You can do the questions properly and get your feelings back, but you don't have to delve into them. Just get to know them.
Calculus recommends a foreign textbook: Thomas's Calculus has a Chinese version in China.
Easy to understand, very easy to get started, much better than Tongji edition used by domestic universities.
If you feel interested in strict calculus after study, you can learn a few points and recommend them to higher education press.
Although the content of limit definition in the previous chapters is a bit difficult for real number theory, it will suddenly become clear when you chew it down.
I don't recommend the textbook Principles of Mathematical Analysis, which is commonly used in foreign universities, because its theoretical system is based on the definition of basic topological metric space and limit, and the proof is a bit simple, and the score is not easy to get started.
After calculus (or learning), you can begin to learn the content of linear algebra for line generation. I think it is enough to master the concepts, especially the Euclidean space of linear transformation inner product space of vector space; The algorithm of matrix The concept of Cramer's law does not need to be very demanding in calculation. The textbook recommended Tsinghua University Publishing House Linear Algebra.
With the foundation of line generation, we can learn an abstract algebra (or modern algebra) which is very important in the mathematical system. The specific learning methods are not limited to junior students. Personally, I think it is enough to know some basic definitions of group ring domain. If you are interested in going deeper, that's better.
See my ID name = = for the topology.
Regarding probability theory, I personally feel that I can quickly find a mainstream textbook of domestic universities, and if I am interested, I can continue to study stochastic analysis.
Markov chain ITO theory, etc.
Finally, I want to say that it is very important to cultivate interest in mathematics:
Personally, I think the history of mathematics must be read, so as to have a clear understanding of the development of mathematics.
You will also know how these things you have learned came from in history, and the thinking of predecessors is very helpful.
Just write a simple history of mathematics.
The recommended series "Mathematical Circle" (7 books in total) is very good, and anecdotes of various mathematicians are very interesting.
There are also ***5 series of "Mathematical Pioneer" published by Shanghai Science and Technology Literature Publishing House.
Watching American TV series: numb3rs is called "digital pursuit" in Chinese, which is quite good. Every episode will have an introduction to a mathematical concept, although it is a bit pretentious.
But it's good to cultivate interest.
Finally (= =) is the problem of mathematical literacy.
I think many times people will mention this, but it is abstract. How to cultivate?
I suggest (I'm serious) that you can buy a primary school's oral arithmetic book and do four more calculations when you have time.
This is very good for cultivating the sharpness of numbers and mental arithmetic ability, both of which are very important parts of mathematical literacy.
There is also proficiency in basic mathematical formulas, such as trigonometric binomial expansion, etc., as long as you do the questions properly, you can get them.
If you plan to take the postgraduate entrance examination, please ignore the above nonsense (what doesn't need to be calculated. . . )
Do more questions, do more questions, do more questions, do more questions, do more questions.
Do more questions, do more questions, do more questions, do more questions, do more questions.
This is the only way.
I won't say anything about the postgraduate entrance examination.
I admire people who are really interested in mathematics, not complaining about high numbers before exams or taking mathematics as a stepping stone.
I wish you a comfortable life in math study!