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How can we learn mathematical analysis well in college?
As a mathematics department of Peking University, my personal experience in studying mathematical analysis is that I must read more books.

If you study mathematics, no matter what textbook you use, it is most important to read that textbook four or five times and understand the concepts thoroughly. Especially the concept of initial limit, ε-δ language used to express limit, and the expression of his counter-proposition. The second step is to abstract the concepts of sequence, function, derivative and so on in your own mind, and achieve handy results.

At this point, you have mastered the basic skills of mathematical analysis, entered the study of college mathematics, and started the next step of problem-solving and refining methods.