He said in the first class he gave us:
If a person works and studies in his own field without calculus and linear algebra, then I'm sure his work is not excellent enough, cutting-edge enough or even professional enough.
The teacher didn't say what field it was. In his view, even the humanities and social sciences may not be spared. I used to be unable to understand this sentence. Although I am a math major.
However, it was not until I read the book Linear Algebra and Its Applications that I gradually understood.
1.
Linear algebra is a language. You need to learn it by learning a foreign language.
If we rank college mathematics courses (in fact, I prefer to say all college courses), the course "Linear Algebra" is almost undisputed in the first place!
I recommend every science and engineering student to read this textbook when he is a freshman, so that you can really understand why you want to learn linear algebra and how to use what you have learned.
The sooner you read this book, the greater the benefits! It will have a far-reaching impact on your future research, study and work.
Give a chestnut:
Many people have studied the eigenvalues and eigenvectors of matrices, and I believe that most of the students who have studied have forgotten the specific definitions and contents. So, how did this eigenvalue and eigenvector come from and how should they be applied?
In this book, the concepts of eigenvalues and eigenvectors (or the reason why scientists put forward this concept) come from the study of owl population dynamics formula by mathematical ecologists. Then, I will tell you what amazing applications this concept has in discrete dynamic systems.
Only in this way can this concept be defined, inferred and proved, and it has geometric significance. ...
Only by combining this theory with practical application can you really understand the source and use of this knowledge point. It also made me really realize what the dry knowledge of matrix and linear algebra we have learned is really useful!
Compared with China's textbooks, the content of this book has not increased much. But different from domestic books, it explains the ins and outs of each formula and its algebraic and geometric significance in detail, so that readers can improve their understanding of those formulas.
In fact, there is really more than one grade. Will subvert some of your understanding of mathematics.
Douban users gave this book a high score of 8.9, which is really high.
Inspired by linear algebra, according to its theory and some mathematical logic thinking, I once wrote how to establish my own knowledge system:
How to establish your own knowledge system and viewpoint?
This is also what you have learned (manual dog head ~)
In addition, for students who have never studied linear algebra, it is highly recommended to look at the following answers in reverse, which will enable you to understand linear algebra in the right direction from the beginning and avoid many detours ~
For students who feel a little dizzy after learning linear algebra, you can also have a look, and you may have a deeper understanding and understanding ~
Welcome to correct me ~
How to understand matrix and linear algebra intuitively?
2.
If you need to learn mathematical analysis or calculus, then this book is your best choice.
In the first math analysis class, the teacher told us to go back and buy a set of books ourselves and told us:
This textbook is much better than all textbooks in China, but it is too complicated and contains too much content. If you have spare capacity, you can study this textbook.
There is also a matching problem set-Jimidovich, which is not recommended here. I only know that the students who can finish this problem set in their freshman and sophomore years are worthy of my hope.
Closer to home, this book is a calculus textbook known as "few words"-the famous calculus course (Fichkingolz)!
Because the name "Calculus Course" is not good, everyone uses this name in the textbook, so only by adding a prefix can we reflect the particularity of this book.
This course of mathematical analysis is really bit by bit, let you know the ins and outs of every tiny knowledge point and lead you to prove it again! (real indoctrination)
Similarly, his "Principles of Mathematical Analysis" is also excellent (mathematical analysis is a compulsory course for mathematics majors, so you can refer to this book, which is not very useful for non-mathematics majors, but a little deep).
If you want to learn mathematical analysis well, this book is the first choice. Even douban has a high score of 9.3.
Let's go back to what our differential equation teacher said at the beginning. Let's put it another way:
If you want to be professional and outstanding in your field, then you must study calculus and linear algebra.
Finally, these two books are enough for every science and engineering student (except the department of mathematics) who wants to learn advanced mathematics (including calculus and linear algebra).
In addition, I recommend a book-Descartes methodology, a real philosophical book that reshapes the world outlook and thoughts. Whether it is a math book is a matter of opinion. The specific content can be seen in this answer:
What math courses have changed your thinking/viewpoint/understanding of things/the world?
In view of the fact that many students want to know about books on probability and statistics, I also recommend two:
However, there is one thing that needs special explanation here: because probability statistics is easier to understand and the content is similar, unlike advanced algebra and mathematical analysis. So I don't think the gap between different books will be too big. In my opinion, the key point of probability statistics is application.
The following books I have read and think are good:
The book Introduction to Probability was written by MIT. The advantage of this book is its clear and intuitive explanation of the theory. As a science developed from gambling, did all the students who studied probability theory dream of making a fortune by buying lottery tickets? (manual fat firewood ~)
Give a small chestnut in the name of the beginning of the book:
Patient: What are the chances of this medicine being effective?
Nurse: I hope this medicine works. We'll know tomorrow.
Patient: I want to know the probability that this medicine is effective.
Nurse: Every patient's situation is different. It depends.
Patient: Let me put it this way. How many of the 65,438+000 patients who used this drug are effective?
Nurse: I have already told you that every patient's situation is different.
Patient: If you had to bet, which side would you bet, effective or invalid?
Nurse: My bet stands.
Patient: Well, if you are willing to make a bet like this: If this medicine doesn't work, you lose in 2 yuan; if it works, you win 1 yuan. What would you do?
Nurse: You are so boring, wasting my time!
Well, so the development of probability and gambling really complement each other.
As for statistics, I recommend this book.
Statistics is a knowledge widely used in practice. Therefore, it is best to explain the relevance of each knowledge or statistical method to reality, what role it plays in the real world, when it should be used, and what significance and value it has. This book did it.
In fact, the focus of this book may be practical application, and the book also focuses on the application examples of statistical software (including SAS and SPSS). You know, statistics in the real world are almost inseparable from statistical software! (After all, if it is manual statistics, it may be too hard. )
Finally, give me a messy desk, lest some students think I'm talking nonsense ~
Finally, I found the pdf versions of Linear Algebra and Its Application and Calculus Course mentioned in this paper. You can download it and watch it on ipad, saving a sum of money ~
Pay attention to the research institute on the twentieth floor of the official WeChat account, and reply to the keyword "Math Book" to get it.
Finally, friends who are studying, I recommend a column about personal improvement. Go and have a look sometime. This column may really change your life ~
Handbook of thinking hacker growth
Not limited to mathematics, many friends are really confused about how to choose books and which books to read. I simply recommend some broader books (humanities and thoughts) based on my reading and thinking:
How to choose books? Read too little, want to read more?
Finally, many friends asked me what's the use of studying mathematics. I may not be able to make money with math, but I still think math is very useful. I hope the following answers can give you some inspiration: