MSC2010

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Mathematics Subject Classification 2010 {Info & Stats}

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Joint revision by Mathematical Reviews and Zentralblatt für Mathematik (done 2007 – 2009)


This wiki version of the current MSC was initialized in July 2007 with MSC2000 by Patrick Ion at MR/AMS. It was designed to be collaboratively editable by editorial staff of Mathematical Reviews and Zentralblatt für Mathematik so as to produce this joint draft of a proposed MSC2010 ready in January 2009. It now represents the final state of the revision process, namely our MSC2010 usable from July 2009.


  • 00-XX General
  • 01-XX History and biography [See also the classification number –03 in the other sections]
  • 03-XX Mathematical logic and foundations
  • 05-XX Combinatorics {For finite fields, see 11Txx}
  • 06-XX Order, lattices, ordered algebraic structures [See also 18B35]
  • 08-XX General algebraic systems
  • 11-XX Number theory
  • 12-XX Field theory and polynomials
  • 13-XX Commutative algebra rings and algebras
  • 14-XX Algebraic geometry
  • 15-XX Linear and multilinear algebra; matrix theory
  • 16-XX Associative rings and algebras {For the commutative case, see 13-XX}
  • 17-XX Nonassociative rings and algebras
  • 18-XX 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-XX $K$-theory [See also 16E20, 18F25]
  • 20-XX Group theory and generalizations
  • 22-XX Topological groups, Lie groups {For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX}
  • 26-XX Real functions [See also 54C30]
  • 28-XX Measure and integration {For analysis on manifolds, see 58-XX}
  • 30-XX Functions of a complex variable {For analysis on manifolds, see 58-XX}
  • 31-XX Potential theory {For probabilistic potential theory, see 60J45}
  • 32-XX Several complex variables and analytic spaces {For infinite-dimensional holomorphy, see 46G20, 58B12}
  • 33-XX Special functions (33-XX deals with the properties of functions as functions) {For orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; for representation theory see 22Exx}
  • 34-XX Ordinary differential equations
  • 35-XX Partial differential equations
  • 37-XX Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
  • 39-XX Difference and functional equations
  • 40-XX Sequences, series, summability
  • 41-XX 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-XX Harmonic analysis on Euclidean spaces Fourier analysis
  • 43-XX Abstract harmonic analysis {For other analysis on topological and Lie groups, see 22Exx}
  • 44-XX 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}
  • 45-XX Integral equations
  • 46-XX Functional analysis {For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx}
  • 47-XX Operator theory
  • 49-XX Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]
  • 51-XX Geometry {For algebraic geometry, see 14-XX}
  • 52-XX Convex and discrete geometry
  • 53-XX Differential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx}
  • 54-XX General topology {For the topology of manifolds of all dimensions, see 57Nxx}
  • 55-XX Algebraic topology
  • 57-XX Manifolds and cell complexes {For complex manifolds, see 32Qxx}
  • 58-XX Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15}
  • 60-XX Probability theory and stochastic processes {For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX}
  • 62-XX Statistics
  • 65-XX Numerical analysis
  • 68-XX Computer science {For papers involving machine computations and programs in a specific mathematical area, see Section –04 in that area}
  • 70-XX Mechanics of particles and systems {For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX}
  • 74-XX Mechanics of deformable solids
  • 76-XX Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX}
  • 78-XX Optics, electromagnetic theory {For quantum optics, see 81V80}
  • 80-XX Classical thermodynamics, heat transfer {For thermodynamics of solids, see 74A15}
  • 81-XX Quantum theory
  • 82-XX Statistical mechanics, structure of matter
  • 83-XX Relativity and gravitational theory
  • 85-XX Astronomy and astrophysics {For celestial mechanics, see 70F15}
  • 86-XX Geophysics [See also 76U05, 76V05]
  • 90-XX Operations research, mathematical programming
  • 91-XX Game theory, economics, social and behavioral sciences
  • 92-XX Biology and other natural sciences
  • 93-XX Systems theory; control {For optimal control, see 49-XX}
  • 94-XX Information and communication, circuits
  • 97-XX Mathematics education
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