasticity 

Finite deformations 

Stability (linear and nonlinear) 

Mechanics of structures 

Basic methods in solid mechanics [See also 

Mechanics of deformable solids


Generalities, axiomatics, foundations of continuum mechanics of solids


Elastic materials


Plastic materials, materials of stressrate and internalvariable type


Materials of strainrate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)


Material properties given special treatment


Coupling of solid mechanics with other effects


Equilibrium (steadystate) problems


Dynamical problems


Waves


Thin bodies, structures


Special subfields of solid mechanics


Special kinds of problems


Phase transformations in solids
[See also


Optimization
[See also


Homogenization, determination of effective properties


Fracture and damage


Numerical methods
[See also


Fluid mechanics
{For general continuum mechanics, see
// 

Foundations, constitutive equations, rheology


Incompressible inviscid fluids
/:< , Potential theory 

Incompressible inviscid fluids, vorticity flows 

Incompressible viscous fluids


Hydrodynamic stability


Turbulence
[See also
/:< 

Basic methods in fluid mechanics
[See also


Compressible fluids and gas dynamics, general


Diffusion and convection


Twophase and multiphase flows


Biological fluid mechanics
[See also
/:> 

Optics, electromagnetic theory
{For quantum optics, see


General


Basic methods


Classical thermodynamics, heat transfer
{For thermodynamics of solids, see
// 

Thermodynamics and heat transfer


Basic methods


Quantum theory


Axiomatics, foundations, philosophy


General mathematical topics and methods in quantum theory


Groups and algebras in quantum theory


General quantum mechanics and problems of quantization


Quantum field theory; related classical field theories
[See also
/:> [See also 

Scattering theory
[See also
/:> 

Applications to specific physical systems


Statistical mechanics, structure of matter


Equilibrium statistical mechanics


Timedependent statistical mechanics (dynamic and nonequilibrium)


Applications to specific types of physical systems


Relativity and gravitational theory


General relativity


Unified, higherdimensional and super field theories


Astronomy and astrophysics
{For celestial mechanics, see


Geophysics
[See also
/:< 

Operations research, mathematical programming
Economics, operations research, programming, games 

Mathematical economics {For econometrics, see 

Operations research and management science


Mathematical programming
/:< [See also 

Game theory 

Game theory, economic, social and behavioral sciences


Game theory


Mathematical economics
{For econometrics, see


Social and behavioral sciences: methodology
{For statistics, see


Mathematical sociology (including anthropology)


Mathematical psychology


Other social and behavioral sciences (mathematical treatment)


Biology and other natural sciences
/:< , Behavioral sciences 

Mathematical biology in general


Physiological, cellular and medical topics


Genetics and population dynamics


Chemistry
{For biochemistry, see


Social and behavioral sciences: methodology {For statistics, see 

Mathematical sociology (including anthropology) 

Mathematical psychology 

Other social and behavioral sciences (mathematical treatment) 

Systems theory; control
{For optimal control, see


General


Controllability, observability, and system structure


Control systems, guided systems


Stability


Stochastic systems and control


Information and communication, circuits


Communication, information


Theory of errorcorrecting codes and errordetecting codes
/:> And errordetecting codes 

Circuits, networks


Mathematics education


General


Educational policy and educational systems


Psychology of and research in mathematics education


Education and instruction in mathematics


Educational material and media.
Educational technology
