1, History of Mathematics

2. Mathematical logic and mathematical foundation

3. Number theory

4. algebra

5. Algebraic geometry

6. Geometry

7. Topology

8. Mathematical analysis

9. Non-standard analysis

10, function theory

1 1, ordinary differential equation

12, partial differential equation

13, power system

14, integral equation

15, functional analysis

16, computational mathematics

17, probability theory

18, mathematical statistics

19, Applied Statistical Mathematics

20. Other disciplines of applied statistical mathematics

2 1, operational research

22. Combinatorial mathematics?

23, fuzzy mathematics

24. Quantum Mathematics

25. Applied Mathematics (specific application in related disciplines)

26, other disciplines of mathematics

Extended data:

Various fields of mathematics

Fundamentals and philosophy

In order to understand the basis of mathematics, mathematical logic and set theory are developed. Mathematical logic focuses on putting mathematics on a solid axiomatic framework and studying the results of this framework. It is the birthplace of Godel's second incomplete theorem, which is perhaps the most widely spread achievement in logic-there is always a true theorem that cannot be proved.

Modern logic is divided into recursion theory, model theory and proof theory, which are closely related to theoretical computer science. P/NP problem in Millennium Prize is a famous problem in theoretical computer science.

Discrete mathematics

Discrete mathematics refers to the general name of the most useful mathematical fields for theoretical computer science, including computability theory, computational complexity theory and information theory. Computable theory tests the limits of different theoretical models of computer, including the most powerful model-Turing machine.

Computers can make the study of complexity theory easier to deal with; Even if some problems can be solved by computer in theory, it will take too much time or space to solve these problems. Despite the rapid progress of computer hardware, it is still unrealistic.

Finally, information theory focuses on the total amount of data that can be stored in a specific medium, so there are concepts such as compression and entropy. As a relatively new field, discrete mathematics has many basic unsolved problems. One of the most famous problems is the P/NP problem-one of the Millennium Prize problems. It is generally believed that the answer to this question is no.

applied mathematics

Applied mathematical thinking applies abstract mathematical tools to solve practical problems in science, industry and commerce. An important field in applied mathematics is statistics, which uses probability theory as a tool to allow the description, analysis and prediction of phenomena with contingent components.

Most experiments, investigations and observation studies need to make statistical analysis of their data. Many statisticians don't consider themselves mathematicians, but feel that they are part of a cooperative group. Numerical analysis studies which calculation methods can effectively solve those mathematical problems that cannot be solved due to the limitation of manpower; It also includes studying rounding errors or errors from other sources in calculation.

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