Complete list of math branches

[ErichFranz]

I want to compile a list of every branch of mathematics, for my studies.

This is what I got from wiki:

1. Basic mathematics
2. Advanced mathematics
2.1 Pure mathematics
2.1.1 Algebra
2.1.2 Calculus and analysis
2.1.3 Geometry and topology
2.1.4 Combinatorics
2.1.5 Logic
2.1.6 Number theory
2.2 Applied mathematics
2.2.1 Dynamical systems and differential equations
2.2.2 Mathematical physics
2.2.3 Computing
2.2.4 Information theory and signal processing
2.2.5 Probability and statistics
2.2.6 Game theory
2.2.7 Operations research

Let me know if any are missing

 

[icystrike]

Galois theory?

 

[micromass]

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. But for more information (and descriptions of the above fields), I refer to the site I mentioned...

 

[ErichFranz]

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. But for more information (and descriptions of the above fields), I refer to the site I mentioned...

Great site. Thanks for letting me know.

 

[CellCoree]

or need to be added/edited.

As a scientist, it is important to have a clear understanding of the different branches of mathematics in order to effectively apply them in our research and studies. The list provided from wiki is a comprehensive and accurate representation of the main branches of mathematics. However, I would like to add a few more branches that are also important in the field of mathematics:

1. Graph theory
2. Number systems (such as complex numbers, quaternions, etc.)
3. Cryptography
4. Differential geometry
5. Numerical analysis
6. Topological data analysis
7. Game theory
8. Mathematical modeling
9. Econometrics
10. Mathematical biology

It is also worth mentioning that there are many sub-branches within these main branches, and the field of mathematics is constantly evolving and expanding. Therefore, this list may not be exhaustive, but it serves as a good starting point for your studies. I encourage you to explore and learn about these different branches and how they can be applied in various fields of science and beyond.