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I'm specifically interested in problem sets in Real Analysis that have solutions. I have a few books on it, but I'd like to compare my solutions with some given answers in a lot of cases to ensure that I've mastered the material as much as possible.

I've searched Real Analysis books on this site, and came up with this question.

I'm really wondering about books (maybe teacher's manuals), PDFs, or other resources that have solutions to questions. I'm self-studying, and I do have some good books that explain things fairly well, but I haven't yet been satisfied that I've mastered the material well enough. Thus my want for solutions, besides just having problems without solutions.

For example, this PDF has some solutions, but I'm wondering if I can find more books, etc.

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Matt Groff
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    At the level of beginning graduate studies in Real Analysis, it's hard for me to see a "solutions manual" as providing much value in mastering the discovery and articulation of proofs. Reading someone else's proof might on occasion help to identify an overlooked case or unstated/unwarranted assumption, but in general you need someone to read your proofs and give feedback on presentation as well as correctness/completeness. – hardmath Jul 19 '14 at 00:27
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    "Problems and Theorem in Analysis" by Polya and Szego is nice. – Pedro Jul 19 '14 at 00:58
  • Ash's Probability & Measure Theory has complete solutions to many of the exercises. I discovered this about (the first edition of) Ash's book many years ago simply by browsing in a university library. If you have access to such a library, I suggest you simply go to the locations where real analysis texts are shelved (in the U.S., this will be in the QA 300 and QA 330 vicinities) and flip through the dozens (maybe hundreds, if a good library) books until you get one or more that have what you're looking for. – Dave L. Renfro Jul 21 '14 at 16:06

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Here are two more hints which could be helpful

Problems and Theorems in Analysis I and Problems and Theorems in Analysis II from Pólya and Szegö

This two volume book is a problem based classic (first edition from 1924). It is a highly inspiring source of many interesting problems in different fields of analysis together with detailed solutions.

A modern Analysis book with lots of solved problems is the two volume book

Principles of Real Analysis and Problems in Real Analysis from Aliprantis and Burkinshaw.

They present more than $600$ problems in their Principles and they provide complete solutions to these problems in their Problems book which was sometimes very helpful for me.

Note: To be honest the problem books from Pólya and Szegö are really gold books in the same sense as the wonderful books from Rudin. They belong to the sources which I look through from time to time with great pleasure.

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Markus Scheuer
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For undergraduate analysis, Rudin's Principles of Mathematical Analysis is the gold standard. At the end of each chapter, there are challenging and interesting problem sets whose solutions may be found here.

Gamma Function
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    WARNING: USE AT YOUR RISK. Don't copy for homework, the lack of knowledge you'll gain is your loss. Even if self studying, make sure to make a fair attempt at a solution. – abnry Jul 19 '14 at 00:59