Classification and branches of mathematics?

Classification: from vertical division:

1, elementary mathematics and ancient mathematics: this refers to1mathematics before the 7th century. Mainly Euclidean geometry established by ancient Greece, arithmetic established by ancient China, ancient Indian and ancient Babylon, algebraic equations developed during the European Renaissance, etc.

2. Variable mathematics: refers to mathematics established and developed at the beginning of 17- 19 century. The period of variable mathematics from the first half of17th century can be divided into two stages: the establishment stage of17th century (heroic age) and the development stage of18th century (creative age).

3. Modern mathematics: refers to19th century mathematics. The19th century of modern mathematics is the stage of comprehensive development and maturity of mathematics, and the face of mathematics has undergone profound changes. Most branches of mathematics were formed in this period, and the whole mathematics showed a comprehensive prosperity.

4. Modern mathematics: refers to mathematics in the 20th century. 1900 famous german mathematician Hilbert (d.

Hilbert) delivered a famous speech at the World Congress of Mathematicians, and put forward 23 mathematical problems to predict and understand the future development of mathematics (see below), which opened the prelude of modern mathematics in the 20th century.

From the horizontal division:

1, Basic Mathematics (English: Pure

Mathematics), also known as pure mathematics or pure mathematics, is the core part of mathematics, including algebra, geometry and analysis, which study numbers, shapes and the relationship between numbers and shapes respectively.

2. Applied mathematics. Simply put, it is the application of mathematics.

three

, computational mathematics. Learn calculation methods (numerical analysis), mathematical logic, symbolic mathematics, computational complexity, programming and other issues. This subject is closely related to computers.

4. Probability statistics. Divided into probability theory and mathematical statistics.

5. Operational research and cybernetics. Operational research is a subject that solves the operation, organization and management problems of complex systems such as manpower, material resources and financial resources by mathematical methods on the basis of establishing models.

Branch: 1. arithmetic

2. Elementary algebra

3. Advanced Algebra

number theory

5. European geometry

6. Non-Euclidean geometry

7. Analytic geometry

8. Differential geometry

9. Algebraic geometry

10. Projective geometry

1 1. Topological geometry

12. Topology