Introductory Real Analysis for Beginners and Experts

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This is an excellent book for learning Real Analysis/Advanced Calculus.
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We appreciate your insights. Keep making an impact on the community.

sophiaisabelle

Sounds like a great book, but clearly high level. Probably a good alternative to Baby Rudin, but not for simpler books like the first one by Terence Tao or Elon's Análise Real(which are great first courses in Analysis).

BlueHue-thecelestialblue

I just want to take a moment and admire that you are going to be 1M soon. I have been following you since you had like a couple of thousands of subs. I am happy for you. ❤

surajpowar

Someday I hope I can take some time to really study this book. I've heard people often use it as a text for graduate analysis or as a companion. If you have any books on the calculus of variations I'd love to see them. I know Fomin was a coauthor with I.M. Gelfand on a well known variational calculus book from Mir Publishers. It is dense, just the first chapter alone gave me enough of the theory for many applied variational problems.

chasefoxen

I just got a PDF copy of it and glanced through it. And I will say, it rightfully deserves to be called a legendary book. Period.

samrubenabraham

This book is an introduction to linear functional analysis. It almost assumes you know Analysis on R. It’s a great reference, but not a good book to learn analysis from if you’re new to the subject. The authors develop a lot of theory in the exercises so it’s easy to miss a lot. I would go with Kreyszig for this topic.

joef

The Russian intelligentsia back in the 60’s were really good at math (and other STEM subjects like shooting off rockets etc) because they didn’t have any other distractions. (It was like living in a tomb, to quote someone quite famous at the time.) “Let’s build socialism together!” Corollary: this is a really good math book, it’s a pleasure that it’s still in print.

But like the Landau & Lifschitz physics series, it can be somewhat unforgiving. ;^)

declanfarber

The Cosmic Doctrine by Dion Fortune does this with pictures.

davesnowdon

Math Sorcerer are you familiar with nonstandard analysis? Would you recommend learning this without standard analysis? My current background is only calculus.

joshux

I echo the comment by @joef4309. This is not a book on Real Analysis but on Functional Analysis instead, which assumes you already have RA.
If you were going to use it w/o having RA, it could be deceiving because it's so well written that it gives you the impression you understand what's going on but, yes, you could be missing a lot of fine, subtle and important points, and risking to develop a shaky foundation.
Also, I wish The Math Sorcerer had elaborated a bit more on the chapters of Linear Functionals and Linear Operators (5 and 6) which are where the "entree of the book" takes places. Really good stuff

erickleuro