[rayuela]

Watch some lectures or pick up an undergrad book on Real Analysis. You don't have to become an expert in it by any means, but the motivation and logic underlying most of the math you will encounter will become much clearer. It's hard, but don't give up on it. It will be worth it. Before delving into analysis I felt like I was just memorizing and following formulas. It really is like the fundamentals of Math.

[ghufran_syed]

I know real analysis(or abstract algebra) is the traditional first “proofy” course in the US, but I disagree with this way of teaching proofs - think its better to learn one thing at a time. So instead of learning how to do proofs while also learning real analysis, I think its better to learn the basic proof skills in the context math you are fluent with i.e. basic algebra and basic number theory (e.g. what integers divide easily into another integer). The books by Hammack and Chartrand do that well I think, see elsewhere in this discussion for more info.