Sorting and recommendation of reference books for mathematics majors

 

I want to read more books in mathematics, but it is hard for beginners to know those books well. I collected them online and sorted them out based on my own experience:
Start with mathematical analysis:
Mathematical Analysis is the most important course in the Mathematics Department. It will often extend a course in the future at one point, and it will be the basis of most of the courses in the Mathematics Department in the future. It is also a difficult course at the beginning. The difficulty here is mainly due to the inadaptability to mathematical analysis ideas and methods. In fact, it will be a little easier as the course goes deeper. I feel much easier when I look at my senior one's review. The Mathematical Analysis of mathematics involves a total of 15 credits and 270 hours in three semesters. Delete the difficult part of Mathematical Analysis and add the ordinary differential equations. The simplest part is the advanced mathematics of China's non-mathematics major, or the high part of mathematics 1.
Remember the following:
1. Diligence is always more important than learning mathematical analysis.
2. It is not difficult to learn mathematical analysis. It is rare to read a group of books that have persisted for a long time.
3. Don't expect the first time to remember and master anything. Please read the second time, the third time ,..., Dialefel.
4. You can read it carefully.
5. After reading a textbook with one word, read at least one reference book and try to create a exercise set.
6. reading a book three times is better than reading three books three times. The fourth time is the opposite.
7. I often look back at my path.
For more information, see.
Mathematical Analysis book:
A reference book is enough for beginners to select a textbook. I strongly recommend 11, 1, 2, and 8. In addition, it is recommended that you take a look at the number of teaching materials at 16 or 20.
Written by the Chinese themselves:
1 mathematical analysis: Chen chuanjie, Jin Fulin, Zhu Xueyan, Ouyang Guangzhong (the new version of the author's order is reversed)
It should be from Xin Qin's concise course of mathematical analysis, which is the longest and most widely used book in the Mathematics Department. It is a designated teaching material used by most schools for postgraduate analysis. I used the second edition in my freshman year. Now I have the third edition, but there are still some printing errors in it, But Ke can see it at a glance. On the Internet, you can find the reference answers for the exercises after class, but we suggest you do it yourself. Many economic engineering schools also use this book. It is difficult to explain in some places, and there is one or two knowledge points missing from other books. For example, it seems that there is no Stolz theorem, and the definition of real numbers is unclear. But it is still a good book. It has some advantages to be widely used.
2 mathematical analysis: Department of mathematics, East China Normal University
Normal Students use the most books. After-school exercises are well organized. They are also a lot of books used for postgraduate entrance exams. At the end of the textbook, we talk about calculus on some manifold. Although it is a normal book, the difficulty is somewhat lower than the previous one, but it is worth reading.
3. Mathematical Analysis
The above three books are the most used for postgraduate entrance exams.
4 mathematical analysis, Li chengzhang, Huang Yumin
It is a mathematical analysis sub-book in a series of Nankai University. All the books in this set of teaching materials are often used, and the overall situation is good, it is a textbook written for each course in the mathematics department after the decrease in the number of hours after the teaching reform.
5 mathematical analysis handout Liu yuchain
I did not read a book recommended by my math analytics teacher. I should have released a new version recently, which seems to be the fifth? It was originally a correspondence textbook and should be detailed and easy to understand. Don't look down on it because it is a correspondence teaching material. In fact, the original Correspondence work was done by the best professors. Let's take a look.
6 mathematical analysis: Cao zhijiang
The textbooks of the Inner Mongolia university mathematical base focus on physical implementation and will lay a good foundation and will not blindly expand to the n-dimensional model. Suitable for beginners. Textbooks for national high-quality courses.
7 new lecture on Mathematical Analysis Zhang zhusheng
It is recognized as a new book with no exercises after class. The processing of materials is quite novel. The author has died.
8. Mathematical Analysis tutorial Chang gengzhe, Shi jihuai
The textbooks of China University of Science and Technology are extremely difficult to exercise after class.
9 mathematical analysis by Xu Forest
This is the same as the previous one. It is a textbook of Tsinghua University. You can take a look. The book is very thick and looks very slow.
10 concise tutorial on Mathematical Analysis by Deng Dong
It is also a book that can be seen frequently. The author has died. Textbooks for national high-quality courses.
11 Xu shaopu's mathematical analysis tutorial Nanjing University Press
These books should be enough. Other books are not listed one by one. Select a textbook.
Foreign mathematical analysis teaching materials:
11. Course of calculus by fekhengerz
The first masterpiece of mathematical analysis should not be scared by its big part. I started to look at it in the first half of my senior year and found that it was very clear and looks very fast. We strongly recommend that you take a look, even if you have bought a favorite. It is not recommended to read books at a price, but to read books. A good textbook can lay a solid foundation for future study.
12 fekhengerz, mathematical analysis principles
The abbreviation of the previous book does not advocate reading. You can only read it if you want to read it.
13 mathematical analysis Zhuo LiQi
The idea is quite new and has been popular in recent years, but it does not seem necessary.
14 Xin Qin, a concise tutorial on Mathematical Analysis
I did not have any exercises after class, but I recommended the corresponding exercises in the JI midorvic mathematical analysis exercise set. However, as the exercise set is updated, the question is no longer correct, but Xin Qin's article is still good.
15 lectures on Mathematical Analysis
The handout of Moscow University is just a handout, which is very difficult to see, but it is good to use it.
16 Xin Qin, lecture 8 on Mathematical Analysis
The master is the master and is strongly recommended.
17 mathematical analysis principles Rudin
China's mathematics was learned from the former Soviet Union, which is similar to Russian textbooks. Reading Russian books is not very difficult. However, this American book is worth reading. The description is simple and clear. You can deduce the theorem above.
18 Introduction to calculus and analysis kulang
Another American classical mathematical analysis book. Some people think that the idea is no longer popular, but mathematical analysis is a basic course to lay a good foundation.
19. Calculus on a manifold
Further analysis. Mathematical Analysis in China generally does not talk about calculus on the manifold, but the calculus on the manifold is a trend.
20 speech at Nankai University
There will be some insights, but unfortunately it seems that the versions circulating on the Internet are missing some content.
21 Hua Luogeng advanced mathematics introduction Science Press
Mathematical Analysis question set
If you do not do the question, you just have never learned it. I hope to finish all the exercises after the textbook without looking at the answer. If you want to buy a question set, you also need to buy a question set.
1 jimidovich mathematical analysis exercise set
In recent years, people have said that this book is so bad that it has been criticized for a large number of computing questions and is not suitable for mathematics. However, the reason why this exercise set is no longer widely used is the emergence of this exercise answer. Students' plagiarism in the answer has lost the value of this book. If you don't look at the answer, it is still the first exercise set of mathematical analysis. Do not blindly criticize your mistakes. Have you ever been aware of it and will affect your future study.
2. The first version of "mathematical analysis exercise course materials" or the second version of "Mathematical Analysis Problem Solving Guide", Lin Yuanqu, Fang qiqin, etc.
The two books are the same. The first version has an electronic version, and the second version can buy a paper version. And 3.
3 mathematical analysis topic set Lin Yuanqu, Fang qiqin, etc.
The appearance of answers to jimidovich's mathematical analysis exercise set has led to a higher rating for this book, because this book has no answer. You can only do it yourself.
4. mathematical analysis exercises, Science Press, and Qian Liwen or Qian Jilin
I have passed the test well. I do not recommend that I study mathematical analysis.
5 answers to various teaching materials
A pile of garbage. Destroyed.
Resolution ry:
There is a tendency to be eaten by algebra in analytic ry. However, for mathematics students, I should be eager to learn about it. I was not so eager to learn about it in my freshman year. Later I learned other lessons and I always felt a little uncomfortable, later I found that my mathematical skills, especially geometric skills, were not well prepared.
1 Wu Guanglei: A Concise tutorial on analytic ry; Higher Education Press
I did not have a good foundation, but I have learned a lot from this book. However, I chose one of the following three books as a reference book.
2 Resolution ry Qiu Weisheng, Peking University Press
My freshman textbook
3 Resolution ry Lu genlin, Xu zandao
4 Resolution ry
The similarities between 2, 3, and 4 are similar.
The exercise set includes the analytical geometric exercise set by Bach wallv, which is not so easy to find.
Algebra
As mentioned above, algebra tends to eat ry, so there are many "Algebra and ry" that keep pace with the times. However, it is recommended to study separately and lay a solid foundation for one course. Many so-called concise tutorials and textbooks that combine algebra and analytic ry are not very mature yet. It is not recommended.
1 "advanced algebra": Department of mathematics, Peking University, Department of algebra and ry, algebra team
At present, Chinese universities, especially General Universities, have a long tradition of Algebra Teaching materials widely used in mathematics. Currently, the third edition is usually used. It is also a designated book for postgraduate entrance exams of various universities. This book focuses more on teachers, giving teachers a lot of space to play and is widely welcomed by teachers. However, it is difficult for students with poor foundations in some places. All the content that should be discussed.
2 "Higher Algebra" Zhang He Rui, Hao xinxin
It is widely used by the mathematics department of each Normal University, and is located in the same world. Zhang hurui has died, but the book has been published to the fifth edition.
3 linear algebra Li yinsheng, China University of Science and Technology Press
It is difficult for the University of Science and Technology to write a book.
4 linear space introduction ye mingxun, Wuhan University Press
5. Zhang xianke, Tsinghua University Press
6. Xu yichao, linear algebra and matrix theory, published by Higher Education Press
The above three books are written in a book order. I took them, but I know 5 is good.
7 Introduction to substitute mathematics kosterlijin
He is a famous book on mathematics in the course of calculus by fikhgorz. There is nothing to say about a classic book. Recently, a new Chinese translation has been published in three copies, but it is neither thick nor expensive.
8 linear algebra topic set petrokrow
9 Higher Algebra topic set fajeyev and sominski
Two thousand is the classic algebra exercise set of the former Soviet Union, which has one thousand and questions respectively. It will lay a very good basic skill after completion.
10 Qiu Weisheng of Higher Algebra
Well written, but it is just a book used by the Department of mathematics of Peking University. The teaching content and focus of Peking University have always been different from those of other universities in China, qiu Weisheng adopts a different arrangement from other teaching materials, so he may not be able to use this book. It is recommended to be used as reference books rather than teaching materials.
11 Yang Zi, question set of Higher Algebra
Relatively 8, 9 is easy to buy. Many people use it as reference books for postgraduate entrance exams and comply with the so-called teaching or postgraduate entrance syllabus.
12 linear algebra Jiang erxiong, Gao Yumin, Wu Jing
Linear Algebra is actually a textbook for advanced algebra. It was a very old book written for the computing and mathematics major at that time. I can't find it on the market, but there must be a collection of university books.
Modern algebra: it is not only the most important course of mathematics, but also has many applications in computer science. The second part of general discrete mathematics is modern algebra, also called abstract algebra.
1 Introduction to modern algebra Feng keqin
2 modern algebra Xiong quanyan
3. Substitute mathematics Mo zongjian
4. The introduction to substitute mathematics
5 Modern algebra Sheng decheng

Subsequent courses of analysis include ordinary differential equations, partial differential equations, Real Variable Functions, complex variable functions, and functional analysis. The following is a one-to-one introduction:
Ordinary differential equations:
1 tutorial on ordinary differential equations Ding Tongren, Li Chengzhi, Higher Education Press
It is recognized as the best teaching material written in China.
2 ordinary differential equations Wang Kaohsiung et al
Widely used teaching materials. Recommended for beginners: 1, 2
3. Ordinary Differential Equations v. I. Arnold
Books that are often classified as unreadable.
4. pontriyajin
The author of the textbooks of the former Soviet Union was a mathematical wizards. due to an accident in a chemical experiment, his eyes were blind and he had to turn to mathematics and become a first-generation mathematical master.
5 Ordinary Differential Equations exercise set Phillips
It's easy to get through this book. It is not a simple question, but a simple requirement for you.

Complex Function:
1. Concise Analysis
A special book.
2 complexanalysis L. V. Ahlfors
I still advocate reading more Masters' books when I study mathematics.
3 complex functions Yu Jiarong
4. Variable Function Zhong Yuquan
The above two books are the most widely used books in the Chinese Mathematics Department, but there are usually one or two chapters left.
5. Preliminary Analysis of functions H. cart
6. Ren Yaofu, Application Analysis
7. Complex Variable Function Theory topic set walkovis

Real-time functions:
1 Zheng weixing, Summary of real-time variable functions and Functional Analysis
A good entry book.
2 theory of Real Variable Functions Zhou Minqiang
It is generally regarded as a very good book, but I personally think it is difficult for people with poor foundations. The writing method is not the same as that of other versions.
3. Real Variable Functions Jiang zejian and Wu zhiquan
I prefer to use this book and 4 compared to 2.
4. Xia daoxing, Wu Zhuoren, Yan shaozong, and Shu Wuchang
In the 1980s S, the standard textbook of the mathematics department of the Chinese University was released in March 2009. We strongly recommend this and the previous version. Although thick, it is quite detailed.
5. Theorem and exercises of Real Variable Function Theory
6 Real Variable Function Theory topic set liakski
As with analysis, you need to do more questions.
Functional Analysis:
1 functional analysis handout Zhang Gongqing
I personally feel that writing is quite confusing, but the mathematics department of each university is in use.
2 Xia daoxing, Real Variable Functions and Functional Analysis
As mentioned above, it is recommended again, although a little thick.
3 Zheng weixing, Summary of Real Variable Functions and Functional Analysis
4 Functional Analysis question set antoinevich
5 "function theory and functional analysis preliminary" Kolmogorov
After reading this article, you will be rewarded. Master's classic masterpiece, including real-time functions, functional analysis, and grading
6. Answers to functional analysis theory exercises Kirov

Partial Differential Equation:
1 partial differential equations Chen zuyu
2. Qi minyou, Generalized Functions and Mathematical Physical Equations
3 Lecture on Mathematical Physical equations Jiang lishang
4. Mathematical and physical equations Gu chaohao and Li dasqian
5 tutorial on partial differential equations Huazhong Normal University
6 mathematical physical equation exercise set flakimrov
Gu chaohao and Li dasqian's book is an old teaching material that has been used for quite a long time. 5. They added some new content and added the solution of the first-order equation.
7. Liang Kunyu, mathematical and physical methods.
Non-mathematical physics is equivalent to partial differential equations and complex variable functions of mathematics.
8. Mathematical and physical equations ke Lang
Physical learners are still able to lay a solid foundation when they are young.
9 Introduction to special functions Wang ZhuXi
A proud book written by Chinese people. Mr. Wang is a teacher of Yang zhenning.
Probability Theory is divided into three parts: probability theory, mathematical statistics, and random processes.
Probability Theory:
1. Basis of probability theory Li XianPing
2 Introduction to probability theory Wang renguan
3 probability theory and mathematical statistics (upper and lower layers), edited by the department of mathematical mechanics, Sun Yat-sen University
Probability Theory is easy to learn, but it is not the same thing to do.
Mathematical Statistics:
1. Mathematical Statistics tutorial
2 mathematical statistics handout
3. Lu Xuan, mathematical statistics Basics
4 mathematical statistics topic set: Department of Statistics and finance, China University of Science and Technology
5. Zhao voter of mathematical statistics
Random Process:
1 Random Process and Application Lu Dajin
2 random process sun hongxiang
3 random process theory Qian minping, Lu Guang
Many schools do not have a random process, but this part is quite important, either in engineering or economics or mathematics.
Differential ry:
1 "differential ry" Peng Jiayu
2 Differential ry
3. Lecture on differential ry
4. Chen Weiyuan, differential ry
5 Differential Geometric question set Fei jinke
6 lipxitz, Differential Geometric Theory and exercises
Topology:
1 "Point Set Topology handout (second edition)" Xiong Jincheng
2 topological space theory: eryu Zhihong
3 basic topology M. A. Armstrong
4 "Point Set Topology" "Point Set Topology solution and counterexample" Chen jizang
5. The exercise set of ry and Topology
Again, ignore the ry, including the analytic ry, the differential ry, And the topology will regret it.
Mathematical Basics
1 mathematical basics Wang fangting
2 mathematical overview Godin
In the beginning, I will know what mathematics is.
3 What is mathematics krona, Robin
A generation of famous books.
Discrete Mathematics: separate learning is recommended.
1 Basic Set Theory Beijing Normal University
2 Lu zhongwan, mathematical logic for computer science
3. Wang Shuhe, Graph Theory and Algorithm
4 Graph Theory and Its Applications bondy, Murty
5 Discrete Mathematics, Qu wanling
6. Specific mathematics, such as grahan and Gartner
There are English and Chinese versions. it is not difficult for me to take English versions in my senior year. It is recommended that you take a look at the books that combine mathematics.
Algorithm:
1 <introductiontoalgorithms> Corman
Numerical analysis: Traditional mathematics subjects include numerical approximation, numerical algebra, numerical optimization, and numerical solution of differential equations. Numerical approximation, numerical algebra, Numerical Solutions of differential equations collectively called numerical analysis, numerical optimization and operational research are somewhat like.
The following four traditional textbooks (not counted as 1) are all published by the People's Education Press.
1 Jiang erxiong, Gao kunmin, and Wu jingkun's Linear Algebra
2 Li yuesheng and Huang youqian's Numerical Approximation
3 CaO Zhihao, Zhang Deyu, and Li Rui's matrix calculation and equation Root
4 Wang degren's solution to nonlinear equations and Optimization Methods
5 Li Ronghua and Feng guoyun's "Numerical Solution of Differential Equations"
In addition
6 "numerical analysis method" Gong meicheng
7. Numerical Calculation Method Lin chengsen
8. Wang renhong, Numerical Approximation
9 Ma Zhidong, matrix Numerical Analysis
10 Optimization Theory and Algorithm Chen Baolin
They are all good books.
If the requirements are not high, it is enough to read only a book on numerical analysis. Some universities seem to be doing this. They only talk about numerical analysis and use the rest of the time to talk about computer content.
11 "Numerical Analysis" Li Qingyang, Wang nengchao, Yi dayI
It seems to be a good choice. It seems that mathematics majors are all using this book.
12 base on Numerical Analysis Li Qingyang, Wang nengchao, Yi dayI
13 Jiang erxiong, Zhao fengguang, Numerical Approximation
14. differential equation numerical solution: Yu dehao, Tang Huazhong
15 differential equation numerical solution law Li likang, Yu CHONGHUA, Zhu zhenghua
To see whether a school's computing mathematics is actually a computing mathematics or a so-called information and computing, just look at the numerical solution of the differential equation.
16 "Numerical Optimization" Yuan yaxiang and Sun Wenyu
This is not the title of the book.
17 Introduction to Numerical Analysis
Information Theory:
1. Ye Zhongxing of Information Theory
Information Theory specially written for the mathematics department
2 "information theory, coding and cryptography" ranjanbose
Mathematical Software
1 MATLAB
2 mathematic
3 Maple
4 specialized software
Some software will be used and it will be very convenient for future study. You don't have to read books. You can read the help of the software yourself.
Mathematical Modeling and Mathematical Experiments
There are many books, but they are case-based teaching. It does not seem as rigorous as other classes in mathematics. The four volumes of books written by Americans are good books.
Common Physics:
1 mechanics Zheng yongling
2 "Mechanics" paint Anshen
3 New Concept physical mechanics Zhao Kaihua, Luo weiyin
4 basic physics tutorial --- Thermal Science Zhang Yumin
5 "thermal" Qin yunhao
6. Zhao Kaihua and Luo weiyin
7 Hu youqiu of electromagnetism
8. electromagnetism Zhao Kaihua
9. Guo guangcan
10 optical Zhao Kaihua
11 Yang fujia of Atomic Physics
12 Xu kzun, Modern Physics
13 America physics test compilation
The new version is called the physics topic.
14 Feynman physics handout
15 Lu Xianzhi
16 mechanics and Thermal Science Tsinghua University
Quantum mechanics:
1. Guan Hong, quantum mechanics Basics
2 Guan Hong, basic concepts of Quantum Mechanics
After learning the introduction to quantum mechanics, Mr. Zeng Shuyan looks at it again, which is helpful for understanding quantum mechanics.
3 Introduction to quantum mechanics
4. exam 6 for U.S. graduate physics
The new version is called the physics topic. From here, the Postgraduate Entrance Exam has a strong physical taste and a strong foundation in mathematics. It is strongly recommended that many questions in the north have been adapted.
5. Qian bochu, the answer to questions about quantum mechanics
It's useless to think about it. You must master what you will do.
Electrodynamics
1 electrodynamics Guo shuohong
2. Yu yunqiang, a concise tutorial on Electrodynamics
In comparison, Mr. Yu's formula theorem is easy to remember and easy to understand. Guo's book has a clear reasoning. I think Guo's book is still well written in the chapter of electromagnetic waves. reflection and refraction derivation are very clear. I can still follow his methods when I can't remember the formula. The electromagnetic field and relativity chapter have their own strengths. It is best to combine these two books.
3 electrodynamics solution Lin xuanying, Zhang zhixiang
After you finish, you can say that you will be electrodynamic, except for those who have worked as Jackson. It is essential for normal study and examination.
4. Classical Electrodynamics Jackson
The only way to become a master is to torture talented children's books. It makes you regret that you haven't learned the mathematical physical equations.
5 quantum mechanics handout Zhang yongde
Statistical Mechanics
1. Wang Zhicheng
It is appropriate to teach the layman about physics. Apart from the imbalance and the last chapter, we should be familiar with each chapter.
2 U.S. postgraduate physics question answer fifth volume
This is an excellent exercise set. Many questions from Peking University have been adapted here. See above.
3 Liu Chuan thermal handout
4. Lang Dao, statistical physics.
Check whether you have time.
Classic mechanics:
1. Classical Mechanics, Goldston
Famous Books.
2. The golden year of Classical Mechanics
3 Theoretical Mechanics Zhou Yanbo
C language programming:
1. C language programming
It's a good start. After reading it again, I will continue to read it from other famous books.
Data structure:
1 Data Structure ellishorowitz
2. Yan Weimin, Wu Weimin, Data Structure
Microcomputer principle:
1 16-bit microcomputer principle Interface Technology and Its Application Zhou Peiling
2 computer Composition and Structure Wang aiying
Electronic Circuit:
1 Circuit Analysis
2 circuit Qiu Guanyuan
Analog Electronic Technology:
1 Conway's electronic technology BASICS (Simulation Part)
2. simulation electronic technology Tong shibai
Digital Electronic Technology:
1 Conway's electronic technology BASICS (digital part)
2 digital electronic technology YAN Shi
Computer composition principle and operating system:
1 computerorganizationandubuntureesigningforperformance
2 computerarchitecture: aquantitativeapproach Patterson, Hennessy.
3 kernel design and implementation of the Operating System
4. Modern Operating System
5. Operating System Zhang yaoxue
6 Windows operating system principle Machinery Industry Press
7. compilerconstructionprinciplesandpractice (compilation principles and practices)
Computer network:
1 computernetworks Tanenbaum
2 computer network tutorial Xie xiiren
Assembly language:
1 "IBM-PC assembly language programming" Shen meiming
2 "80*86 Assembly Language Programming Tutorial"
Computer Culture:
1 themathematicalunderpinningofcomputerscience (mathematical basics of computer science)
2 newperspectiveofcomputer Computer Culture
3. Zhao zhizhuo, Introduction to computing science
Java:
1. Java2 core technology (corejava2) cays. horstmann, garycornell
This is a classic reference of Java technology.
2 thinkinginjava bruceeckel
It is not hard to tell from the awards and comments from readers around the world that this book has won. It is a perfect book for improving Java programming ethics and a must-have book for learning Java.
3. JAVA Programming Tutorial deitel
Learning this book will save you a lot of detours. After reading it, you will become a professional Java programmer.
4 Java obfuscation joshuabloch, Neal, gafter
How to avoid traps and defects at the underlying layer
5 thejavaprogramminglanguage kenarnold, jamesgosling, and David Holmes
Java programming guidelines
6 Java language guide
C ++:
1 thinkinginc ++ Eckel
There are many reference books after the Book.

Sorting and recommendation of reference books for mathematics majors