Mathematics Subject Classification
The Mathematics Subject Classification ( MSC ) is a classification for the field of mathematics . It is published by the American Mathematical Society and the Zentralblatt MATH for the subject indexing of the literature databases Mathematical Reviews (MR) and Zentralblatt MATH . Every mathematical article that appears in a specialist journal is provided with one or more classes that assign it to a mathematical sub-area. The classification also plays an important role in finding relevant work.
Versions
The original version from 1991 was revised in 2000, adding new categories for modern research areas and removing rarely used categories. Another revision, MSC 2010, was completed in May 2009.
construction
The MSC consists of over 5,000 classes and is structured hierarchically on three levels. The first is indicated by two digits, the second by a letter and the third by two more digits.
For example, category 11B05 is structured as follows:
- 11 = Number theory
- 11B = Sequences and sets
- 11B05 = Density, gaps, topology
- Top level structure
- 01: History of mathematics , biographies
- 03: logic
- 05 to 22: Discrete Mathematics / Algebra
- 05: Combinatorics
- 06: Orderly structures
- 08: General Algebraic Systems
- 11: Number Theory
- 12: Body theory and polynomials
- 13: Commutative algebra
- 14: Algebraic Geometry
- 15: multilinear and linear algebra algebra, matrix theory
- 16: Associative rings and algebras
- 17: Non-associative rings and algebras
- 18: Category theory , homological algebra
- 19: K theory
- 20: group theory
- 22: Topological groups , Lie groups
- 26 to 49: Analysis
- 26: Real functions
- 28: Measure and Integration
- 30: Functions of a complex variable
- 31: potential theory
- 32: Functions of several complex variables
- 33: Special functions
- 34: Ordinary differential equations
- 35: Partial differential equations (PDGL)
- 37: Dynamic systems and ergodic theory
- 39: Functional and difference equation
- 40: Series , sequences , summation
- 41: Approaches and series expansion
- 42: Fourier Analysis
- 43: Harmonic Analysis
- 44: Integral transformations
- 45: Integral equations
- 46: Functional Analysis
- 47: Operator theory
- 49: Calculus of Variations
- 51 to 58: Geometry / topology
- 51: geometry
- 52: Discrete and Convex Geometry
- 53: differential geometry
- 54: General topology
- 55: Algebraic topology
- 57: manifolds
- 58: Global Analysis , Analysis on Manifolds
- 60 to 97: Applied Mathematics / Other
- 60: Probability Theory
- 62: Statistics
- 65: Numerical Analysis
- 68: Computer science
- 70: Point mechanics
- 74: Solid mechanics
- 76: Fluid mechanics
- 78: optics , electromagnetism
- 80: Classical thermodynamics
- 81: Quantum Mechanics
- 82: Statistical Mechanics
- 83: Relativity and gravitation theory
- 85: Astronomy and Astrophysics
- 86: geophysics
- 90: optimization
- 91: game theory , social sciences
- 92: Biomathematics and Applied Mathematics in Other Natural Sciences
- 93: systems theory
- 94: Circuits
- 97: Mathematics Education Pedagogy