Advanced mathematics is an important basic subject in universities of science and engineering. As a science, advanced mathematics has its inherent characteristics, namely, high abstraction, strict logic and wide application. Abstract is the most basic and remarkable feature of mathematics-high abstraction and unity, which 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. Therefore, it is very important for us to learn advanced mathematics well.

If you want to learn advanced mathematics well, you must at least do the following four things:

First, understand the concept. There are many concepts in mathematics. Concepts reflect the essence of things. Only by figuring out how it is defined and what its essence is can we really understand a concept.

Secondly, master the theorem. Theorem is a correct proposition, which is divided into two parts: condition and conclusion. In addition to mastering its conditions and conclusions, we should also understand its scope of application and be targeted.

Third, do some exercises on the basis of understanding the examples. Especially remind learners that the examples in the textbook are very typical, which is helpful to understand concepts and master theorems. Pay attention to the characteristics and solutions of different examples, and do appropriate exercises on the basis of understanding examples. When writing a topic, you should be good at summing up-not only the methods, but also the mistakes. You will gain something after doing this, so you can draw inferences from others.

Fourth, clear the context. We should have an overall grasp of the knowledge we have learned and summarize the knowledge system in time, which will not only deepen our understanding of knowledge, but also help us to further study.

Advanced mathematics includes calculus and solid analytic geometry, series and ordinary differential equations. Calculus is the most systematic and widely used in other courses. The theory of calculus was completed by Newton and Leibniz. (Of course, calculus was applied before them, but it was not systematic enough. ) The basic concepts of calculus and extreme calculus are difficult to understand.