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I've always loved the theorem-proof format in textbooks, e.g. Hardy and Wright's Introduction to the theory of numbers. However, the problem is that I can't remember anything I read in this format because usually books of this kind don't have exercises at the end (not all, but usually). What do you think is the best way to actually learn from theorem-proof type books? Should I read a section, write down all the theorems and then close the book and try proving them myself a week later or so? Should I just take notes as I read and construct my own problems to practise with as I go along?

Thanks! :)

Winther
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user92570
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1 Answers1

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I think no textbook is really only Theorem Proof, next Theorem, next Proof. Watch out for the motivation for theorems, look at the examples, try to consider the history. My suggestion is basically to not only look at one book. It won't help you in mathematical research to know a list of theorems. The theorems are just the cornerstones in a theory and what you really want is to understand the entire theory. This understanding comes from working within and with the theory, for instance by trying to prove for yourself new theorems in this area.

One concrete hint: You can always make your own exercises by checking why all the requirements of any given theorem are necessary.

Thomas
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