Optimal Strategies for Studying Textbooks in Mathematics: Tips from a Scientist

[ronaldor9]

I am curious about how others read and study from textbooks. Do you generally do all the exercises in the text; a sample from all difficulty levels; only the medium level questions.
For me, personally, I get fixated on trying to do all the questions. Currently I have discovered this isint the most realistic, but I can't help myself, I often feel as if i will miss something important if I don't do them all.

What about you? what strategies have you developed, recommend, and use?

 

[Mentallic]

There are numerous factors to weigh in, and this is why what anyone else does to study from a textbook could be a completely wrong approach for you to take.
- How easily do you understand the topic?
- Are you comfortably answering the beginner questions, intermediate questions, etc.?
You must also realize that a lot of Mathematics is about applying what you already know, so doing millions of questions all based on the same idea could touch up your skills, but may also give you too much dependence on completing repetitive tasks and thus hinder your ability to put much thought into questions.

Basically, if you find the topic easy, skip a few questions that look to be just another slight variation to all the others you've already done.

 

[symbolipoint]

Do just a portion of any set of similar problems, like if three problems seem to be too much the same, just do two of them. Before reaching the exercise sets at the back of the section, try to solve the example exercises on your own, and try to only use the book-displayed solutions and hints and help before you check how the book solution is.

 

[qntty]

Try to do the proofs and examples yourself before reading them. Even if you don't succeed, you'll learn more from reading the solution than if you hadn't tried it. Don't rush through a theorem that you don't completely understand. Math isn't like reading a novel in that you might need to stare at a single sentence for several minutes before getting it. After you've read and understand the chapter, do all or most of the proofs and the problems that require ingenuity but not necessarily all the repetitive computations.