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Do I need to take notes when studying advanced mathematics? How?
First of all, you basically have no chance to communicate with teachers in college; Secondly, if the teacher doesn't draw the scope, you will be abolished. So I still suggest that you can learn advanced mathematics well. Otherwise, you can't pass the courses of probability and statistics, complex variable function and integral transformation, college physics and so on.

As for how to learn advanced mathematics well, notes are necessary. However, maybe the teacher in your class has no notes, so you need to know the knowledge involved in the class by yourself. Before doing a lot of questions, I hope to read more textbooks (Tongji Advanced Mathematics (five or six books will do)), deeply understand the explanation of a basic knowledge point in each textbook, and then understand each example. Freshmen don't recommend reading postgraduate books, which is easy to hurt self-esteem. It is worth mentioning that 100 minutes is very important, and your own understanding ability is limited. Listening to the teacher in class and consolidating yourself later can also achieve twice the result with half the effort.

Personal opinion: no one can say what is useful and useless in college. It's better to study hard before you know whether this subject is useful or not.