In fact, advanced mathematics is not as unattainable as imagined. The most important thing is to pay attention to the learning method. The learning of advanced mathematics is different from that of advanced mathematics. Here, I will introduce my skills in learning advanced mathematics in detail.
1) Senior One (or technical school) must first have solid basic skills, because Senior One is mainly calculus, which is actually various operations related to functions. So first of all, we should be familiar with the nature and operation of various functions. These contents are all in high school textbooks, but they are only an introduction in a high school book. Therefore, for those friends who are going to study in Grade One, they should first look at their own foundation. If you return all the knowledge of middle school to the teacher, I suggest you finish reading the middle school books first, especially exponential function, power function, logarithmic function, trigonometric function and so on. You must be familiar with them, otherwise it may take a lot of time to learn senior one well.
With a solid foundation, you can start studying advanced mathematics now. Because each chapter of advanced mathematics is interrelated and promoted layer by layer, each chapter is the foundation of the next chapter, so we must learn it step by step. Only when you really understand this chapter can you enter the next chapter. Don't learn fast for speed, haste makes waste. Especially when we don't learn well in the front and in the back, we will gather more and more questions that we don't understand. At this time, the mentality of self-learners will become more and more agitated, and they don't know where to start to improve. So we must study chapter by chapter.
When studying each chapter, it is recommended to read the content of the textbook first. If it is still unclear after reading it once, read it again. Then read the examples in the book and try to do the exercises at the end of the book. If you have the conditions, you can buy some reference books to read and do problems. After doing some questions, take a set of previous exam questions and see if there are any problems in this chapter, so you can see the way this chapter is written. Be sure to do more questions. When you are in high school, you should pay attention to "Practice makes perfect". "If you are familiar with 3,000 questions, you will certainly do well in the exam." ?
Learning senior one is a long-term process, so in the later learning process, we must make plans and do some problems in the previous chapters regularly. In the process of learning, many candidates often forget the previous content when learning the later content. Learning while forgetting is definitely not enough, and it will also affect the later study.
Advanced mathematics has been a subject with a low pass rate for a year, because it is very sad that you can only learn it if you really study hard. Its problems are ever-changing and impossible to estimate. Moreover, because the chapters are interrelated, it is impossible to distinguish between key and non-key points. Many students asked if they could draw the key points. My answer was that there were no key points, because they were all key points. In addition, it is strongly recommended that learners take part in some training or have an expert who can consult, so that they can solve problems in time and learn various problem-solving methods (there are too few problem-solving methods in general books).
In addition, it should be emphasized that learning advanced mathematics is a coherent process, that is to say, a phased learning plan must be made, such as six months or one year. Many friends who have failed to study advanced mathematics repeatedly may have this experience: if they are going to take the advanced mathematics exam in 10 and sign up for class, but after watching it for an hour and a half, they may not be able to study for various reasons and will only give up after learning the integral chapter. They may think, alas, it's so difficult to get high numbers, so let's take the exam next year. I gave up the 10 exam as soon as I had an excuse. Then next year, this situation may repeat itself, so that all subjects have passed, leaving only the hard bone of high number, and the mind naturally gives birth to the idea that high number is difficult. This kind of situation often happens in my previous class. At the beginning of the class, the classroom was crowded with people, but before the course was halfway through, half of them left, and few people persisted until the end, and it was these students who finally passed the exam. So sometimes I think that when students are preparing for the advanced mathematics test, it is best to just take the advanced mathematics test and devote themselves to learning. When you feel that you can't stick to half of it, don't make any excuses to escape, but think about what the problem is and why you can't learn. Find the problem and overcome it, and you will eventually succeed!
2) There is a great difference in learning between Grade Two and Grade One. First, let's talk about the similarities and differences between them. First, high number two does not need much basic knowledge, and there are simple calculations of integrals and derivatives in probability. Second, the whole content of senior one runs through the line of differential derivation and integration, while the content of senior two is not very coherent; Third, the study of senior one should fundamentally strengthen the understanding of basic concepts and theories, broaden the thinking of solving problems, strengthen the analysis and comprehensive exercises of typical examples, and draw inferences about typical problems, so it is necessary to do a lot of questions, while senior two should strengthen the understanding of basic concepts and master the basic examples in books, so there is no need to draw inferences. Most of the exam questions, especially the big question of probability, are the same, except to change the number of examples in the book.
According to the above points, let's talk about the study of senior two. First of all, in the process of learning, we must really understand the contents, concepts and theorems of each chapter, which can be done by reading books several times more. When reading a book, you must calm down, because the content of high school number two is difficult to understand. Don't give up when you can't stand it. You must grit your teeth and read on. One thing to note here is that there may be many theorems and inferences to prove in Grade Two. These proofs are long and complicated. I suggest that you don't have to look at these proof processes. You just need to grasp the essence-theorems and inferences, and understand them well.
When you understand the contents of a chapter, you can do the exercises at the end of the book, and you must know how to do it, not just finish it. The main questions in senior two are: (1) calculation of determinant; (2) matrix operation; (3) solving linear equations; (4) Calculation of eigenvalues and eigenvectors; (5) simplification of quadratic form; (6) Seeking probability in probability theory; (7) Looking for distribution and digital features; (8) Find the point estimation, interval estimation and rejection domain of the test in mathematical statistics. Be sure to read all the topics about these aspects in the book and understand how to do it.
Generally speaking, the content of Shu Gao Yi seems to be less, which is not difficult to understand. However, due to the variety, close relationship and variety of questions, a question may involve several chapters, which is more difficult. Senior two, the content is more, but also more difficult to understand, but the topic is relatively simple, the topic is relatively single, and it is possible to read them all. For their study, a very incisive sentence: first, do more questions; Senior two, read more books, understand!
Give you some information that I think is good.
/ShowForum.asp？ ForumID=22 This is an advanced mathematics learning forum.
Cai Gaoting's advanced mathematics teaching video is very good. I suggest you have a look. You can find it online.
I am also a liberal arts student, and I have already learned advanced mathematics. Wish you success!