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Which MSCs are covered in this service?

The AMS has condensed the Mathematics Subject Classification into the following eleven subject areas. You may sign-up for email notification of most recent articles in any journal or
combination of journal and subject area.

Mathematics Subject Classification by Subject Area

Algebra and Algebraic Geometry

  • 06 (1940-now) Order, lattices, ordered algebraic structures [See also 18B35]
  • 08 (1959-now) General algebraic systems
  • 12 (1959-now) Field theory and polynomials
  • 13 (1959-now) Commutative rings and algebras
  • 14 (1940-now) Algebraic geometry
  • 15 (1940-now) Linear and multilinear algebra; matrix theory
  • 16 (1959-now) Associative rings and algebras [For the commutative case, see 13-XX]
  • 17 (1940-now) Nonassociative rings and algebras
  • 18 (1940-now) Category theory, homological algebra [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]
  • 19 (1986-now) $K$-theory [See also 16E20, 18F25]
  • 20 (1940-now) Group theory and generalizations
  • 22 (1940-now) Topological groups, Lie groups [For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX]

Analysis

  • 26 (1940-now) Real functions [See also 54C30]
  • 28 (1940-now) Measure and integration [For analysis on manifolds, see 58-XX]
  • 30 (1940-now) Functions of a complex variable [For analysis on manifolds, see 58-XX]
  • 31 (1940-now) Potential theory [For probabilistic potential theory, see 60J45]
  • 32 (1940-now) Several complex variables and analytic spaces [For infinite-dimensional holomorphy, see also 46G20, 58B12]
  • 33 (1940-now) Special functions [ 33-XX deals with the properties of functions as functions. For orthogonal functions, see also 42Cxx; for aspects of combinatorics, see 05Axx; for number-theoretic
    aspects, see 11-XX; for representation theory, see 22Exx]
  • 37 (2000-now) Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
  • 40 (1940-now) Sequences, series, summability
  • 41 (1940-now) Approximations and expansions [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]
  • 42 (1940-now) Fourier analysis
  • 43 (1973-now) Abstract harmonic analysis [For other analysis on topological and Lie groups, see 22Exx]
  • 44 (1940-now) Integral transforms, operational calculus [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]
  • 46 (1940-now) Functional analysis [For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx]
  • 47 (1959-now) Operator theory
  • 49 (1940-now) Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]
  • 58 (1973-now) Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx; for geometric integration theory, see 49Q15]

Applications

  • 49 (1940-now) Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]
  • 65 (1940-now) Numerical analysis
  • 68 (1940-now) Computer science [For papers involving machine computations and programs in a specific mathematical area, see Section --04 in] that area}
  • 90 (1940-now) Operations research, mathematical programming
  • 91 (2000-now) Game theory, economics, social and behavioral sciences
  • 92 (1940-now) Biology and other natural sciences
  • 93 (1940-now) Systems theory; control [For optimal control, see 49-XX]
  • 94 (1940-now) Information and communication, circuits

Differential Equations

  • 34 (1940-now) Ordinary differential equations
  • 35 (1940-now) Partial differential equations
  • 37 (2000-now) Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
  • 39 (1940-now) Difference and functional equations
  • 45 (1940-now) Integral equations

Discrete Mathematics and Combinatorics

  • 05 (1940-now) Combinatorics [For finite fields, see 11Txx]
  • 68 (1940-now) Computer science [For papers involving machine computations and programs in a specific mathematical area, see Section --04 in] that area}
  • 90 (1940-now) Operations research, mathematical programming

General Interest

  • 00 (1940-now) General
  • 01 (1940-now) History and biography [See also the classification number -03 in the other sections]
  • 97 (2000-now) Mathematics education

Geometry and Topology

  • 32 (1940-now) Several complex variables and analytic spaces [For infinite-dimensional holomorphy, see also 46G20, 58B12]
  • 51 (1980-now) Geometry [For algebraic geometry, see 14-XX]
  • 52 (1940-now) Convex and discrete geometry
  • 53 (1940-now) Differential geometry [For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx]
  • 54 (1940-now) General topology [For the topology of manifolds of all dimensions, see 57Nxx]
  • 55 (1940-now) Algebraic topology
  • 57 (1959-now) Manifolds and cell complexes [For complex manifolds, see 32Qxx]

Logic and Foundations

  • 03 (1980-now) Mathematical logic and foundations

Mathematical Physics

  • 70 (1940-now) Mechanics of particles and systems [For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX]
  • 74 (2000-now) Mechanics of deformable solids
  • 76 (1940-now) Fluid mechanics [For general continuum mechanics, see 74Axx, or other parts of 74-XX]
  • 78 (1940-now) Optics, electromagnetic theory [For quantum optics, see 81V80]
  • 80 (1940-now) Classical thermodynamics, heat transfer [For thermodynamics of solids, see 74A15]
  • 81 (1940-now) Quantum theory
  • 82 (1940-now) Statistical mechanics, structure of matter
  • 83 (1940-now) Relativity and gravitational theory
  • 85 (1940-now) Astronomy and astrophysics [For celestial mechanics, see 70F15]
  • 86 (1940-now) Geophysics [See also, 76U05, 76V05]

Number Theory

  • 11 (1985-now) Number theory
  • 12 (1959-now) Field theory and polynomials
  • 14 (1940-now) Algebraic geometry

Probability

  • 60 (1940-now) Probability theory and stochastic processes [For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX.]
  • 62 (1940-now) Statistics
  • 80 (1940-now) Classical thermodynamics, heat transfer [For thermodynamics of solids, see 74A15]
  • 82 (1940-now) Statistical mechanics, structure of matter