Principles of Mathematical Analysis

Principles of Mathematical Analysis, by Rudin You might be ready for this after Spivak's Calculus, but it can be rough.

on HN, 2019

The classic text on analysis is Principles of Mathematical Analysis by Rudin. Its very difficult and leaves it to the reader to understand the terse proofs. It starts from the beignning, with no math background assumed about the reader. The terse proofs are written in such a way to force the reader to gain deep mathematical intuition. Some of the proofs are elegant and beautiful. I would absolutely recommend it.

on HN, 2020

I studied math in university and the book that really improved me mathematically was baby rudin. I really struggled with this the first time I worked through it and had to also fall back on Abott's analysis book, but after my first analysis course I worked through Rudin again and it just clicked. The exercises are really well chosen and the text is just so on point. Every sentence in the book is extremely carefully chosen and of fundamental importance to what Rudin wants to teach you.

on HN, 2022

Baby Rudin, Principles of Mathematical Analysis, was that book for me. It was that book for a lot of people, which I guess means it felt "perfect" for people with a broad range of backgrounds.

on HN, 2022

Idk, I tried to self study the first two chapters of a very hated textbook (Principles of Mathematical Analysis). If you’d have asked me if I understood the material I would have said no. But by the time I took the actual class on that material I made high As on all the exams and could call out mistakes my professor made on metric sets with counter examples.

on HN, 2019

In general, it kicks up the mathematical rigor you're used to a notch. Seeing ">" defined as "not <" really blew my mind when I first read it! "<" is just something that satisfies some axioms, like anything else in math.

on HN, 2023