From a simple and simple point of view, the purpose of learning is to enrich knowledge and improve cognitive ability, and the other is to acquire methods and solve practical problems. Learning advanced mathematics is to better serve these two purposes. It is hoped that readers can understand the origin of advanced mathematics from the perspective of pursuit, the thought of advanced mathematics from the perspective of philosophy and the application of advanced mathematics from the perspective of methods.

First of all, advanced mathematics is the knowledge base of all subsequent courses in universities. The knowledge related to quantitative problems in subsequent courses can hardly be separated from advanced mathematics. Learning advanced mathematics well is the basis of learning other professional courses well. On the contrary, if you can't learn advanced mathematics well, it will bring great difficulties to the subsequent professional courses. Secondly, advanced mathematics provides a stage for everyone to exercise and improve their logical thinking ability. Mastered the ideas and methods of advanced mathematics. It can greatly improve the rigor of understanding and thinking and improve the quality and ability of logical thinking. Third, advanced mathematics can provide thinking methods to solve problems. ?

A remarkable feature that distinguishes this way of thinking from elementary mathematics is that the solution of elementary mathematics is mostly "one thing and one discussion", while the solution of advanced mathematics is characterized by "one thought is consistent and one method is widely used". With advanced mathematics, a series of problems that can't be solved by elementary mathematics are often solved. It is precisely because of advanced mathematics that the basic position of mathematics in the inheritance and progress of human civilization is self-evident, which makes mathematics play an irreplaceable role in modern society.

Most students majoring in science and engineering must study advanced mathematics in their first year of college. Now many liberal arts majors also offer advanced mathematics. This is because advanced mathematics plays an increasingly important role in cultivating college students' quality and ability, and its position in the university knowledge system is becoming more and more important, which is inseparable from the wide application of mathematics. Modern mathematics has become a powerful driving force for the development of science and technology, and has penetrated into all fields of social life more and more widely.