What are the best books to self study real analysis? I am a physics masters student and am looking forward to study representation theory. I want to study the real analysis I need for studying functional analysis.
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For self-study, I strongly recommend Abbott's "Understanding Analysis". He does an excellent job of motivating the abstract concepts and introducing the frequently unintuitive behavior of infinite sets and processes.
Cassius12
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Any recommendations for functional analysis? – pinaki nayak Dec 12 '18 at 17:03
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functional analysis (and other modern math topics) --- Introductory Functional Analysis with Applications by Erwin Kreyszig (1978) AND Introduction to Topology and Modern Analysis by George F. Simmons (1963) AND the books here AND Paul Roman's 2-volume work Some Modern Mathematics for Physicists and Other Outsiders Volume 1 contents. – Dave L. Renfro Dec 12 '18 at 19:51
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We used Folland's "Real Analysis" in my graduate RA class, but I found that I wanted more of a Topology/Measure Theory background to really understand it. You might find some useful comments at this discussion: https://math.stackexchange.com/questions/3025828/should-i-learn-measure-theory-before-learning-probability/3025932#3025932 – Cassius12 Dec 12 '18 at 21:29
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There are many available books for this topic because this is a very lengthy topic so by a single topic you can't be satisfied, so it is better to take different books for the different topics but for overall development I suggest following:
- Real Analysis by Bertle Shebert ( for basic)
- Mathematical Analysis by Apostol ( this one is my favourite, containing a lot of topics)
- Real Analysis by Royden ( mainly for Theory of Integrals, and measure)
- Principles of Mathematical Analysis by Walter Rudin ( contains a lot of standard problems)
Thank you.
Albert
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