Compared with high school, the advanced mathematics course in university is different, and the textbook is only used as a main reference book. Students are required to take the key and difficult points in class as clues, read a lot of textbooks and similar reference books, fully digest and master the contents taught in class, and then do exercises after class to consolidate their knowledge. This is repeated creative learning. This is a hard mental work, which requires students not only to study actively and consciously, but also to restrain themselves in a relaxed environment, master better learning methods, learn what they want to learn solidly, and lay a good foundation for the study of professional courses.

Second, do three links well.

What is the best way to learn advanced mathematics? This varies according to everyone's study habits and ability to understand problems, but in general, we should do the following three links well. First, preview before class. This process is very important, because only by previewing before class can you know what the teacher says is difficult to understand and what is the key point, so that when you listen to the teacher with some questions, the effect will be obvious, and at the same time, you will cultivate your self-learning ability in the preview process, which will benefit you for life. It doesn't take much time to preview. Generally, a class takes about 30 to 40 minutes. You don't have to understand all the questions in the preview, just take these questions you don't understand to class. Second, listen carefully in class and take notes in class.

Everyone knows that it is necessary to listen attentively in class, but the importance of taking notes in class is not appreciated by some students. They think that these are all in the teaching materials, so there is no need to take notes. Some students even said: the middle school teacher told us that we don't need to take notes in math class. In fact, this understanding is wrong, and it is also a bad study habit brought by middle school. First of all, it can be said that the teacher's teaching of advanced mathematics is definitely not a simple repetition of the contents in the textbook, but a large number of similar reference books, and combined with his own teaching experience and experience, he repeatedly pondered how to teach, so that students can better understand and master it before writing a lecture. Therefore, it is no exaggeration to say that teachers' lesson plans have both successful experiences and lessons. Moreover, the content of a class is summarized into several organized points, and some typical examples and exercises are appropriately selected, which are not available in textbooks. Therefore, students must take good class notes when listening to lectures, and this good study habit, that is, writing diligently, is also of great benefit to the cultivation of their learning and working ability. Third, review after class, take notes and finish your homework carefully. Self-study after class, many people do their homework quickly, which is also a bad habit. In fact, they should further study the textbooks or teaching reference books after class. After fully understanding the content of this lesson, they should sort out and enrich the class notes, add their own experiences and understandings in some places that need to be understood, truly turn the knowledge in books into their own knowledge, and then finish their homework. This is much better than making up homework after class, and the speed of finishing homework is much faster.

Third, be good at induction and go through the process of "from coarse to fine"

It is often said that reading and learning should be good at "from thin to thick, from thick to thin". In the study of advanced mathematics, this experience can be said to be very real. Because learning itself is the continuous accumulation of knowledge, so the book will be "from thin to thick" and the content will be more and more, but people's memory is limited. It is very difficult to remember all the useful things without forgetting them. What should I do? This requires summarizing the knowledge learned, finding out the internal relationship between them and things with the same essence, and then sorting it out systematically and orderly, so as to remember the most representative knowledge points, and the rest can be inferred and understood on this basis, which is "from coarse to fine". Therefore, at the end of each chapter or after the content of a unit is finished, you should summarize the basic concepts, theorems, basic formulas and calculation methods, and then memorize them in an orderly way with your brain, so that what you have learned will belong to you completely.