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Classificació AMS
- 00 General
  - 00A General and miscellaneous specific topics
  - 00B Conference proceedings and collections of papers
- 01 History and biography
  - 01A History of mathematics and mathematicians
- 03 Mathematical logic and foundations
  - 03A05 Philosophical and critical
  - 03B General logic
  - 03C Model theory
  - 03D Computability and recursion theory
  - 03E Set theory
  - 03F Proof theory and constructive mathematics
  - 03G Algebraic logic
  - 03H Nonstandard models
- 05 Combinatorics
  - 05A Enumerative combinatorics
  - 05B Designs and configurations
  - 05C Graph theory
  - 05D Extremal combinatorics
  - 05E Algebraic combinatorics
- 06 Order, lattices, ordered algebraic structures
  - 06A Ordered sets
  - 06B Lattices
  - 06C Modular lattices, complemented lattices
  - 06D Distributive lattices
  - 06E Boolean algebras (Boolean rings)
  - 06F Ordered structures
- 08 General algebraic systems
  - 08A Algebraic structures
  - 08B Varieties
  - 08C Other classes of algebras
- 11 Number theory
  - 11A Elementary number theory
  - 11B Sequences and sets
  - 11C Polynomials and matrices
  - 11D Diophantine equations
  - 11E Forms and linear algebraic groups
  - 11F Discontinuous groups and automorphic forms
  - 11G Arithmetic algebraic geometry (Diophantine geometry)
  - 11H Geometry of numbers
  - 11J Diophantine approximation, transcendental number theory
  - 11K Probabilistic theory: distribution modulo $1$; metric theory of algorithms
  - 11L Exponential sums and character sums
  - 11M Zeta and $L$-functions: analytic theory
  - 11N Multiplicative number theory
  - 11P Additive number theory; partitions
  - 11R Algebraic number theory: global fields
  - 11S Algebraic number theory: local and $p$-adic fields
  - 11T Finite fields and commutative rings (number-theoretic aspects)
  - 11U Connections with logic
  - 11Y Computational number theory
  - 11Z05 Miscellaneous applications of number theory
- 12 Field theory and polynomials
  - 12D Real and complex fields
  - 12E General field theory
  - 12F Field extensions
  - 12G Homological methods (field theory)
  - 12H Differential and difference algebra
  - 12J Topological fields
  - 12K Generalizations of fields
  - 12L Connections with logic
  - 12Y05 Computational aspects of field theory and polynomials
- 13 Commutative rings and algebras
  - 13A General commutative ring theory
  - 13B Ring extensions and related topics
  - 13C Theory of modules and ideals
  - 13D Homological methods
  - 13E Chain conditions, finiteness conditions
  - 13F Arithmetic rings and other special rings
  - 13G05 Integral domains
  - 13H Local rings and semilocal rings
  - 13J Topological rings and modules
  - 13K05 Witt vectors and related rings
  - 13L05 Applications of logic to commutative algebra
  - 13M Finite commutative rings
  - 13N Differential algebra
  - 13P Computational aspects of commutative algebra
- 14 Algebraic geometry
  - 14A Foundations
  - 14B Local theory
  - 14C Cycles and subschemes
  - 14D Families, fibrations
  - 14E Birational geometry
  - 14F (Co)homology theory
  - 14G Arithmetic problems. Diophantine geometry
  - 14H Curves
  - 14J Surfaces and higher-dimensional varieties
  - 14K Abelian varieties and schemes
  - 14L Algebraic groups
  - 14M Special varieties
  - 14N Projective and enumerative geometry
  - 14P Real algebraic and real analytic geometry
  - 14Q Computational aspects in algebraic geometry
  - 14R Affine geometry
- 15 Linear and multilinear algebra; matrix theory
- 16 Associative rings and algebras
  - 16B General and miscellaneous
  - 16D Modules, bimodules and ideals
  - 16E Homological methods
  - 16G Representation theory of rings and algebras
  - 16H05 Orders and arithmetic, separable algebras, Azumaya algebras
  - 16K Division rings and semisimple Artin rings
  - 16L Local rings and generalizations
  - 16N Radicals and radical properties of rings
  - 16P Chain conditions, growth conditions, and other forms of finiteness
  - 16R Rings with polynomial identity
  - 16S Rings and algebras arising under various constructions
  - 16U Conditions on elements
  - 16W Rings and algebras with additional structure
  - 16Y Generalizations
  - 16Z05 Computational aspects of associative rings
- 17 Nonassociative rings and algebras
  - 17A General nonassociative rings
  - 17B Lie algebras and Lie superalgebras
  - 17C Jordan algebras (algebras, triples and pairs)
  - 17D Other nonassociative rings and algebras
- 18 Category theory; homological algebra
  - 18A General theory of categories and functors
  - 18B Special categories
  - 18C Categories and theories
  - 18D Categories with structure
  - 18E Abelian categories
  - 18F Categories and geometry
  - 18G Homological algebra
- 19 K-theory
  - 19A Grothendieck groups and $K_0$
  - 19B Whitehead groups and $K_1$
  - 19C Steinberg groups and $K_2$
  - 19D Higher algebraic $K$-theory
  - 19E K-theory in geometry
  - 19F K-theory in number theory
  - 19G K-theory of forms
  - 19J Obstructions from topology
  - 19K K-theory and operator algebras
  - 19L Topological K-theory
  - 19M05 Miscellaneous applications of K-theory
- 20 Group theory and generalizations
  - 20A Foundations
  - 20B Permutation groups
  - 20C Representation theory of groups
  - 20D Abstract finite groups
  - 20E Structure and classification of infinite or finite groups
  - 20F Special aspects of infinite or finite groups
  - 20G Linear algebraic groups (classical groups)
  - 20H Other groups of matrices
  - 20J Connections with homological algebra and category theory
  - 20K Abelian groups
  - 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms)
  - 20M Semigroups
  - 20N Other generalizations of groups
  - 20P05 Probabilistic methods in group theory
- 22 Topological groups, lie groups
  - 22A Topological and differentiable algebraic systems
  - 22B Locally compact abelian groups (LCA groups)
  - 22C05 Compact groups
  - 22D Locally compact groups and their algebras
  - 22E Lie groups
  - 22F Noncompact transformation groups
- 26 Real functions
  - 26A Functions of one variable
  - 26B Functions of several variables
  - 26C Polynomials, rational functions
  - 26D Inequalities
  - 26E Miscellaneous topics
- 28 Measure and integration
  - 28A Classical measure theory
  - 28B Set functions, measures and integrals with values in abstract spaces
  - 28C Set functions and measures on spaces with additional structure
  - 28D Measure-theoretic ergodic theory
  - 28E Miscellaneous topics in measure theory
- 30 Functions of a complex variable
  - 30A General properties
  - 30B Series expansions
  - 30C Geometric function theory
  - 30D Entire and meromorphic functions, and related topics
  - 30E Miscellaneous topics of analysis in the complex domain
  - 30F Riemann surfaces
  - 30G Generalized function theory
  - 30H05 Spaces and algebras of analytic functions
- 31 Potential theory
  - 31A Two-dimensional theory
  - 31B Higher-dimensional theory
  - 31C Other generalizations
  - 31D05 Axiomatic potential theory
- 32 Several complex variables and analytic spaces
  - 32A Holomorphic functions of several complex variables
  - 32B Local analytic geometry
  - 32C Analytic spaces
  - 32D Analytic continuation
  - 32E Holomorphic convexity
  - 32F Geometric convexity
  - 32G Deformations of analytic structures
  - 32H Holomorphic mappings and correspondences
  - 32J Compact analytic spaces
  - 32K Generalizations of analytic spaces
  - 32L Holomorphic fiber spaces
  - 32M Complex spaces with a group of automorphisms
  - 32N Automorphic functions
  - 32P05 Non-Archimedean complex analysis
  - 32Q Complex manifolds
  - 32S Singularities
  - 32T Pseudoconvex domains
  - 32U Pluripotential theory
  - 32V CR manifolds
  - 32W Differential operators in several variables
- 33 Special functions
  - 33B Elementary classical functions
  - 33C Hypergeometric functions
  - 33D Basic hypergeometric functions
  - 33E Other special functions
  - 33F Computational aspects
- 34 Ordinary differential equations
  - 34A General theory
  - 34B Boundary value problems
  - 34C Qualitative theory
  - 34D Stability theory
  - 34E Asymptotic theory
  - 34F05 Equations and systems with randomness
  - 34G Differential equations in abstract spaces
  - 34H05 Control problems
  - 34k Functional-differential and differential-difference equations
  - 34L Ordinary differential operators
  - 34M Differential equations in the complex domain
- 35 Partial differential equations
  - 35A General theory
  - 35B Qualitative properties of solutions
  - 35C Representations of solutions
  - 35D Generalized solutions of partial differential equations
  - 35E Equations and systems with constant coefficients
  - 35F General first-order equations and systems
  - 35G General higher-order equations and systems
  - 35H Close-to-elliptic equations
  - 35J Partial differential equations of elliptic type
  - 35K Parabolic equations and systems
  - 35L Partial differential equations of hyperbolic type
  - 35M Partial differential equations of special type (mixed, composite, etc.)
  - 35N Overdetermined systems
  - 35P Spectral theory and eigenvalue problems for partial differential operators
  - 35Q Equations of mathematical physics and other areas of application
  - 35R Miscellaneous topics involving partial differential equations
  - 35S Pseudodifferential operators and other generalizations of partial differential operators
- 37 Dynamical systems and ergodic theory
  - 37A Ergodic theory
  - 37B Topological dynamics
  - 37C Smooth dynamical systems: general theory
  - 37D Dynamical systems with hyperbolic behavior
  - 37E Low-dimensional dynamical systems
  - 37F Complex dynamical systems
  - 37G Local and nonlocal bifurcation theory
  - 37H Random dynamical systems
  - 37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
  - 37K Infinite-dimensional Hamiltonian systems
  - 37L Infinite-dimensional dissipative dynamical systems
  - 37M Approximation methods and numerical treatment of dynamical systems
  - 37N Applications
- 39 Difference and functional equations
  - 39A Difference equations
  - 39B Functional equations and inequalities
- 40 Sequences, series, summability
  - 40A Convergence and divergence of infinite limiting processes
  - 40B05 Multiple sequences and series
  - 40C General summability methods
  - 40D Direct theorems on summability
  - 40E Inversion theorems
  - 40F05 Absolute and strong summability
  - 40G Special methods of summability
  - 40H05 Functional analytic methods in summability
  - 40J05 Summability in abstract structures
- 41 Approximations and expansions
- 42 Fourier analysis
  - 42A Fourier analysis in one variable
  - 42B Fourier analysis in several variables
  - 42C Nontrigonometric Fourier analysis
- 43 Abstract harmonic analysis
- 44 Integral transforms, operational calculus
- 45 Integral equations
  - 45A05 Linear integral equations
  - 45B05 Fredholm integral equations
  - 45C05 Eigenvalue problems
  - 45D05 Volterra integral equations
  - 45E Singular integral equations
  - 45F Systems of linear integral equations
  - 45G Nonlinear integral equations
  - 45H05 Miscellaneous special kernels
  - 45J05 Integro-ordinary differential equations
  - 45K05 Integro-partial differential equations
  - 45L05 Theoretical approximation of solutions
  - 45M Qualitative behavior
  - 45N05 Abstract integral equations, integral equations in abstract spaces
  - 45P05 Integral operators
  - 45Q05 Inverse problems
  - 45R05 Random integral equations
- 46 Associative rings and algebras
  - 46A Topological linear spaces and related structures
  - 46B Normed linear spaces and Banach spaces; Banach lattices
  - 46C Inner product spaces and their generalizations, Hilbert spaces
  - 46E Linear function spaces and their duals
  - 46F Distributions, generalized functions, distribution spaces
  - 46G Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
  - 46H Topological algebras, normed rings and algebras, Banach algebras
  - 46J Commutative Banach algebras and commutative topological algebras
  - 46K Topological (rings and) algebras with an involution
  - 46L Selfadjoint operator algebras (C*-algebras, von Neumann (W*-) algebras, etc.)
  - 46M Methods of category theory in functional analysis
  - 46N Miscellaneous applications of functional analysis
  - 46S Other (nonclassical) types of functional analysis
  - 46T Nonlinear functional analysis
- 47 Operator theory
  - 47A General theory of linear operators
  - 47B Special classes of linear operators
  - 47C Individual linear operators as elements of algebraic systems
  - 47D Groups and semigroups of linear operators, their generalizations and applications
  - 47E05 Ordinary differential operators
  - 47F05 Partial differential operators
  - 47G Integral, integro-differential, and pseudodifferential operators
  - 47H Nonlinear operators and their properties
  - 47J Equations and inequalities involving nonlinear operators
  - 47L Linear spaces and algebras of operators
  - 47N Miscellaneous applications of operator theory
  - 47S Other (nonclassical) types of operator theory
- 49 Calculus of variations and optimal control; optimization
  - 49J Existence theories
  - 49K Necessary conditions and sufficient conditions for optimality
  - 49L Hamilton-Jacobi theories, including dynamic programming
  - 49M Methods of successive approximations
  - 49N Miscellaneous topics
  - 49Q Manifolds
  - 49R50 Variational methods for eigenvalues of operators
  - 49S05 Variational principles of physics
- 51 Geometry
  - 51A Linear incidence geometry
  - 51B Nonlinear incidence geometry
  - 51C05 Ring geometry (Hjelmslev, Barbilian, etc.)
  - 51D Geometric closure systems
  - 51E Finite geometry and special incidence structures
  - 51F Metric geometry
  - 51G05 Ordered geometries (ordered incidence structures, etc.)
  - 51H Topological geometry
  - 51J Incidence groups
  - 51K Distance geometry
  - 51L Geometric order structures
  - 51M Real and complex geometry
  - 51N Analytic and descriptive geometry
  - 51P05 Geometry and physics
- 52 Convex and discrete geometry
  - 52A General convexity
  - 52B Polytopes and polyhedra
  - 52C Discrete geometry
- 53 Differential geometry
  - 53A Classical differential geometry
  - 53B Local differential geometry
  - 53C Global differential geometry
  - 53D Symplectic geometry, contact geometry
  - 53Z05 Applications to physics
- 54 General topology
  - 54A Generalities
  - 54B Basic constructions
  - 54C Maps and general types of spaces defined by maps
  - 54D Fairly general properties
  - 54E Spaces with richer structures
  - 54F Special properties
  - 54G Peculiar spaces
  - 54H Connections with other structures, applications
  - 54J05 Nonstandard topology
- 55 Algebraic topology
  - 55M Classical topics
  - 55N Homology and cohomology theories
  - 55P Homotopy theory
  - 55Q Homotopy groups
  - 55R Fiber spaces and bundles
  - 55S Operations and obstructions
  - 55T Spectral sequences
  - 55U Applied homological algebra and category theory
- 57 Manifolds and cell complexes
  - 57M Low-dimensional topology
  - 57N Topological manifolds
  - 57P Generalized manifolds
  - 57Q PL-topology
  - 57R Differential topology
  - 57S Topological transformation groups
  - 57T Homology and homotopy of topological groups and related structures
- 58 Global analysis, analysis on manifolds
  - 58A General theory of differentiable manifolds
  - 58B Infinite-dimensional manifolds
  - 58C Calculus on manifolds; nonlinear operators
  - 58D Spaces and manifolds of mappings
  - 58E Variational problems in infinite-dimensional spaces
  - 58H Pseudogroups, differentiable groupoids and general structures on manifolds
  - 58J Partial differential equations on manifolds; differential operators
  - 58K Theory of singularities and catastrophe theory
  - 58Z05 Applications to physics
- 60 Probability theory and stochastic processes
  - 60A Foundations of probability theory
  - 60B Probability theory on algebraic and topological structures
  - 60C05 Combinatorial probability
  - 60D05 Geometric probability, stochastic geometry, random sets
  - 60E Distribution theory
  - 60F Limit theorems
  - 60G Stochastic processes
  - 60H Stochastic analysis
  - 60J Markov processes
  - 60K Special processes
- 62 Statistics
  - 62A01 Foundational and philosophical topics
  - 62B Sufficiency and information
  - 62C Decision theory
  - 62D05 Sampling theory, sample surveys
  - 62E Distribution theory
  - 62F Parametric inference
  - 62G Nonparametric inference
  - 62H Multivariate analysis
  - 62J Linear inference, regression
  - 62K Design of experiments
  - 62L Sequential methods
  - 62M Inference from stochastic processes
  - 62N Survival analysis and censored data
  - 62P Applications
  - 62Q05 Statistical tables
- 65 Numerical analysis
  - 65A05 Tables
  - 65B Acceleration of convergence
  - 65C Probabilistic methods, simulation and stochastic differential equations
  - 65D Numerical approximation and computational geometry
  - 65E05 Numerical methods in complex analysis (potential theory, etc.)
  - 65F Numerical linear algebra
  - 65G Error analysis and interval analysis
  - 65H Nonlinear algebraic or transcendental equations
  - 65J Numerical analysis in abstract spaces
  - 65K Mathematical programming, optimization and variational techniques
  - 65L Ordinary differential equations
  - 65M Partial differential equations, initial value and time-dependent initial-boundary value problems
  - 65N Partial differential equations, boundary value problems
  - 65P Numerical problems in dynamical systems
  - 65Q05 Difference and functional equations, recurrence relations
  - 65R Integral equations, integral transforms
  - 65S05 Graphical methods
  - 65T Numerical methods in Fourier analysis
  - 65Y Computer aspects of numerical algorithms
  - 65Z05 Applications to physics
- 68 Computer science
  - 68M Computer system organization
  - 68N Software
  - 68P Theory of data
  - 68Q Theory of computing
  - 68R Discrete mathematics in relation to computer science
  - 68T Artificial intelligence
  - 68U Computing methodologies and applications
  - 68W Algorithms
- 70 Mechanics of particles and systems
  - 70A05 Axiomatics, foundations
  - 70B Kinematics
  - 70C20 Statics
  - 70E Dynamics of a rigid body and of multibody systems
  - 70F Dynamics of a system of particles, including celestial mechanics
  - 70G General models, approaches, and methods
  - 70H Hamiltonian and Lagrangian mechanics
  - 70J Linear vibration theory
  - 70K Nonlinear dynamics
  - 70L05 Random vibrations
  - 70M20 Orbital mechanics
  - 70P05 Variable mass, rockets
  - 70Q05 Control of mechanical systems
  - 70S Classical field theories
- 74 Mechanics of deformable solids
  - 74A Generalities, axiomatics, foundations of continuum mechanics of solids
  - 74B Elastic materials
  - 74C Plastic materials, materials of stress-rate and internal-variable type
  - 74D Materials of strain-rate type and history type, other materials with memory
  - 74E Material properties given special treatment
  - 74F Coupling of solid mechanics with other effects
  - 74G Equilibrium (steady-state) problems
  - 74H Dynamical problems
  - 74J Waves
  - 74K Thin bodies, structures
  - 74L Special subfields of solid mechanics
  - 74M Special kinds of problems
  - 74N Phase transformations in solids
  - 74P Optimization
  - 74Q Homogenization, determination of effective properties
  - 74R Fracture and damage
  - 74S Numerical methods
- 76 Fluid mechanics
  - 76A Foundations, constitutive equations, rheolog
  - 76B Incompressible inviscid fluids
  - 76D Incompressible viscous fluids
  - 76E Hydrodynamic stability
  - 76F Turbulence
  - 76G25 General aerodynamics and subsonic flows
  - 76H05 Transonic flows
  - 76J20 Supersonic flows
  - 76K05 Hypersonic flows
  - 76L05 Shock waves and blast waves
  - 76M Basic methods in fluid mechanics
  - 76N Compressible fluids and gas dynamics, general
  - 76P05 Rarefied gas flows, Boltzmann equation
  - 76Q05 Hydro- and aero-acoustics
  - 76R Diffusion and convection
  - 76S05 Flows in porous media; filtration; seepage
  - 76T Two-phase and multiphase flows
  - 76U05 Rotating fluids
  - 76V05 Reaction effects in flows
  - 76W05 Magnetohydrodynamics and electrohydrodynamics
  - 76X05 Ionized gas flow in electromagnetic fields; plasmic flow
  - 76Y05 Quantum hydrodynamics and relativistic hydrodynamics
  - 76Z Biological fluid mechanics
- 78 Optics, electromagnetic theory
  - 78A General
  - 78M Basic methods
- 80 Classical thermodynamics, heat transfer
  - 80A Thermodynamics and heat transfer
  - 80M Basic methods
- 81 Quantum theory
  - 81P Axiomatics, foundations, philosophy
  - 81Q General mathematical topics and methods in quantum theory
  - 81R Groups and algebras in quantum theory
  - 81S General quantum mechanics and problems of quantization
  - 81T Quantum field theory; related classical field theories
  - 81U Scattering theory
  - 81V Applications to specific physical systems
- 82 Statistical mechanics, structure of matter
  - 82B Equilibrium statistical mechanics
  - 82C Time-dependent statistical mechanics (dynamic and nonequilibrium)
  - 82D Applications to specific types of physical systems
- 83 Relativity and gravitational theory
  - 83A05 Special relativity
  - 83B05 Observational and experimental questions
  - 83C General relativity
  - 83D05 Relativistic gravitational theories other than Einstein's, including asymmetric field theories
  - 83E Unified, higher-dimensional and super field theories
  - 83F05 Cosmology
- 85 Astronomy and astrophysics
- 86 Geophysics
- 90 Operations research, mathematical programming
  - 90B Operations research and management science
  - 90C Mathematical programming
- 91 Game theory, economics, social and behavioral sciences
  - 91A Game theory
  - 91B Mathematical economics
  - 91C Social and behavioral sciences: general topics
  - 91D Mathematical sociology
  - 91E Mathematical psychology
  - 91F Other social and behavioral sciences (mathematical treatment)
- 92 Biology and other natural sciences
  - 92B Mathematical biology in general
  - 92C Physiological, cellular and medical topics
  - 92D Genetics and population dynamics
  - 92E Chemistry
  - 92F05 Other natural sciences
- 93 Systems Theory; Control
  - 93A General
  - 93B Controllability, observability, and system structure
  - 93C Control systems, guided systems
  - 93D Stability
  - 93E Stochastic systems and control
- 94 Information And Communication, Circuits
  - 94A Communication, information
  - 94B Theory of error-correcting codes and error-detecting codes
  - 94C Circuits, networks
  - 94D05 Fuzzy sets and logic
- 97 Mathematics Education
  - 97A General
  - 97B Educational policy and educational systems
  - 97C Psychology of and research in mathematics education
  - 97D Education and instruction in mathematics
  - 97U Educational material and media. Educational technology

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