Mathematics knowledge related to competition is a professional knowledge, which is called competition mathematics, but this course is only offered to normal mathematics majors, and non-normal mathematics majors are not allowed.

I am a sophomore now. In a non-normal university, there is a big difference between advanced mathematics and competition mathematics. The most important derivatives, calculus and Fourier series in higher mathematics, whether it is middle school mathematics league or IMO, do not belong to the category of middle school mathematics competition, because mathematics competition examines students' insight into mathematics, not how much you have learned.

Mathematical analysis should be closely related to competition mathematics, but mathematical analysis mainly focuses on calculus, and the theory related to competition only lies in some chapters related to numbers.

Competition mathematics can be divided into algebra, geometry and combinatorial mathematics. Analytic geometry and set are still tested in the middle school mathematics league, but they are no longer the focus of IMO.

The most important thing is that mathematical competitions often combine these three propositions-objectively, IMO has many knowledge points and only seven topics, so we can't think that they are irrelevant.

Simply put, elementary geometry is mainly based on triangles, quadrangles and circles in junior high school geometry, but this is only a shell, because junior high school geometry can only be said to be the basis of competition geometry. For example, IMO geometry topics often involve several important theorems, such as Mené lios, Ptolemy, Seva and siemsen, which will not be discussed in junior high school geometry classes.

Combinatorial mathematics only involves one thing in high school, that is, arranging combinatorial binomials, but that is less than one tenth of combinatorial mathematics. When students go to college, students who apply mathematics will learn discrete mathematics, which will involve the pillars of combinatorial mathematics such as graph theory.

Personally, I think the most closely combined knowledge of college mathematics and middle school mathematics competition is elementary number theory, which is not only a compulsory course of college mathematics, but also a hot topic of IMO.

As for the book you mentioned, I haven't read it, but I can recommend you a competition textbook: Mathematical Olympiad Course published by Hunan Normal University, edited by Jun Ye, which is the best textbook I have ever used. High school attached to hunan normal university is the most successful school in our national academic competition for middle school students. There are nearly ten IMO gold medal winners in mathematics alone, and there is one almost every year in recent years. There are also tutorials on algebra, geometry and combination, which are really useful.