MSC2010

1 MSC 분류체계의 구조

MSC는 알파벳-숫자 혼용 조합으로서 3단계로 나타내어진다. 다음은 하나의 예시이다. 1단계는 두 자리의 자연수, 2단계는 알파벳, 3번째 단계는 또 하나의 두 자리의 자연수로 나타내어진다.
  • 53은 differential geometry(미분기하학)을 지칭한다.
  • 53A는 classical differential geometry를 지칭한다.
  • 53A45는 vector and tensor analysis를 지칭한다.
ACM Computing Classification System과 많은 유사점을 가지기도 한다.

1.1 1단계

1단계는 00부터 99까지 숫자로 64개의 수학적 대분야에 고유의 두 자리수를 부여한다. 이중 특별사항으로는 00분류 기호를 가지는 General항목이 있다. 이 항목은 Recreational mathematics, Philosophy of mathematics, 수학교육학, 다른 분야와의 융합적 요소, 등을 모두 총괄하고 있어서 다른 항목보다 많은 서적을 포함하며 물리학술지 등에도 등장하기도 한다. 1단계의 요목표는 아래 참고.

1단계 위의 하나의 분류단계가 더 있음으로, 총 4단계로 보는 경우들도 있다.

1.2 2단계

1.3 3단계

2 MSC 요목표

  • 대분류; General/foundations
    • 00: General
    • 01: History and biography
    • 03: Mathematical logic(논리학) and foundations, including model theory, computability theory, set theory(집합론), proof theory, and algebraic logic
  • 대분류; Discrete mathematics(이산수학)/algebra(대수학)
    • 05: Combinatorics(경우의 수,확률,등)
    • 06: Order theory
    • 08: General algebraic systems
    • 11: Number theory(정수론)
    • 12: Field theory and polynomials
    • 13: Commutative rings and algebras
    • 14: Algebraic geometry
    • 15: Linear and multilinear algebra(선형대수학,등); matrix(행렬) theory
    • 16: Associative rings and associative algebras(가환,등)
    • 17: Non-associative rings and non-associative algebras (비가환,등)
    • 18: Category theory; homological algebra
    • 19: K-theory
    • 20: Group theory(군론) and generalizations
    • 22: Topological groups, Lie groups, and analysis upon them
  • 대분류; Analysis(해석학)
    • 26: Real functions, including derivatives and integrals
    • 28: Measure and integration
    • 30: Complex functions, including approximation theory in the complex domain
    • 31: Potential theory
    • 32: Several complex variables and analytic spaces
    • 33: Special functions
    • 34: Ordinary differential equations(미분방정식)
    • 35: Partial differential equations(편미분방정식)
    • 37: Dynamical systems and ergodic theory
    • 39: Difference equations and functional equations
    • 40: Sequences, series(수열), summability
    • 41: Approximations and expansions
    • 42: Harmonic analysis, including Fourier analysis, Fourier transforms, trigonometric approximation, trigonometric interpolation, and orthogonal functions
    • 43: Abstract harmonic analysis
    • 44: Integral transforms, operational calculus
    • 45: Integral equations
    • 46: Functional analysis, including infinite-dimensional holomorphy, integral transforms in distribution spaces
    • 47: Operator theory
    • 49: Calculus of variations and optimal control; optimization (including geometric integration theory)
  • 대분류; Geometry(기하학) and topology(위상수학)
    • 51: Geometry(기하학)
    • 52: Convex geometry and discrete geometry
    • 53: Differential geometry
    • 54: General topology
    • 55: Algebraic topology
    • 57: Manifolds
    • 58: Global analysis, analysis on manifolds (including infinite-dimensional holomorphy)
  • 대분류; Applied mathematics / other
    • 65 Numerical analysis(수치해석)
    • 68 Computer science
    • 70 Mechanics (including particle mechanics)
    • 74 Mechanics of deformable solids
    • 76 Fluid mechanics(유체역학)
    • 78 Optics(광학), electromagnetic theory(전자기학)
    • 80 Classical thermodynamics(열역학), heat transfer
    • 81 Quantum theory
    • 82 Statistical mechanics, structure of matter
    • 83 Relativity and gravitational theory, including relativistic mechanics
    • 85 Astronomy(천문학) and astrophysics
    • 86 Geophysics
    • 90 Operations research, mathematical programming
    • 91 Game theory, economics(경제학), social and behavioral sciences
    • 92 Biology(생명과학) and other natural sciences(자연과학)
    • 93 Systems theory; control, including optimal control
    • 94 Information(정보) and communication, circuits
    • 97 Mathematics education(수학교육학)