TITLE: What is the best way to study graduate level mathematics?
QUESTION [7 upvotes]: 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,

REPLY [5 votes]: 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."