Is the maximal path through a math book necessarily linear?

Question

I'm studying with two main math books (Munkres and D&F) these couple of months. My method so far is just going through the book page by page constructing everything in it (independently if I can) in my notebook. At the end of a section I try to do all the exercise. The ones I don't manage to solve I either post here or save for later. All in all I’m enjoying myself.

My progress is slow (chapter per month) which is not a problem in itself but lately I find myself not remembering things discussed in previous chapters (although I seldom skip any materiel).

Are there any other approaches to reading a math book that anyone could recommend besides the "linear" one?

Answer 1

I was trained to use a textbook in teaching in a different way - this can be applied to your self learning and it is based on that some (not all) textbooks switch topics with each chapter.

Pick a topic, then proceed through linked topics, which in a textbook will not necessarily be in sequential chapters. As you go through the increasing complexity of a topic, seek out other resources (online) to aid in your understanding of that topic.

This is an example of the Spiral Approach, where you start with mastery of the basics, then proceed to more complex examples of the same topic.

For example, say you start with trigonometry, and it is in chapters 1, 5 and 11 - work through each chapter in that order, testing yourself as you go. Then go on to a different topic once you are satisfied that understand the concepts sufficiently.

Also, as has been mentioned, continuously test yourself.

Answer 2

For some personalities, like mine, it helps to test yourself. I like to look up graduate exams or other tests on the material I'm learning, and pick out problems related to the chapters I'm on. If I can answer them, great; if not, it helps me see what I need to refocus on.

In general, I try to spend an equal amount of time on new material and self-assigned work.