In order to improve the level, it is the best way to start with the standard textbooks of the school and do more related questions and examination questions over the years.
If you win the math contest, you can get extra points in the college entrance examination. The following is a recommendation for a math contest book:
1. The Orsay Classic Series published by Hunan Normal University Press is a set of books that I like very much. The content is comprehensive, and the selection of examples is novel and difficult. Suitable for students who focus on the second test of the league and the winter camp.
2. For students who are mainly preparing for the high school league, they can choose the classic course of Olympic Mathematics and the series of small blueprints (both published by East China Normal University Press). The advantage of Olympic Mathematics course is that it is closely related to textbook knowledge, which is suitable for you to improve your mathematics knowledge in high school and help you lay a good foundation. Small blueprint series is professional and accurate, covering many wonderful topics such as leagues and winter camps, and students can read it easily.
3. In elementary number theory, I especially recommend Elementary Number Theory (edited by Feng Zhigang) in the proposer's lecture series, which is a very systematic and difficult book in number theory at present, and many students feel that they have benefited a lot after reading it. In number theory, of course, there are two gentlemen, one is Professor Pan Chengbiao and the other is Professor Yu. Teacher Pan's Elementary Number Theory is a must-read textbook when we study, and it is also a textbook in universities. Not limited to competitions. Teacher Yu's pamphlet on number theory is very classic-"The Problem of Number Theory in Mathematics Competition", but I'm afraid it's hard to buy it now.
I haven't read much about geometry. Teacher Shen Wenxuan recently published a new book. I forgot my name. Someone recommended it to me. There are several geometry books in Russia, which are very thick. I think it is very necessary for the competition coach to read, refine and organize carefully before teaching the students. At first, it is not suitable for students to follow the book, but they can read it again when their level is high (after completing the competition foundation of geometry) (so good books should be read in the right way and at the right stage);
5. In the stage of preparing for actual combat, it is needless to say that Gift Magazine and Towards IMO, as long as you are careful not to be entangled in the topic, the thinking method behind the topic is often more exciting and beneficial;
6. Mr. Denton has written many good books, especially many pamphlets (similar to other teachers at the same time), which are suitable for supplementary reading or interesting reading to improve his mathematical understanding. Of course, there is also the course "Research on Mathematical Competition", which has been reprinted several times by several publishing houses. This book is the top reading when I was studying, and it is also a true portrayal of many students in the competition at that time. It is regarded as a classic. The advantages of this book don't need to be elaborated, just reminding students to lay a good foundation first and use it with other special topics and basic books, and the effect is better;
7. There are many reference books for students who are preparing for the actual combat in the league, such as "Intensive Lecture and Test of Olympic Mathematics" and "Preparation Manual". The Russian (Soviet) competition questions are also good materials, and the combination questions are suitable for thinking and choosing at any time regardless of the results.