Learning mathematics should follow the characteristics of mathematics specialty. Engels said that mathematics is a science that studies quantitative relations and spatial forms in the real world. Objective things are described by "number" and "shape" In the process of developing from classical mathematics to modern mathematics, the concepts and categories of "number" and "shape" have been expanding, which has gone far beyond people's daily intuitive understanding and can include any relationship and form in objective reality. For example, the concept of "number" extends from natural number, real number, complex number, vector and tensor to the elements of abstract set; The object of "shape" has also shifted from the intuitive geometric properties of low-dimensional vector space to the structural characteristics of high-dimensional vector space, infinite-dimensional function space, topological space and probability space. Generally speaking, according to the idea and viewpoint of set theory, classical mathematics mainly studies the set and mapping of finite dimensional vector space (especially the function and geometric transformation), while modern mathematics mainly studies the general set and mapping of abstract space. Therefore, modern mathematics is the abstract result of classical mathematics. In essence, the abstraction of mathematics is to generalize and synthesize different things in the objective world according to their * * * characteristics, study them in a unified way at a higher level, and reveal their * * * identical laws, thus forming a structured modern mathematical theoretical system based on kilometers.

The abstraction and unity of mathematics complement each other.

Mathematics major study