To learn advanced mathematics, we should learn the basics well, master high school courses such as trigonometry, geometry, algebra and probability, and at least master the basic theory, and advanced mathematics is to learn these things further. Only by understanding these basic courses can we learn advanced mathematics well.

As a basic science, advanced mathematics has its inherent characteristics, namely, high abstraction, strict logic and wide application. Abstraction and computability are the most basic and remarkable characteristics of mathematics. With a high degree of abstraction and unity, we can profoundly reveal its essential laws and make it more widely used.

Strict logic means that in the induction and arrangement of mathematical theory, whether it is concept and expression, or judgment and reasoning, we must use the rules of logic and follow the laws of thinking. Therefore, mathematics is also a way of thinking, and the process of learning mathematics is the process of thinking training. The progress of human society is inseparable from the wide application of mathematics.

Especially in modern times, the appearance and popularization of electronic computers have broadened the application field of mathematics. Modern mathematics is becoming a powerful driving force for the development of science and technology, and it has also penetrated into the field of social sciences extensively and deeply.