I'm a bachelor student of Math major. The question is about the better way to select and read maths text- or non-text- books, without considering the course and exam. (Because we follow the lecture notes during the course, and the exam is totally covered in lecture notes, so it's not an issue, but just about how to really learn)
(1) Reading the book one by one, or just focus and re-read lots of times on one certain book, and then continue with little others ? Because recently I've tried the first way, for example, to learn Calculus, I took one book, the read it from first page to the last and finish some exercises, and then immediately read another calculus book, doing the same thing, and then the third one, and so forth. After this, I realize it is really bad result, it seems that I don't master the calculus pretty well, just memorize lots of things. So, I'm thinking about whether the second way is better. Because some friends told me before, said that there're lots of good maths textbooks, I should read as much as possible.
(2): If the second way is better, could I just use the UTM and GTM series(published by Springer, Undergraduate Texts in Mathematics) for all the maths courses ? Because there're too many, tons of books in the market, I'm not sure how to select the perfect books. But lots of people said that the UTM & GTM are two perfect series in Maths. And my teacher told me that it is better to spend more time on the books written by the famous mathematicians who are the masters in their areas. Less time on the so-called popular textbooks, like thousand-page widely-used textbooks. He's not saying that the latter one is bad, it just means that the latter one is too specified for the general course in university, passing exam , or something like that. Although it's organized well, ton's of exercises, examples and so on, the former one is better to grab the deep insight of the field and focus more on thinking, not just knowledge. So, briefly, is it good to just use to the whole UTM series for every course in math bachelor program?