Mathematics Subject Classification 2010 

• 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