What are the best textbooks for Real Analysis?

[SiddharthM]

So I just wanted to hear about other people's experiences with undergraduate (and introductory graduate) analysis textbooks. There are the standards and some new great texts as well. Which are your favorite? Recommendations?

Kenneth Ross: The theory of Calculus, Elementary Analysis. Very readable text and some difficult problems (nothing craze though). All in all great for the first analysis class.

Rudin: I'm using this for review. It's very comprehensive, but can be difficult for someone who hasn't read or done hardened mathematics before. Problems are fantastic methinks. Even some treatment of the Lebesgue theory as well!

Real Mathematical Analysis, Pugh - I haven't read through a lot of this one, just a few sections (Cantor Lore is fantastic). Although I have to say I don't like the way he writes math. The selection of problems is golden.

Royden: Probably my favorite analysis textbook. Good problems and bridges the gap from undergraduate to graduate analysis well whereas the 2nd Rudin doesn't so much.

Because I live in third world countries I have purchased most of these for next to nothing: Pugh is the only unavailable in a soft print here in Delhi, the rest cost less than 5 dollars a piece. I even got munkres for that price! To think that some are forced to shell out 130 odd US dollars on a textbook smaller than a novel is NUTTY. The classics are all available online via bittorent for free though (this is VERY illegal but hey so is that mp3 ur listening to).

 

[ice109]

understanding analysis by stephen abbott is supposed to be really good. i just bought softcover calculus by tom apostol from somewhere in asia for 20$ which is supposed to be a good calculus-analysis bridge

 

[Daverz]

Foundations of Mathematical Analysis
by Johnsonbaugh and Pfaffenberger.

 

[supraanimo]

I had a good time with:
An Introduction to Analysis (2nd Edition)
by James R. Kirkwood

fairly easy to understand, well worked through proofs, decent problems (some were way too advanced).

 

[kmgh]

Siddhartha,
I am planning to review my Analysis, and was wondering which would be a batter book between Rudin(baby) and Pugh. Can you help me out with the choice - I do not want to sacrifice on rigor. What if any are your grudges with Pugh?

 

[leon1127]

Calculus-Spivak. But this is more about advance calculus.

 

[SiddharthM]

I just don't like the way Pugh writes mathematics. I say go with both - pugh is around 50$ (im sure u can find it cheaper) and you can get an international edition of Rudin on abebooks for under 30$. Both are very comprehensive but Pugh definitely has MORE stuff and his problem sets are awesome.

www.bigwords.com

 

[tronter]

In my opinion, Pughs book is the best for content and problems. Rudin is too terse, and his coverage of multivariable analysis is not good. Pugh starts out with dedekind cuts and topology from the start. Rudin doesn't like topology too much, and his book has no pictures, so you can't get an intuitive idea of real analysis when you are first learning it.

 

[SiddharthM]

rudin is best for those preparing to read higher mathematics but i'd definitely go with pugh for the student with no previous experience in the subject.