The Real Analysis Lifesaver: All the Tools You Need to Understand Proofs (Princeton Lifesaver Study Guides)

Category: Mathematics
Author: Raffi Grinberg
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by thousandpounds   2017-08-19
I am in the same boat. I get the feeling that most Calculus books are just a compilation of tips and tricks. So I am suggesting you invest time into learning real analysis proper. Right now I am learning from [1]. It follows Rudin closely and as opposed to many other analysis books meant to "better explain" stuff, it goes deep into the trenches and actually tackles the subject.


I think time invested into studying real analysis pays off because then you can later study measure theory, functional analysis and more advanced probability to deal with curse of dimensionality and whatnot.

edit: I started studying the book linked above starting from chapter 4 since the first 3 chapters are familiar from discrete math. Then did chapter 5, skimmed chapters 6(little linear algebra), 7, 8 (most "transition to higher math" books contain this stuff) and am currently in chapter 9.