Reading, doing, and writing proofs
If you are a new graduate student
taking this class, I suggest reading some material about writing mathematics
and how to prove things.
You can find some good books (eg. the one by Krantz)
and plenty of stuff on the web--eg.\ the articles below:
Remarks on Writing Mathematical Proofs (Lee) .
Some Help on Reading Mathematics and Creating Proofs (Bender).
More advice (L N Stout) .