<p>Any advice for a math major (sophomore) on upper div courses?
Lower div was ok, but how would you recommend getting better on proofs?</p>
<p>How much do you spend studying for each class?</p>
<p>Practice.</p>
<p>Many proofs that undergraduate math majors write are purely mechanical. You manipulate your hypotheses, unpack definitions and appeal to theorems you have already proven until you get to the statement you are trying to prove. The more you practice, the better you get at it.</p>
<p>Later on, proofs will more heavily rely on insights and less on mechanical manipulations. You might have to play with the problem and work out examples until you see why the theorem is true, and then translate your intuitive reasoning back into formal mathematics. Proofs of this sort might take several pages to write up, as opposed to a few paragraphs for straight-forward mechanical manipulations.</p>