Complete list of math branches

In summary, math is a vast field that can be divided into several branches, including arithmetic, algebra, geometry, trigonometry, calculus, and statistics. Each branch focuses on different aspects of mathematical concepts and techniques, such as basic operations, equations, shapes, angles, functions, and data analysis. These branches are interconnected and build upon each other, providing a solid foundation for higher-level mathematical concepts. Understanding the different branches of math can help individuals solve problems, make predictions, and analyze data in various fields, including science, finance, engineering, and technology.
  • #1
ErichFranz
8
0
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
 
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  • #2
Galois theory?
 
  • #3
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...
 
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Likes tuxscholar, Trip and Demystifier
  • #4
micromass said:
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.
 
  • #5
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.
 

FAQ: Complete list of math branches

1. What is meant by a "complete list of math branches"?

A complete list of math branches refers to a comprehensive compilation of all the different fields and subfields of mathematics. It includes all the major areas of study within mathematics, as well as their corresponding sub-disciplines.

2. How many branches of math are there?

The exact number of branches of math is difficult to determine, as new fields and subfields are constantly emerging. However, a conservative estimate puts the number at around 90 different branches.

3. What are some examples of math branches?

Some examples of math branches include algebra, geometry, calculus, statistics, number theory, game theory, topology, and differential equations.

4. What is the purpose of organizing math into different branches?

Organizing math into different branches allows for a more focused and systematic approach to understanding and studying the various concepts and theories within mathematics. It also makes it easier for researchers and educators to specialize in a particular area and make advancements within that specific field.

5. Can one branch of math be applied to another?

Yes, many branches of math have overlapping concepts and can be applied to other branches or fields of study. For example, calculus is used in physics and engineering, and game theory has applications in economics and social sciences.

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