Topic & Subtopic Index

#

• 14Fxx (Co)homological methods

A

• 20Kxx Abelian groups
• 14Kxx Abelian varieties and complex tori
• 40Fxx Absolute and strong summability
• 20Dxx Abstract finite groups
• 43 Abstract harmonic analysis
• 65Bxx Acceleration of convergence
• 11Pxx Additive number theory
• 76Lxx Aerodynamics and gas dynamics
• 05Exx Algebraic combinatorics
• 14 Algebraic geometry
• 14Lxx Algebraic groups
• 03Gxx Algebraic logic
• 11Rxx Algebraic number theory (global fields)
• 11Sxx Algebraic number theory (local fields)
• 08Axx Algebraic structures
• 55 Algebraic topology
• 68Wxx Algorithms and complexity-related methods
• 30Lxx Analysis on metric spaces
• 51Nxx Analytic and projective geometry
• 32Cxx Analytic spaces
• 47Nxx Applications
• 53Zxx Applications
• 58Zxx Applications and related topics
• 13Lxx Applications of logic
• 70Pxx Applications to engineering and sciences
• 19Lxx Applications to operator algebras
• 46Nxx Applications to other sciences
• 37Nxx Applications to sciences
• 62Pxx Applications to specific fields
• 81Vxx Applications to specific physical systems
• 55Uxx Applied algebraic topology
• 41Axx Approximation in the real domain
• 41 Approximations and expansions
• 11Gxx Arithmetic algebraic geometry
• 13Fxx Arithmetic and multiplicative structures
• 37Pxx Arithmetic and non-Archimedean dynamics
• 14Gxx Arithmetic problems
• 68Txx Artificial intelligence
• 97Qxx Assessment and evaluation
• 16 Associative rings and algebras
• 85 Astronomy and astrophysics
• 85Axx Astronomy and astrophysics topics
• 34Exx Asymptotic theory
• 11Fxx Automorphic forms
• 31Dxx Axiomatic potential theory

B

• 82Mxx Basic and computational methods
• 54Bxx Basic constructions
• 33Dxx Basic hypergeometric functions
• 78Mxx Basic methods
• 80Mxx Basic methods
• 76Mxx Basic methods and computational fluid mechanics
• 37Gxx Bifurcation and singularity theory
• 76Txx Biofluid and physiological flows
• 92 Biology and other natural sciences
• 74Mxx Biomechanics and composite materials
• 14Exx Birational geometry
• 06Exx Boolean algebras (Boolean rings)
• 76Jxx Boundary layers and wall-bounded flows
• 65Nxx Boundary value and elliptic problems
• 34Bxx Boundary value problems

C

• 49 Calculus of variations and optimal control; optimization
• 58Cxx Calculus on manifolds; nonlinear operators
• 18Dxx Categorical structures
• 18Cxx Categories and algebraic theories
• 18Exx Categories in geometry and topology
• 18 Category theory; homological algebra
• 70Fxx Celestial mechanics
• 57Pxx Cell complexes and generalized manifolds
• 13Exx Chain conditions and finite conditions
• 16Pxx Chain conditions and finite-dimensionality
• 92Exx Chemistry and molecular systems
• 94Cxx Circuits and switching theory
• 53Axx Classical differential geometry
• 28Axx Classical measure theory
• 80 Classical thermodynamics, heat transfer
• 55Mxx Classical topics
• 35Hxx Close-to-elliptic equations
• 51Dxx Closure systems and related geometry
• 60Cxx Combinatorial probability
• 05 Combinatorics
• 94Axx Communication and information theory
• 13 Commutative algebra
• 46Jxx Commutative Banach algebras
• 32Jxx Compact analytic spaces
• 22Cxx Compact groups
• 32Mxx Complex manifolds
• 76Nxx Compressible and transonic/supersonic/hypersonic flows
• 03Dxx Computability and recursion theory
• 16Zxx Computational aspects
• 33Fxx Computational aspects
• 13Pxx Computational commutative algebra
• 65Uxx Computational geometry
• 11Yxx Computational number theory
• 65Zxx Computer implementation aspects
• 68 Computer science
• 68Mxx Computer system organization
• 68Uxx Computing methodologies and applications
• 00Bxx Conference proceedings and collections of articles
• 20Jxx Connections with homological algebra
• 11Uxx Connections with logic
• 12Lxx Connections with logic
• 28Exx Connections with logic and fuzzy sets
• 54Gxx Connections with order structures
• 54Hxx Connections with other structures
• 74Qxx Constitutive modeling
• 70Mxx Control and optimization in mechanics
• 93Bxx Controllability and observability
• 40Axx Convergence and divergence of infinite processes
• 52 Convex and discrete geometry
• 52Axx Convex sets in linear spaces
• 83Fxx Cosmology
• 74Exx Coupling with other physical phenomena
• 14Hxx Curves
• 14Cxx Cycles and subschemes

D

• 68Pxx Data structures and information storage
• 91Cxx Decision and choice models
• 62Cxx Decision theory
• 32Gxx Deformations and moduli
• 62Kxx Design of experiments
• 05Bxx Designs and configurations
• 39 Difference and functional equations
• 65Qxx Difference and functional equations numerics
• 39Axx Difference equations
• 58Axx Differentiable manifolds and differential forms
• 12Hxx Differential and difference algebra
• 53 Differential geometry
• 32Wxx Differential operators in complex analysis
• 57Rxx Differential topology
• 58Nxx Differential-geometric aspects in mathematical physics
• 11Jxx Diophantine approximation
• 11Dxx Diophantine equations
• 40Dxx Direct theorems on summability
• 52Cxx Discrete geometry
• 68Rxx Discrete mathematics in relation to CS
• 37Lxx Dissipative systems
• 51Kxx Distance geometry
• 60Exx Distribution theory and characterizations
• 62Exx Distribution theory and statistical transform methods
• 46Fxx Distributions and generalized functions
• 06Dxx Distributive lattices
• 16Kxx Division rings and simple Artinian rings
• 34Nxx Dynamic equations on time scales
• 74Hxx Dynamical problems
• 65Pxx Dynamical systems and chaos numerics
• 37 Dynamical systems and ergodic theory
• 58Fxx Dynamical systems on manifolds
• 70Exx Dynamics of particle systems
• 70Dxx Dynamics of rigid bodies

E

• 97Mxx Education and computing technologies
• 97Gxx Education in algebra
• 97Hxx Education in analysis
• 97Exx Education in arithmetic and number systems
• 97Ixx Education in combinatorics and discrete mathematics
• 97Fxx Education in geometry
• 97Kxx Education in probability and statistics
• 97Uxx Educational media and resources
• 45Cxx Eigenvalue problems
• 74Bxx Elastic materials
• 11Axx Elementary number theory
• 33Bxx Elementary special functions
• 58Jxx Elliptic and parabolic operators
• 35Jxx Elliptic equations and systems
• 30Dxx Entire and meromorphic functions
• 05Axx Enumerative combinatorics
• 76Yxx Environmental and industrial applications
• 47Jxx Equations and inequalities involving operators
• 65Jxx Equations in abstract spaces
• 35Exx Equations with constant/variable coefficients
• 34Fxx Equations with randomness
• 74Gxx Equilibrium and stability
• 82Bxx Equilibrium statistical mechanics
• 97Rxx Equity and inclusion perspectives
• 37Axx Ergodic theory
• 65Gxx Error analysis and interval methods
• 94Bxx Error-correcting codes
• 49Jxx Existence theories
• 11Lxx Exponential and character sums
• 05Dxx Extremal combinatorics

F

• 54Dxx Fairly general properties
• 14Dxx Families and moduli
• 55Rxx Fiber spaces and bundles
• 32Lxx Fiber spaces and vector bundles
• 12Fxx Field extensions
• 12 Field theory and polynomials
• 91Gxx Finance, insurance, and actuarial mathematics
• 11Txx Finite fields and commutative rings
• 51Exx Finite geometry and special incidence structures
• 35Fxx First-order PDEs
• 76Sxx Flows in porous media
• 76 Fluid mechanics
• 11Exx Forms and quadratic forms
• 62Axx Foundational and philosophical topics
• 14Axx Foundations
• 20Axx Foundations
• 76Axx Foundations and constitutive equations
• 60Axx Foundations and measure-theoretic probability
• 70Axx Foundations and mechanics principles
• 42Axx Fourier analysis in one variable
• 42Bxx Fourier analysis in several variables
• 65Txx Fourier and transform methods
• 74Fxx Fracture and damage mechanics
• 45Bxx Fredholm integral equations
• 46Kxx Function algebras on topological spaces
• 46 Functional analysis
• 39Bxx Functional equations and inequalities
• 34Kxx Functional-differential equations
• 30 Functions of a complex variable
• 26Axx Functions of one variable
• 26Bxx Functions of several variables

G

• 91Axx Game theory
• 91 Game theory, economics, social and behavioral sciences
• 08 General algebraic systems
• 74Axx General and foundational topics
• 81Pxx General and foundational topics
• 97Axx General and historical aspects
• 00Axx General and miscellaneous specific topics
• 70Sxx General and miscellaneous topics
• 00 General and overarching topics; collections
• 16Bxx General and structure theory
• 18Axx General category theory
• 13Axx General commutative algebra
• 12Exx General field theory
• 03Bxx General logic
• 17Axx General nonassociative rings and algebras
• 78Axx General optics and electromagnetic topics
• 30Axx General properties
• 83Cxx General relativity
• 93Axx General systems and control theory
• 34Axx General theory
• 47Axx General theory of linear operators
• 35Axx General topics
• 54 General topology
• 54Axx Generalities
• 12Kxx Generalizations of field theory
• 35Dxx Generalized solutions
• 92Dxx Genetics, evolution, and population dynamics
• 74Nxx Geomechanics
• 53Exx Geometric evolution equations
• 30Cxx Geometric function theory
• 60Dxx Geometric probability and stochastic geometry
• 57Lxx Geometric structures on low-dimensional manifolds
• 51 Geometry
• 49Nxx Geometry and constraints
• 51Pxx Geometry and physics
• 70Nxx Geometry in mechanics
• 11Hxx Geometry of numbers
• 86Axx Geophysical processes and methods
• 86 Geophysics
• 58 Global analysis, analysis on manifolds
• 53Cxx Global differential geometry
• 76Uxx Granular and particulate flows
• 05Cxx Graph theory
• 65Sxx Graphical and image methods
• 19Axx Grothendieck groups ($K_0$)
• 20 Group theory and generalizations
• 81Rxx Groups and algebras in quantum theory
• 47Dxx Groups and semigroups of linear operators

H

• 49Lxx Hamilton-Jacobi theories
• 70Gxx Hamiltonian and Lagrangian mechanics
• 37Jxx Hamiltonian and Lagrangian systems
• 42 Harmonic analysis on Euclidean spaces
• 43Axx Harmonic analysis on groups and semigroups
• 19Dxx Higher algebraic K-theory
• 18Nxx Higher categories
• 57Txx Higher-dimensional manifolds
• 31Bxx Higher-dimensional potential theory
• 35Gxx Higher-order PDEs
• 01 History and biography
• 01Axx History of mathematics and mathematicians
• 37Fxx Holomorphic and complex dynamics
• 32Exx Holomorphic convexity
• 32Axx Holomorphic functions
• 32Hxx Holomorphic mappings
• 18Gxx Homological algebra
• 12Gxx Homological methods
• 13Dxx Homological methods
• 16Dxx Homological methods
• 55Nxx Homology and cohomology theories
• 55Qxx Homotopy groups and related invariants
• 55Pxx Homotopy theory
• 16Txx Hopf algebras and quantum groups
• 76Exx Hydrodynamic stability
• 35Lxx Hyperbolic equations and systems
• 58Kxx Hyperbolic equations and wave phenomena
• 37Dxx Hyperbolic systems
• 33Cxx Hypergeometric functions

I

• 76Bxx Incompressible inviscid fluids
• 76Cxx Incompressible viscous fluids
• 47Cxx Individual operators and spectra
• 26Dxx Inequalities
• 62Mxx Inference from stochastic processes
• 20Fxx Infinite groups and combinatorial group theory
• 58Bxx Infinite-dimensional manifolds
• 37Kxx Infinite-dimensional systems
• 94 Information and communication, circuits
• 46Cxx Inner product spaces and geometry
• 70Hxx Integrable and nonintegrable systems
• 47Gxx Integral and pseudodifferential operators
• 45 Integral equations
• 45Pxx Integral equations in abstract spaces
• 65Rxx Integral equations numerics
• 44Axx Integral transforms and operational calculus
• 44 Integral transforms, operational calculus
• 45Jxx Integro-ordinary differential equations
• 45Kxx Integro-partial differential equations
• 76Rxx Interfacial and multiphase flows
• 74Rxx Inverse and identification problems
• 40Exx Inversion theorems

J

• 76Wxx Jets and wakes
• 17Cxx Jordan structures

K

• 19 K-theory
• 19Exx K-theory in geometry and topology
• 19Fxx K-theory in number theory and arithmetic
• 70Bxx Kinematics
• 57Mxx Knots and 3-manifolds

L

• 06Bxx Lattices
• 17Bxx Lie algebras and Lie superalgebras
• 22Exx Lie groups
• 58Lxx Lie theory and analysis on manifolds
• 60Fxx Limit theorems
• 20Gxx Linear algebraic groups
• 15Axx Linear and multilinear algebra
• 15 Linear and multilinear algebra; matrix theory
• 46Exx Linear function spaces
• 51Axx Linear incidence geometry
• 62Jxx Linear inference and regression
• 45Axx Linear integral equations
• 70Jxx Linear vibrations
• 32Bxx Local analytic geometry
• 53Bxx Local differential geometry
• 16Lxx Local rings and related classes
• 13Gxx Local rings and related topics
• 14Bxx Local theory
• 22Bxx Locally compact abelian groups
• 22Dxx Locally compact groups and their representations
• 37Exx Low-dimensional dynamical systems
• 57Kxx Low-dimensional topology

M

• 76Hxx Magnetohydrodynamics
• 57 Manifolds and cell complexes
• 49Qxx Manifolds and geometric measure methods
• 54Cxx Maps and general topological spaces
• 60Jxx Markov processes
• 74Dxx Materials with special properties
• 92Bxx Mathematical biology in general
• 91Bxx Mathematical economics
• 03 Mathematical logic and foundations
• 81Qxx Mathematical methods in quantum theory
• 90Cxx Mathematical programming
• 65Kxx Mathematical programming and optimization
• 97 Mathematics education
• 20Hxx Matrix groups
• 40Cxx Matrix methods of summability
• 28 Measure and integration
• 28Dxx Measure-theoretic ergodic theory
• 46Gxx Measures and integration in abstract settings
• 28Cxx Measures and integration on spaces with additional structure
• 74Pxx Mechanical systems with constraints
• 74 Mechanics of deformable solids
• 70 Mechanics of particles and systems
• 46Mxx Methods of category theory in analysis
• 51Fxx Metric geometry
• 19Mxx Miscellaneous applications
• 45Mxx Miscellaneous applications
• 76Zxx Miscellaneous fluid mechanics topics
• 35Rxx Miscellaneous PDE topics
• 26Exx Miscellaneous topics
• 35Mxx Mixed-type and composite-type equations
• 03Cxx Model theory
• 06Cxx Modular and complemented lattices
• 16Cxx Modules, bimodules, and related theory
• 18Mxx Monoidal and enriched categories
• 40Bxx Multiple sequences and series
• 11Nxx Multiplicative number theory
• 62Hxx Multivariate analysis

N

• 76Dxx Navier-Stokes equations and related flows
• 91Fxx Networked and strategic interaction systems
• 94Dxx Networks and related structures
• 17 Nonassociative rings and algebras
• 46Sxx Noncommutative geometry and analysis
• 65Hxx Nonlinear equations
• 46Txx Nonlinear functional analysis
• 51Bxx Nonlinear incidence geometry
• 45Gxx Nonlinear integral equations
• 47Hxx Nonlinear operators
• 70Kxx Nonlinear vibrations and oscillations
• 62Gxx Nonparametric inference
• 03Hxx Nonstandard models
• 42Cxx Nontrigonometric harmonic analysis
• 46Bxx Normed linear spaces and Banach spaces
• 11 Number theory
• 65 Numerical analysis
• 65Dxx Numerical approximation and interpolation
• 65Fxx Numerical linear algebra
• 45Qxx Numerical methods
• 49Mxx Numerical methods
• 70Qxx Numerical methods
• 74Sxx Numerical methods
• 37Mxx Numerical methods and simulation
• 65Lxx Numerical methods for ODEs
• 65Mxx Numerical methods for PDEs
• 65Exx Numerical methods in complex analysis

O

• 83Bxx Observational and experimental relativity
• 19Gxx Obstructions and regulators
• 34Mxx ODEs in the complex domain
• 55Sxx Operations and obstructions
• 90Bxx Operations research and management science
• 90 Operations research, mathematical programming
• 47 Operator theory
• 47Kxx Operator theory in abstract spaces
• 78 Optics, electromagnetic theory
• 49Kxx Optimality conditions
• 06 Order, lattices, ordered algebraic structures
• 06Fxx Ordered algebraic structures
• 06Axx Ordered sets
• 16Hxx Orders, arithmetic, and geometric aspects
• 34 Ordinary differential equations
• 47Exx Ordinary differential operators
• 34Lxx Ordinary differential operators and spectral theory
• 08Cxx Other classes of algebras
• 31Cxx Other generalizations
• 20Nxx Other generalizations of groups
• 92Fxx Other natural sciences
• 17Dxx Other nonassociative structures
• 40Jxx Other sequence and series methods
• 33Exx Other special functions
• 47Sxx Other topics in operator theory
• 35Nxx Overdetermined systems

P

• 35Kxx Parabolic equations and systems
• 65Yxx Parallel and high-performance computing
• 62Fxx Parametric inference
• 35 Partial differential equations
• 47Fxx Partial differential operators
• 58Gxx Partial differential operators on manifolds
• 35Qxx PDEs in connection with mathematical physics
• 20Bxx Permutation groups
• 03Axx Philosophical aspects
• 92Cxx Physiological and medical modeling
• 57Qxx PL-topology
• 74Cxx Plastic and inelastic materials
• 97Bxx Policy and curriculum
• 16Rxx Polynomial identity rings
• 11Cxx Polynomials and matrices
• 26Cxx Polynomials and rational functions
• 52Bxx Polytopes and polyhedra
• 31 Potential theory
• 31Exx Potential theory on fractals and metric spaces
• 65Cxx Probabilistic methods and simulation
• 20Pxx Probabilistic methods in group theory
• 11Kxx Probabilistic number theory
• 60Bxx Probability on algebraic/topological structures
• 60 Probability theory and stochastic processes
• 97Nxx Problem solving and competencies
• 14Nxx Projective and enumerative geometry
• 03Fxx Proof theory and constructive mathematics
• 35Sxx Pseudodifferential operators
• 58Hxx Pseudogroups and groupoids
• 91Exx Psychological and cognitive modeling
• 97Cxx Psychological aspects of learning mathematics

Q

• 35Bxx Qualitative properties
• 34Cxx Qualitative theory
• 81Sxx Quantization and semiclassical methods
• 81Txx Quantum field theory
• 81 Quantum theory

R

• 16Nxx Radical theory
• 70Lxx Random and stochastic mechanics
• 37Hxx Random dynamical systems
• 45Lxx Random integral equations
• 76Pxx Rarefied gas dynamics
• 76Qxx Reactive and combustion flows
• 14Pxx Real algebraic and analytic geometry
• 12Dxx Real and complex fields
• 51Mxx Real and complex geometry
• 26 Real functions
• 32Dxx Real methods and analytic continuation
• 57Zxx Relations to quantum topology and physics
• 54Jxx Relationships with applications
• 70Rxx Relativistic and other extended frameworks
• 83Dxx Relativistic field theories
• 83 Relativity and gravitational theory
• 20Cxx Representation theory of groups
• 16Gxx Representation theory of rings
• 35Cxx Representations of solutions
• 97Dxx Research in mathematics education
• 30Fxx Riemann surfaces
• 13Bxx Ring extensions and related structures
• 51Cxx Ring geometry
• 16Yxx Rings with additional structure
• 76Gxx Rotating fluids and geophysical flows
• 60Lxx Rough analysis and related topics

S

• 62Dxx Sampling theory
• 81Uxx Scattering and open quantum systems
• 46Lxx Selfadjoint operator algebras (C*-algebras)
• 20Mxx Semigroups
• 11Bxx Sequences and sets
• 40 Sequences, series, summability
• 62Lxx Sequential methods
• 30Bxx Series expansions
• 28Bxx Set functions and measures with values in abstract spaces
• 03Exx Set theory
• 32 Several complex variables and analytic spaces
• 76Vxx Shock waves and discontinuities
• 45Exx Singular integral equations
• 32Sxx Singularities
• 37Cxx Smooth dynamical systems
• 91Dxx Social and behavioral dynamics
• 68Nxx Software and programming theory
• 47Lxx Spaces and algebras of operators
• 58Dxx Spaces of mappings
• 18Bxx Special categories
• 47Bxx Special classes of operators
• 33 Special functions
• 45Rxx Special kinds of integral equations
• 15Bxx Special matrices
• 54Fxx Special properties of spaces
• 83Axx Special relativity
• 60Kxx Special stochastic processes
• 14Mxx Special varieties
• 40Gxx Specialized summability methods
• 82Dxx Specific physical systems
• 55Txx Spectral sequences and homological methods
• 35Pxx Spectral theory and eigenvalue problems
• 93Dxx Stability and stabilization
• 34Dxx Stability theory
• 70Cxx Statics
• 82 Statistical mechanics, structure of matter
• 62 Statistics
• 62Rxx Statistics on algebraic/topological structures
• 19Cxx Steinberg groups and related theory ($K_2$)
• 60Hxx Stochastic analysis
• 60Gxx Stochastic processes
• 93Exx Stochastic systems and control
• 74Lxx Structural mechanics
• 20Exx Structure and classification of groups
• 16Exx Structure and representation
• 62Bxx Sufficiency and information
• 40Hxx Summability in abstract structures
• 14Jxx Surfaces and higher-dimensional varieties
• 62Nxx Survival analysis and reliability
• 53Dxx Symplectic and contact geometry
• 93Cxx System structure and realization
• 45Fxx Systems of integral equations
• 93 Systems theory; control

T

• 65Axx Tables and hand computation
• 97Pxx Teacher education and professional development
• 68Qxx Theory of computing
• 13Cxx Theory of modules and ideals
• 80Axx Thermodynamics and heat transfer fundamentals
• 74Kxx Thin bodies (plates, shells, rods)
• 82Cxx Time-dependent statistical mechanics
• 22Axx Topological algebraic systems
• 46Hxx Topological algebras
• 51Gxx Topological and differential geometry (synthetic aspects)
• 13Jxx Topological and ordered rings
• 51Hxx Topological and transformation geometry
• 37Bxx Topological dynamics
• 12Jxx Topological fields
• 22 Topological groups, Lie groups
• 19Kxx Topological K-theory
• 46Axx Topological linear spaces
• 57Nxx Topological manifolds
• 54Exx Topological spaces with richer structures
• 57Sxx Topological transformation groups
• 22Fxx Transformation groups
• 76Kxx Transition and wave phenomena
• 14Txx Tropical geometry
• 76Fxx Turbulence
• 31Axx Two-dimensional potential theory

U

• 83Exx Unified and higher-dimensional theories

V

• 49Rxx Variational methods for eigenvalues
• 49Sxx Variational principles in optimization
• 58Exx Variational problems in infinite dimensions
• 08Bxx Varieties
• 45Dxx Volterra integral equations

W

• 74Jxx Waves and vibrations
• 19Bxx Whitehead groups ($K_1$)

Z

• 11Mxx Zeta and $L$-functions