What is the best way to study graduate level mathematics?

Question

I am studying a 400/500 level measure theory math book on my own. Right now, when I read it I try to read the proposition then the following proof. And then try to do the exercises on my own. I wonder if I should change it to:- 1. read the proposition 2. try to prove it on my own. 3. If I could not then proceed to read the proof from the book. 4. Do the exercises.

Or should I stick with everything above minus step 2. It can save me some time but I wonder if that is what good mathematics students do?

Any feedback from your experience would be appreciated.

Best,

Answer 1

With regards to learning from proofs provided in a textbook, it may be very beneficial to

• (step 1) mentally try to guess how a proof is going to substantiate its claim
• (step 2) read the textbook-proof
• (step 3) write a personalized proof while having access to the textbook-proof emphasizing clarity
• (step 4) write a personalized proof while having access to the textbook-proof emphasizing brevity
• (step 5) write a formal proof without having access to the textbook-proof.

Here "formal" means "able to be understood by other mathematicians---most importantly your instructor."