I've been at Baby Rudin for a 3 weeks now; being the very first proof based course I'm (self) learning. I've found my footing and am solving the same using the following tools and it's going GREAT:
1) Bill Kinney makes Rudin fun!
2) So does Winston Ou, but with more rigour!
3) I solve MIT's OCW Real Analysis HW along with Rudin's exercises
TL:DR
My Question: I've never felt slower learning Maths and building conceptual intuition; would like to hear about/have identified one's personal conceptual pitfalls that have occured to seasoned veterans while taking an initial RA course, so I can be wary of it during my learning process?
I also have self-studied Real Analysis from baby Rudin and Winston Ou's lectures. I will share with you the major takeaways that I had as far as mathematical thinking is concerned:
1) Always try to think geometrically and try to draw a picture to visualize the statement of the theorem. Most probably, you will also get the idea of proof reasonably quickly from the diagram itself (I learned this from Ou's lectures). But remember, don't rely too much on these pictures otherwise you won't be able to translate your "geometrical intuition" into mathematical language.
2) Memorize the definitions in their original format as written in the book and let them be your guide while proving theorems. You will notice that most of the proofs are pretty straight-forward except some, which require some new ideas.
3) Last but not least, discuss your doubts or some questions with your friends or any of your professors. It will help you to gain new insight into the subject which would otherwise be missing while studying on your own.