Broad subdivisions of Mathematics
Core branches of mathematics:
Applied and related areas:
Other organization schemes:
Areas not corresponding to MSC headings:
(Few index pages yet; sorry.)
 Areas larger than MSC headings (e.g. Topology)
 Areas identified by nonMSC systems (e.g. Quantum Algebras)
 Topics cutting across MSC boundaries (e.g. Spheres)
 Nowdefunct MSC areas (e.g. Operational calculus)
 Minor but wellpublicized areas (e.g. Fractals)
 Organized by audience (e.g. Financial mathematics)
 Topics too elementary for MSC (e.g. Calculus)
 Peripheral topics (e.g. Accounting)
 Completely misfiled topics (e.g. Numerology)
[Note that the latest revision
of the MSC was put into use for
January 2000; not all pages at
this site have been adapted yet.]

Toplevel subject areas in the MSC
 00: General material including elementary mathematics
 01: History and biography
 03: Mathematical logic and foundations
 05: Combinatorics and graph theory
 06: Order, lattices, ordered algebraic structures
 08: General algebraic systems
 11: Number theory
 12: Field theory and polynomials
 13: Commutative rings and algebras
 14: Algebraic geometry
 15: Linear and multilinear algebra; matrix theory
 16: Associative rings and algebras
 17: Nonassociative rings and algebras
 18: Category theory, homological algebra
 19: Ktheory
 20: Group theory and generalizations
 22: Topological groups, Lie groups
 26: Real functions and elementary calculus
 28: Measure and integration
 30: Functions of a complex variable
 31: Potential theory
 32: Several complex variables and analytic spaces
 33: Special functions including trigonometric functions
 34: Ordinary differential equations
 35: Partial differential equations
 37: Dynamical systems and ergodic theory
 39: Difference and functional equations
 40: Sequences, series, summability
 41: Approximations and expansions
 42: Fourier analysis
 43: Abstract harmonic analysis
 44: Integral transforms, operational calculus
 45: Integral equations
 46: Functional analysis
 47: Operator theory
 49: Calculus of variations and optimal control; optimization
 51: Geometry, including classic Euclidean geometry
 52: Convex and discrete geometry
 53: Differential geometry
 54: General topology
 55: Algebraic topology
 57: Manifolds and cell complexes
 58: Global analysis, analysis on manifolds
 60: Probability theory and stochastic processes
 62: Statistics
 65: Numerical analysis
 68: Computer science
 70: Mechanics of particles and systems
 74: Mechanics of deformable solids
 76: Fluid mechanics
 78: Optics, electromagnetic theory
 80: Classical thermodynamics, heat transfer
 81: Quantum Theory
 82: Statistical mechanics, structure of matter
 83: Relativity and gravitational theory
 85: Astronomy and astrophysics
 86: Geophysics
 90: Operations research, mathematical programming
 91: Game theory, economics, social and behavioral sciences
 92: Biology and other natural sciences
 93: Systems theory; control
 94: Information and communication, circuits
 97: Mathematics education
