Compared with high school mathematics, advanced mathematics is very different, mainly by introducing some brand-new mathematical ideas, especially the infinite division, limit and so on. Formally speaking, the learning methods are also very different, especially in large classes, and it is difficult for teachers to tutor alone, so the requirements for self-study ability are very high. The specific learning methods vary from person to person, but there are some basic rules that everyone must abide by. I specifically say the following points:

1。 Book: textbook+problem set (required), because learning math well is absolutely inseparable from doing more problems (a bit like high school, hehe); It is suggested that the problem set should be related to the postgraduate entrance examination, which will also help you prepare for the postgraduate entrance examination in the future.

2。 Remarks: try to have it. When I say notes, I don't mean copying the blackboard intact. It's boring, and you don't need to use a small notebook alone. Just write it down in the notebook. The key is to have your own summary of each chapter in your notes, similar to an outline (sometimes in a teacher or reference book, you can refer to it), and it is best to have various questions+methods+error-prone points.

3。 Lesson: I suggest you preview before listening. Actually, I never attend classes, except exercises. It doesn't matter if I don't understand. Many college courses are reread after class in combination with teachers' notes. But remember, don't make a surprise attack before the exam, it is absolutely impossible. You should keep up with it at ordinary times and try not to make mistakes step by step.

4。 Learning high numbers well = thorough basic concepts+firm basic theorems+basic network knowledge+basic knowledge+basic problems well. Mathematics is a concept+theorem system (and reasoning), and it is very important to understand concepts, such as limit and derivative. You should not only have an image understanding of them, but also remember their mathematical descriptions. You don't need to remember them. You can give examples to the book yourself, draw a picture (image understanding is actually very important), and then do more questions and experience. It is suggested that you mark all the concepts with colored pens, so that it will be clear at a glance when reading a book (the theorem is boxed).

The basic network is the knowledge outline summarized in the above-mentioned notes, so we should also pay attention to it.

Basic knowledge is what high school teachers often call "quasi-theorem", that is, there are things that can be used as theorems or inferences that are not in books, and some of our own little experiences. These things are informal, but very useful.

I understand all the questions, such as the solution of various limits.

Well, all this has been done. My high number should not be bad, at least I can cope with the exam. If you want to improve, you can do some math problems for the postgraduate entrance examination and experience it. Actually, that's all. If you have enough time, you can also learn math software, such as matlab and mathematic. For example, the calculation of integral has a ready-made function, and the grasp of concepts can be strengthened through practice. In addition, read some books about the application of advanced mathematics. In fact, mathematics is originally applied, and you will know that it is really useful (I don't know what your major is).

Finally, talk about how to improve your understanding ability (a family statement)

1。 Give specific examples. For example, when understanding derivatives, give yourself an example, such as f (x) = x 2+8.

2。 Visualization of metaphor. For example, imagine the graph of a binary function as a straw hat on the girl next door.

3。 Primary analogy. For example, comparing binary function with univariate function, Taylor formula is quadratic function, which is easy to understand.

4。 Multi-book reference method. Go to your library and borrow some advanced mathematics textbooks written by different authors. Although the content is the same, different authors often express the same question from different angles. It is often much easier for you to understand the same problem from many different angles and examples. Give it a try!

5。 I don't know the temporary jump method. If you don't understand the process of proving and deducing some theorems for the time being, it doesn't matter, just let it be for the time being, write down this doubt and solve it later.

Limit is the basis and tool to learn the later knowledge well. Most of the content behind is based on the limit, needless to say how deep it is! Understanding one-dimensional integral is particularly important. Don't think you can do the problem, but you should further master the mystery. When it comes to multiple integrals, you can extrapolate. In fact, it is not difficult to get a high number. I think high school science thinking should be more acceptable, unlike line generation, it is new knowledge, which is a bit abstract to understand. And if you study science and engineering, you have to work hard. It is also important to learn advanced mathematics and make it work hard for professional courses. The teacher who teaches me advanced mathematics is an awesome person. He can apply the knowledge of advanced mathematics to reality, and he can also use it to tell us some great truths that benefit us a lot. The essence of advanced mathematics is not how high your score is (although I am close to perfect score, haha), but a kind of rational thinking cultivated imperceptibly. In short, it is the first time to truly feel the integration of China's educational theory with practice! ! ! Haha, if you want to really understand, study hard by yourself. No matter what others say, it's not yours. I won the first prize in the math contest in this city, so I'm a little excited. Let me say a little more, hehe, it's just the real experience of a person who has experienced it. I hope it works for you!