It is interesting to understand mathematics according to phrases in the history of mathematics and draw some conclusions.
In short, the most important thing is to understand the history of mathematics and do problems. Read the math magazine again. It is really necessary to read the textbook again. The reason why I say this is that I am afraid that the stereotypes in the textbook will bind your thinking and prevent you from establishing your own thoughts.
Therefore, I advised my brother not to look at textbooks specifically to embarrass himself. However, it's good to read it with an open mind.
Reading textbooks is boring. I don't think you can read them. Or you can do some questions, but don't read the textbook specially. Moreover, a big taboo in reading textbooks is to be superstitious about one book and read only one book.
Personally, I don't think math ability can be cultivated by reading textbooks. Mainly interest, don't pursue it deliberately. Have your own ideas.
The main contents of senior high school are derivatives, series, conic curves and functions (trigonometric functions and logarithmic functions). In addition, there is a preliminary study of solid geometry, which should be understood in combination with college textbooks. The college entrance examination is also based on the contents of college textbooks.
Universities are mainly calculus, probability theory and linear algebra.
The content of high school can be seen in the textbook of People's Education Edition, the content of university can be seen in the Mathematical Analysis of Advanced Mathematics published by Tongji Edition and Fudan Edition, the Concise Course of Advanced Algebra written by Blue School published by Peking University Edition, and the probability theory can be seen in Zhejiang University. In addition, we should pay attention to foreign textbooks.
I am a student of Tongji University. He once ranked eighth in the school mathematics competition, and the advanced mathematics course was exempted from examination. But I really haven't read many textbooks.
The content of the university is very complicated, but it has its background. The second volume of Tongji advanced mathematics should be combined with physical understanding, and it is suggested that physical field theory should be understood first. In addition, I personally suggest that unless you use mathematical knowledge, you only understand it and don't delve into it. The reason why you say this is not to make you have a utilitarian attitude, but because mathematics comes from practice and you can't understand the spirit behind it without personal experience. Moreover, no one in China has a good level of compiling textbooks (especially university textbooks). Basically, they don't know the true meaning of mathematics, or they can't express it, or they don't want to say it, or they have different understandings and can't communicate. Don't trust textbooks! ! ! It's bullshit)
In fact, many mathematicians are from philosophy and physics. Even if they are from mathematics, few people don't understand physics. For example, Newton, who invented calculus, discovered Gauss theorem (electromagnetic field and mathematics have different expressions, but the essence is the same), such as Chebyshev, who had a good relationship with Einstein.
Of course, if you feel interested, you can delve into what you can use, not just textbooks. What I said above means that if something is difficult for you, don't be depressed or demanding.
Mathematics is a system, and you know a lot. So when you read the textbook, you don't understand it at first, so bear with it. I understand a little when I see the back, and I understand it after the whole book. Don't be superstitious about the deduction process in textbooks. If you think that theorem is easy to understand, you can take it as an axiom, use it to derive the original axiom, and take the original axiom as an inference.