The exercises in advanced mathematics in Tongji Edition are marked with asterisks as extracurricular reading contents. Teachers usually choose not to talk about it in class, but students can teach themselves if they are interested. Moreover, some content will appear in the postgraduate entrance examination syllabus, so it is also necessary for some students who need to take the postgraduate entrance examination to learn.

Extended data:

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.

It is generally believed that the mathematics disciplines developed before16th century generally belong to the category of elementary mathematics, so the mathematics disciplines established after17th century are basically the contents of advanced mathematics. It can be seen that the category of higher mathematics can not be explained clearly by a few simple sentences or listing its branches.

Of the three branches of mathematics established before19th century, the first two were originally branches of elementary mathematics and later developed into a part of advanced mathematics, and only analysis belonged to advanced mathematics from the beginning.

The computational aspect of mathematics. Even occupies a dominant position in elementary mathematics. Its position in higher mathematics is also obvious. In addition to many theoretical disciplines, there are also a large number of computational disciplines in advanced mathematics.

Such as differential equations, computational mathematics, statistics, etc. With highly abstract theoretical equipment, it is possible for these disciplines to deal with complex computing problems in modern science and technology.

Baidu Encyclopedia: Advanced Mathematics