# learning/teaching approach to rigorous math with the goal of improving

I will state this now: yes, this is a subjective question. But I feel the answers people give may benefit students.

I want to get better at doing non trivial proofs. Real analysis is standard material some students have to learn. I have, broadly speaking, two choices for a textbook: 1) something like "baby Rudin", where I may struggle for long periods of time on problems, often having little direction and no progress, or 2) something easier, where smaller theorems are developed in the book and where there are less sophisticated jumps of reasoning (demonstrated, required) in the proofs.

What are the preferences of educators/students for using one over the other? Do you have reason to believe one is more successful at actually helping students improve? How do you determine success?

My beliefs: I tend to think the easier book may help me develop my own techniques (I could be wrong). I see more examples and I get more confidence in doing basic things. But more advanced material will probably be less accessible, so I know that at some point I will have to just deal with the sort of terseness that occurs in Rudin. Anyway, I can keep going back and forth about this.