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Self Study Analysis

  1. Jun 18, 2008 #1
    I am interested in self-studying analysis and was trying to purchase a textbook, but I am not sure of the appropriate level to start at. I have come across:

    Intro to Analysis:
    Intro to Real Analysis:
    Elementary Real/Complex Analysis:
    Elementary Functional Analysis:
    Elements of the Theory of Functions and Functional Analysis:

    Any suggestions of where to start/what order to go in? or any better textbooks? I was looking at those because I heard Dover Publications were good. On a side note, anyone agree/disagree?
  2. jcsd
  3. Jun 18, 2008 #2


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    I'm only familiar with Kolmogorov & Fomin, having worked through its chapters on Lebesgue integration and Hilbert space theory. (This was the content of second volume of the book. It seems the chapter ordering has been altered in the Dover reprint.) If this is your first attempt at studying analysis, I doubt if this book would be a good/realistic place to start; you'll probably toss it aside after trying to read the first few pages. The same probably applies to Shilov's functional analysis book. There are definitely better treatments out there for beginners.

    What's your background?
  4. Jun 18, 2008 #3


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    the first three look more elementary, hence a better place to start. the third one looks easiest. they all look excellent, if you can read them.

    so the issue is not which book is good, but which can you understand.
  5. Jun 19, 2008 #4
    Sorry for the thread hijack.

    Would Apostol's book "mathematical analysis" be a good intro for a beginner wanting to self-study analysis?
  6. Jun 19, 2008 #5
    I ask because I can get the book at my library, and I liked his Calculus book a lot.
  7. Jun 19, 2008 #6
    I have Elementary Real and Complex Analysis by Shilov, I read through it, without doing any problems, and I found that it was fairly easy to understand, and I was expecting some good old analysis, filled with stuff like differential forms, but it turned out to be nothing more than a little formalization of basic calculus up til the Line Integral. It didn't even go into Green's, Stokes' or the Divergence theorem, which left me a little disappointed. I also got Pugh's Real Mathematical Analysis which is much more in-depth and it's probably my next project, but I say get the Shilov one, it's very cheap, and it'll help you through the tough bits.

    Link to Pugh's: https://www.amazon.com/Real-Mathema...bs_sr_2?ie=UTF8&s=books&qid=1213892621&sr=1-2
    Last edited by a moderator: Apr 23, 2017
  8. Jun 19, 2008 #7


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    yes apostols book is a an excellent high level intro to analysis. it was the desginated text at harvard in fall 1960 for the advanced honors calc course, later the course for which loomis and sternberg's advanced calculus was written.
  9. Jun 19, 2008 #8
    Hi !
    I am doing the same thing!
    I found the book by Arthur mattuck used by me is pretty readable too.
    Maybe we can share what we learned and learn from each other! =)

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