Are there any books that are good for self taught math competitions?

Hello! I was born and loved mathematics, physics and chemistry, and I am now retired. Your spirit is worth learning from, and you are a child with extraordinary talent for mathematics, physics and chemistry.

First of all, I wish you good results, and at the same time, you will win the first place in the Mathematics Olympiad, and you will be the best in your class! I've been asked the same question several times, but I haven't. Today, I will give you a reference based on my personal experience, I hope it will help you!

I remember an education expert who said that teaching is not to teach (the meaning is: first, why you should do it, second, why you can do it, and third, what will happen if you don't do it; Fourth, what is the connection between this knowledge point and the front and back.

That is, it is better to give a fish than to give a fish. This is how my primary and junior high school teachers taught us, most of them are special teachers in primary and secondary schools, and some are even teachers and researchers in Hunan Province or Shaoyang City, and some of them enjoy special Jin. It's a pity that I'm too stupid and haven't learned a lot.

In the same way, this is especially true when we study mathematics, physics, chemistry and other sciences. In the same way, the most important thing about what kind of books to buy is to find the right one for you. No matter how well others recommend it, it is not as good as what they like!

First of all, such books must have an analytical process, including analytical and synthetic methods. The second is that the questions are typical and more representative, and there should be a summary after each question: of course, including tips on how to prevent mistakes.

The third is that there should be corresponding exercises attached to it, and there should be answers. By the way, when I was tutoring in the college entrance examination, the teacher was dual-minded, one textbook is a textbook, and the other is a college entrance examination review guide. Note:

Personally, what I'm talking about may not be right for you. But I hope it will help you, and if I can help you, I am the greatest joy. In the same way, when I ask questions, I analyze them first and then answer them, and sometimes I use my camera to film the process.

In this way, it often takes a lot of time, so I miss a lot of satisfactory answers or recommended answers!

Competition book bookstores sell it, ask your teacher to recommend it, don't buy that kind of topic with a lot of thick questions, you can't finish it, if you have an Olympiad class, you should be able to send out books, right? Your teachers must have books about the Olympiad in their hands, and we have those who buy the Olympiad Pioneer, you can take a look.

1. Tutoring Guide for National College Students' Mathematics CompetitionThe book is divided into 3 parts, the first part is the preliminary test questions and answers of the 5th competition, which is comprehensive; The second part is a direct attack on the test center, which is divided into 6 chapters (Function Limit Continuity, Differential Calculus, Integral Science, Differential Equations, Infinite Series, Vector Algebra and Spatial Analytic Geometry), each chapter contains several sections, each section gives the test requirements and analyzes and summarizes the test points, and gives relevant question methods and problem solving points, which is conducive to the effective improvement of candidates' mathematical level; Part 3 gives the 5th final test questions to broaden the reader's horizons.

2. Guidelines for Mathematical Contest in Modeling for College StudentsThis book is a tutorial book to guide college students to prepare for mathematical modeling competitions in an all-round way, and introduces the background knowledge of mathematical modeling and related competitions from multiple perspectives. According to the entry process, the frequently asked questions of the mathematical modeling competition were answered; This paper introduces the software commonly used in mathematical modeling competitions. The common models of mathematical modeling are explained; Typical questions are selected for detailed explanation; Award-winning students and instructors were invited to share their successful experiences; This paper introduces the commonly used ** in the process of mathematical modeling competition.

3. Geometric Significance of Linear AlgebraThis book uses the concept of vectors to conduct a comprehensive geometric analysis of the course content of "linear algebra" in engineering in domestic universities. Starting from the geometric meaning of vectors, the geometric meanings or geometric explanations of vector groups, vector spaces, determinants, matrices, systems of linear equations and quadratic forms are described, and the physical meanings of important concepts are explained. A large number of algebraic concepts and explanations of the geometric meaning of theorems can also make it a reference manual for you to learn linear algebra.

Tsinghua University Press published on August 1, 2010 in the college students' mathematics competition exercises, written by Chen Zhaodou, Zheng Liancun, Wang Hui and others.

Suggestions for the preparation of the mathematics group, the freshman and sophomore students study hard, and use Pei Liwen and Qiu Weisheng when preparing. It is easier to get points for the professional courses of the senior group, especially if you have already selected the topic after graduation or the future graduate research direction has been determined, you can focus on your future direction.

In fact, the questions are all basic questions, and it is not difficult, but if you want to spend a lot of energy reading carefully, you should choose what you want to do, and the reference books can use your undergraduate textbooks, which is not so difficult.

National Collegiate Mathematics Competition Note:

For non-mathematics majors, first learn the advanced mathematics part of the first graduate school entrance examination, directly correspond to all the content of the preliminary round, and can also perfectly connect with the graduate school entrance examination (if you don't go to the graduate school entrance examination after learning mathematics, you will lose a lot); After learning mathematics, go to brush Zhang Tiande, strictly speaking, Zhang Tiande brushes all the knowledge points and masteres the knowledge points, and you already have the ability to enter the finals, after all, there is not much knowledge in the refinement; Students who still have spare time to learn, please brush Pei Liwen.

1. Getting started. First of all, if you want to dabble in competition, the most basic high school curriculum is the foundation of everything. The following books are built on this foundation. The first thing we do, of course, is to close the gap: the gap between the syllabus and the syllabus.

1) "The New Complete Book of Mathematics Problem Solving Methods for Middle Schools", that is, the basic bridging book.

2) "Olympiad Mathematics Course".

The Blue Book of the Classic Olympiad of Mathematics. The advantage is that it is closely related to textbook knowledge, which is suitable for you to improve the mathematics knowledge of Gaorang Dan Middle School for the first time, helping you to lay a solid foundation, mainly explained, supplemented by tests. (You can choose one of the two with "Peiyou Tutorial", "Peiyou" is slightly difficult, but it is very scattered, and "Olympiad Tutorial" is recommended.)

>2. Improvement. 1) The Olympiad Series

Specialized and precise, many topics are very exciting, the difficulty covers leagues and winter camps, and it is easy to read and interest students. If we only aim at the provincial level, we can ignore the probability and geometric inequalities, graph theory, combinatorial geometry, and number theory are well written, and set transformations, trigonometry, and geometry are well written but not practical.

Others such as functions and collections are fine, you can check them out. There are only two inequalities in algebra in this set of books, and they are very impractical and not recommended. As for the mathematical induction, the problems are very classic, but they are very comprehensive and frank, so you can read them at the back of the book.

For this set of books, you have to read it as soon as possible, and you have to do the questions yourself, which may be more difficult. Overall, this set of books is worth a look, so you should start reading it as early as possible.

2) "Olympiad Classics".

The content is relatively comprehensive, the selection of example questions is relatively new, and the difficulty is also high, which is suitable for students who focus on the second test of the league and the winter camp; The algebraic section can be used as a supplement to the Olympiad Series. Geometry is okay, but theorems can be remembered only for the most basic, and extensions can be ruined for nothing. Combination, number theory has time to look at it, but many of them are duplicated with small series of books, so forget it if you don't have time.

3) "Lecture on Proposers".

It is suitable for systematic learning and sprint winter camp, but it is not necessary to do every book, just pick the better one. Such as "Analytic Geometry", "Function Iteration and Functional Equations", "Number Sequence and Mathematical Induction", "Combinatorial Problems", "Trigonometric Functions and Complex Numbers", "Vector and Solid Geometry", "Elementary Number Theory".

Summary. Related materials, "Advanced Algebra and Analytic Geometry" (content involves advanced algebra, group theory, analytic geometry, etc., suitable for mathematics students), "Combinatorics" (combinatorics occupies an important position in mathematics competitions, this book explains more comprehensively), "Probability Theory and Mathematical Statistics" (probability theory and mathematical statistics are also an important part of mathematics competitions, this book explains in detail) The above books are more classic mathematics competition textbooks, and it is recommended to choose suitable books according to your own mathematical foundation and competition needs. At the same time, you can also combine various mathematics competition resources on the network to learn and practice, such as the mathematics competition question bank on Luogu, Acwing, etc.

Dear Glad to answer for you. The book I bought in the freshman math competition is "Mathematical Analysis Leakage Problem Collection", which is easy to understand and suitable for consolidating the foundation of analysis, "Mathematical Analysis Lifting Cover" For students with a solid foundation in analysis, you can choose this book for more in-depth study "Linear Algebra and Its Applications" Linear algebra is an important part of the mathematics competition, and this book is explained in depth.

Related information, "Advanced Algebra and Analytic Geometry" (content involves advanced algebra, group theory, analytic geometry, etc., suitable for mathematics students) "Combinatorics" (combinatorics occupies an important position in mathematics competitions, this book explains more fully smiling) "Probability Theory and Mathematical Statistics" (probability theory and mathematical statistics in mathematics competitions are also an important part, this book explains in detail) The above books are more classic mathematics competition textbooks, It is recommended to choose suitable books according to your mathematical foundation and competition needs. At the same time, you can also combine various mathematics competition resources on the network to learn and practice, such as the mathematics competition question bank on Luogu, Acwing, etc.