- #1

bacte2013

- 398

- 47

I am an undergraduate at US actively pursuing mathematics and microbiology. Recently, I started to evaluate my methodology of reading books in the mathematics, which raised me some concerns and worry that I want to share with you, and seek advice from you.

Whenever reading math books, I tend to focus more on the concepts presented in the books rather than their corresponding problem set. The way I am reading math book is that I always try to translate the understanding in my own words, doubt everything in the book and come up with reasons to disprove my doubt, try to prove theorems and lemmas by myself without looking any additional source, try to come up with counterexamples, and come up with my own ideas and questions. Also I enjoy formulating my own questions and try to solve them.

The main problem is that I am able to devote enough time for problem sets in each corresponding chapter in the book I am reading. For most of time, I had to skip 40% of the problems since I spent majority of my time on the expositions. Also, my other commitments like undergraduate research and club officials take some of my time too.

My main question is that Is it okay to spend more time on the expositions of the book rather than corresponding problem set? Is it okay to not solve every problem in the book? Should I not try to formulate my own questions and just focus on problem sets? Sometimes, questions I formulated while reading are strikingly similar to problems in the book, but not always.

Do you also take extensive notes per textbook? I used to do so, which ended up consuming a lot of time. I started to take notes inside the book (started when I read Rudin and Dugundji). Recently, I decided to use LaTeX to write notes I took to supplement the book (lectures, my own ideas while reading, etc.).

I apologize for this long post, and I look forward to hear back from you.