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In a recent post I asked about an epsilon delta proof for an Analysis question. Before posting it I searched for similar questions and their proofs on google but all I found were computational style problems. If anybody is aware of a good resource for problems and solutions of upper-undergraduate level real Analysis problems it would be greatly appreciated.

Background: I am an engineering student who is trying to teach myself real analysis.

Thanks in Advance,

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up vote 4 down vote accepted

Interactive Real Analysis is an online, interactive textbook for Real Analysis or Advanced Calculus.... It deals with sets, sequences, series, continuity, differentiability, integrability (Riemann and Lebesgue), topology, power series, and more.

$\quad \quad \quad$ Interactive Real Analysis Overview

  • See also: Basic analysis: Real Analysis. If you scroll to the bottom of the webpage, there are a number of links to resources that appear to be promising.

  • Finally, and perhaps most promising: See Analysis: Resources for links to everything from lecture notes, videos, tutorials, and on-line texts.

Recommendation: Buy W. Rudin's Principles of Mathematical Analysis!
It's worth the expense. At the very least, borrow the text from a library. Solutions and/or solution sketches are readily available by searching on-line, as the exercises in the text are classics. See this search of Math.SE posts using only "Rudin" as search term!

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Thank you for these; many resources for me to explore here. I have another question; there seems to be a general consensus that Rudin is the place best place to start for this subject, is there any similar consensus about what the best textbook is for dealing with the next level up for Real Analysis? To be sure, I’m not there yet, but I’d like to have an idea for what’s around the corner. Thanks again -N – Neil Dec 4 '12 at 0:24
Rudin also has a text: Real and Complex Analyis (RCA) which will take you to the next level, when you're ready. – amWhy Dec 4 '12 at 0:27
Good references even for an small one like me. :+) – Babak S. Sep 9 '13 at 15:34

The solution to virtually every problem of Rudin's PMA can be found online, so get yourself the book.

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