How can I improve my study strategy for Analysis by Rudin?

[czechtog]

Hey guys,

I'm in my university's analysis course right now and it is the final course I need before graduation. The problem is I don't have a ton of experience with writing proofs. I'm surviving so far but am relying too heavily on online workthroughs to the problems. We're using Analysis by Rudin by the way.

I was just wondering if you guys had any good supplemental resources to help the learning process along. Also if anyone has any general study strategies for the course I'm all ears

 

[Fredrik]

Find at least one more book with similar content, so that when you get stuck on a proof, you can check if the other book does it better. I heard that Pugh is good. I've seen praise for other books as well, but I don't remember which ones. You can find recommendations in the science book forum.

Also, don't try to rush through it too fast. When you've made it through a proof, then put the book aside and try to do the proof again. Imagine that you're trying to explain the proof to a classmate. Then do it again, as many times as it takes to get it exactly right. You'll be surprised to see how often you will understand a detail that wasn't quite clear the previous time. In my opinion, it's better to do a smaller number of proofs, with very high ambitions about how well you're going to understand them, than to work through a larger number of proofs that you don't understand perfectly.