数学分类

2.1. 数学分类#

2.1.1. 数学基础：Foundation#

研究数学基础和逻辑。

  1. Model theory

  2. Computability theory

  3. Set theory

  4. Proof theory

  5. Algebraic logic

  6. Type theory

2.1.2. 代数：Algebra#

研究公式、方程、数学抽象的结构。

  1. Number theory

  2. Combinatorics

  3. Field theory

  4. Linear algebras

  5. Category theory

  6. K-theory

  7. Group theory

  8. Lie groups

也有分类把 Number Theory 单分出来，研究整数。Number theory 早期被叫作 arithmetic，如今叫 numerical analysis。

2.1.3. 几何：Geometry#

研究空间。

  1. Geometry

  2. Convex geometry

  3. Discrete geometry

  4. Differential geometry

  5. General topology

  6. Algebraic topology

  7. Manifolds

2.1.4. 分析：Analysis#

研究数量和变化。

  1. Real functions(derivatives, integrals)

  2. Complex functions

  3. Special functions

  4. Ordinary differential equations

  5. Partial differential equations

  6. Series

  7. Harmonic analysis(Fourier analysis, Fourier transforms)

  8. Integral transforms

  9. Integral equations

  10. Functional analysis

Infinitesimal Calculus(微积分)简称 Calculus, 指「分析」中的初等部分。

2.1.5. 应用数学：Applied mathematics#

研究数学抽象在生活中的实际应用。

  1. Probability theory

  2. Stochastic processes

  3. Statistics,

  4. Numerical analysis

  5. Computer science

  6. Mechanics

  7. Fluid mechanics

  8. Optics

  9. Classical thermodynamics

  10. Quantum theory

  11. Statistical mechanics

  12. Relativity and gravitational theory

  13. Astronomy and astrophysics

  14. Geophysics

  15. Game theory

  16. Biology

目录