I am a graduate student in the School of Mathematics, and I have been exposed to mathematics for 10 years. I should say I have some experience. Mathematics is divided into elementary mathematics and advanced mathematics according to learning stages. This sentence is nonsense. But I'll give you a metaphor, so you can understand what I'm talking about. Mathematics is like the classification of people. If there are villains (people who can't achieve great things are small-minded), then elementary mathematics is villains. Little people make us very annoying. In fact, there is no real skill, it will only make things difficult for us everywhere. But you have to see through it, it is nothing and can be used by us. Then advanced mathematics is like a great man who has achieved great things, and it is magnificent. When we learn from her, we look up to her with reverence. Her thoughts are profound and her vision is far-reaching.

From the level of mathematics learning, people who can only do problems are slaves of mathematics, and of course, some champions in the college entrance examination are not excluded. The other level is to learn mathematics, understand mathematical thoughts and understand the historical context of mathematics. This context is not a simple history of mathematics, but the inheritance of ideas, which is the origin, contradiction and perfection of a generation of algebraic ideas. At this level, mathematics is your servant. This level can't be reached by ordinary people, nor can ordinary undergraduates majoring in mathematics, because these people still have little mathematical knowledge and are far from reaching the level of mastery. I'm not at this level. . . .

Talking about the learning method of mathematics is not abstract in the elementary mathematics stage. Maybe solid geometry is a bit, but it is solid after all, and we can touch it every day. In the study of elementary mathematics, we should pay attention to exercises and our own summary. Learning without thinking is useless. This sentence is very incisive, because I just said that elementary mathematics is a villain, and you should know that its intrigues are everywhere. The premise of knowing is to look at his tricks, so it can only be done by doing, but it must be done in order to sum up experience. This is very important and efficient for learning mathematics. I think this is also the key to all science studies.

Let's talk about the experience of high numbers. At this stage, we must pay attention to the study of definition, learn the connotation and extension of definition, know why this is produced (this is more difficult), and know what this definition is for (this is more difficult). Then you need to read more definitions and understand the summaries of several generations, because the general definition is the most rigorous, shortest and abstract mathematical language summed up by several generations.

Well, having said so much, it's all my experience. I have to leave early and answer later when I have time.