I'll major in math at a local University. I've finished High School Calculus and I've self-studied very basic Multivariable Calculus, Linear Algebra, and Real Analysis. I've watched video lectures of them.
While I can read and follow most of the proofs and chapters in Rudin's PMA, I cannot do the exercises. I thought that PMA was an introductory book to Real Analysis so I thought I shouldn't have too much trouble. But I am having a lot, perhaps because I was not exposed to rigorous proofs (I've seen a lot but I don't know how to formulate one myself). I searched and saw many recommendations for How to Prove It by Velleman and another book by Polya.
Will reading one of it be fine as a bridge from non-rigorous high school math to rigorous University-level math like PMA?
Will these books help me with Rudin's PMA's exercises?
Are there any books that help as bridges which are not the "proving-type"?
- Finally, when does one typically take a Real Analysis course with Rudin's PMA in University?