1. Understand knowledge points.

The knowledge points involved in advanced mathematics are: definition, theorem and formula.

1) What do you need to know about the definition?

A) First of all, we should grasp the basic meaning of the definition from the text.

B) Secondly, understand what knowledge the definition involves (what we have learned). For example, when we say "region", then this definition is closely related to interval and set. We can learn by comparison. We should not only analyze the similarities or connections of related concepts, but also pay attention to the differences or differences.

C) Define matters needing attention, or define the elements involved. If you define a set, you need to pay attention to the certainty of the elements in the set. Like tall students, it is hard to say how tall they are in this set, so they are not certain.

D) What is the nature of the definition? Fully understanding these properties can often help us better grasp the true connotation of the definition.

2) Theorem. A), b) and c) have the same definitions as attention.

D) conditions involved in the theorem. This is very important. Many students do not pay attention to the conditions for the existence of theorems, and as a result, theorems are used everywhere in solving problems, and the results often lead to wrong conclusions.

E) If you want to master the theorem well, you must do some related topics. Only in this way can we truly grasp its connotation. If we want to understand theorems in depth, we often have to do some topics involving multiple theorems or formulas. It needs to be understood in practice. If you learn theorems, but you can't do problems, then the knowledge you have learned is dead, and such knowledge is of little use.

3) Formula.

Some formulas are simple, such as derivative formula. As long as you understand the definition of derivative clearly, then using derivative formula is similar to applying multiplication formula.

But some formulas are more complicated, such as Gauss formula in multivariate calculus. These formulas are not so much formulas as theorems. For such a formula, when learning, you can refer to the learning method of the theorem introduced above.

2. Digest and consolidate knowledge points.

In this regard, in addition to doing the above-mentioned 1. The best way is to do exercises. Now we might as well introduce the problem-solving aspect.

Step 3 solve the problem.

Whether learning elementary mathematics or advanced mathematics, it is inseparable from solving problems. But in fact, many students feel that they have done a lot of problems and the effect is not good. Why?

We believe that,

1) First of all, do a good job in the topics in the textbook. These topics are often specially designed to digest and understand definitions, theorems and formulas, and are basic topics. So you must pass every question. These topics are often not difficult, but the digestion and understanding of basic knowledge points can not be underestimated. Some students are not sure about this. Typical negative examples are:

A) Because of the short time, or some problems can't be done, I copied my classmates' homework;

B) No matter whether he is right or wrong in the topic, deal with it first and give the homework to the teacher, which means that he has finished his usual homework, so the teacher will not deduct my usual score.

C) Don't do detailed argumentation and analysis, and calculate the answers to some questions; For some topics, let the wind out first, say what is obvious (actually not obvious), and then declare the original proposition established.

These are irresponsible practices. Some students may say, alas, there will be a meeting in the student affairs office today, or the fellow villagers are here today. Anyway, I really don't have time today. I'll make it up tomorrow. In fact, if you can't finish today's task, don't imagine that you can not only finish tomorrow's work, but also make up for what you left behind today. In the long run, more and more tasks will be left behind, and the more difficult it will be to study in the future.

2) solving problems cannot solve problems for the sake of solving problems.

Some students may be able to solve a problem when they encounter the same problem in the future, but they don't know how to do it if this problem is properly transformed. This kind of situation belongs to the situation of learning without thinking and solving problems in order to solve them. To solve a problem well, we should not only solve a problem, but also summarize the solutions to all similar problems. By analogy, you are not afraid that the questioner will change his moves. We hope that students must think more when solving problems. Every time they do a problem, they should think about it. What kind of problem can this problem boil down to? In this way, doing a problem is equivalent to solving one or more problems.