I am taking my first course in analysis. I like the subject. I study it almost on a daily basis. I try to prove theorems on my own without even looking at the hints. If I really get stuck I just read the first line of the proof and then try to continue on my own. I find this approach to be very rewarding. The problem is that I tend to forget all the proofs later. Some I still remember because I liked the idea of the proof, but most of the others I will forget fast. What am I doing wrong? Any tips on how to study analysis?
Don’t try to memorise the proofs: try to memorise the methods that are used in most analysis proofs. That way you only have to memorise a handful of methods instead of 30-50 proofs, and you can adapt them to prove things you have never seen before as well.