Book recommendation for analysis problems

Solution 1:

E. Stein and R. Shakarchi's Princeton Lectures in Analysis have good selections of problems. Or rather, a good selection of what they call "Exercises," which are comparable to what you might find in other textbooks, and then a few of what they call "Problems," which are more involved than the standard sort of "Exercise."

Also, specifically for real analysis R. Wheeden and Antoni Zygmund's Measure and Integral has a large selection of exercises as well.

Edit: An important remark! Professor Wheeden is updating his book to a second edition. (Source: I'm a student at his institution.)

Solution 2:

I like these:

1) The 3 books of Kaczor by AMS: http://www.amazon.com/Problems-Mathematical-Analysis-Numbers-Sequences/dp/0821820508/ref=sr_1_1?ie=UTF8&qid=1416621683&sr=8-1&keywords=Problems+in+Mathematical+Analysis

2) Real Analysis by Charalambos: http://www.amazon.com/Problems-Analysis-Second-Charalambos-Aliprantis/dp/0120502534/ref=asap_B001IQX9TY_1_2?s=books&ie=UTF8&qid=1416621788&sr=1-2

3) Answers of Lang's analysis book: http://www.amazon.com/Problems-Solutions-Undergraduate-Analysis-Mathematics/dp/0387982353/ref=sr_1_5?ie=UTF8&qid=1416621683&sr=8-5&keywords=Problems+in+Mathematical+Analysis

Exist many other more and less advanced. For example, search by 'Problems in Mathematical Analysis' in Amazon site: http://www.amazon.com/s/ref=nb_sb_noss?url=search-alias%3Daps&field-keywords=Problems+in+Mathematical+Analysis

and here, e.g.: Exercise books in analysis

Solution 3:

I like Richard Bass's Real Analysis for Graduate Students. Carother's book Real Analysis is pretty good too. They're both pretty advanced, but if you're already gone through Apostol, Rudin and Folland, I think you'll be able to handle them.

Solution 4:

There are several wonderful FREE online problem courses in various areas of mathematics by John Erdman of Portland State University available at his website here. 1

There are 5 courses in analysis written by Erdman at the site for his students-one on basic calculus, one at the advanced calculus level, one at the graduate analysis level,one on functional analysis and lastly,one on operator theory, the last 2 for advanced graduate students. These are extremely well written and comprehensive sources you will find a ton of great exercises in and that every student of mathematics should become familiar with.

And best of all,they're free! I think you'll find them very helpful.