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I'm studying Rudin's Principles of mathematical analysis and I was wondering if there are some exercise books (that is, books with solved problems and exercises) that I can use as a companion to Rudin.

The books I'm searching for should be:

  • full of hard, non-obvious, non-common, and thought-provoking problems;
  • rich of complete, step by step, rigorous, and enlightening solutions;
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You can check these books:

http://www.amazon.com/Problems-Analysis-Second-Charalambos-Aliprantis/dp/0120502534/ref=sr_1_1?s=books&ie=UTF8&qid=1411894207&sr=1-1&keywords=problems+in+real+analysis

And

http://www.amazon.com/Problems-Real-Analysis-Advanced-Calculus/dp/0387773789/ref=sr_1_2?s=books&ie=UTF8&qid=1411894207&sr=1-2&keywords=problems+in+real+analysis

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  • $\begingroup$ Thanks. The second one seems very good. $\endgroup$ – Dal Sep 29 '14 at 22:20
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This is what I recommend to students learning analysis as a good companion:

http://minds.wisconsin.edu/handle/1793/67009

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