Broad subdivisions of Mathematics
Core branches of mathematics:
Applied and related areas:
Other organization schemes:
Areas not corresponding to MSC headings:
(No index pages yet; sorry.
Planned but barely usable at this point is a
listing of such other mathematics disciplines.)
 Precalculus
 Calculus
 Vector analysis
 Discrete mathematics
 Organized by audience:
 Finance
 Actuarial science
 Mathematical physics
 Engineering mathematics
 Mathematics for lay audiences
 [Other suggestions welcome]
Future areas of the MSC
These areas will be added in 2000.

Toplevel subject areas in the MSC
 00: General material including elementary mathematics
 01: History and biography
 03: Mathematical logic and foundations
 04: Set theory
 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
 39: Finite differences 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
 73: Mechanics of 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: Economics, operations research, programming, games
 92: Biology and other natural sciences, behavioral sciences
 93: Systems theory; control
 94: Information and communication, circuits
