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Math and its branches

滴水静禅天•2019-09-16•新知备忘• 1229
Check out the great site http://www.math-atlas.org/ it lists the most of the mathematical disciplines, subdisciplines, ...

According to the site, there are the following main fields in mathematics: foundations, algebra, geometry, analysis, probability and statistics, computer sciences and applied math. These can be subdivides in the following:

Foundations:

  • Mathematical logic

  • Set theory


Algebra:

  • Number theory

  • Group theory

  • Lie groups

  • Commutative rings

  • Associative ring theory

  • Nonassociative ring theory

  • Field theory

  • General algebraic systems

  • Algebraic geometry

  • Linear algebra

  • Category theory

  • K-theory

  • Combinatorics and Discrete Mathematics

  • Ordered sets


Geometry

  • Geometry

  • Convex and discrete geometry

  • Differential geometry

  • General topology

  • Algebraic topology

  • Manifolds


Analysis

  • Calculus and Real Analysis:

    • Real functions

    • Measure theory and integration

    • Special functions

    • Finite differences and functional equations

    • Sequences and series

  • Complex analysis

    • Complex variables

    • Potential theory

    • Multiple complex variables

  • Differential and integral equations

    • Ordinary differential equations

    • Partial differential equations

    • Dynamical systems

    • Integral equations

    • Calculus of variations and optimization

    • Global analysis, analysis on manifolds

  • Functional analysis

    • Functional analysis

    • Fourier analysis

    • Abstract harmonic analysis

    • Integral transforms

    • Operator theory

  • Numerical analysis and optimization

    • Numerical analysis

    • Approximations and expansions

    • Operations research


Probability and statistics

  • Probability theory

  • Statistics


Computer Science

  • Computer science

  • Information and communication


Applied mathematics

  • Mechanics of particles and systems

  • Mechanics of solids

  • Fluid mechanics

  • Optics, electromagnetic theory

  • Classical thermodynamics, heat transfer

  • Quantum Theory

  • Statistical mechanics, structure of matter

  • Relativity and gravitational theory

  • Astronomy and astrophysics

  • Geophysics applications

  • Systems theory

  • Other sciences


Of course, every item in this list can be subdivides in even more disciplines.
 
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