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Advanced Calculus/Real Analysis Book

  1. Oct 8, 2009 #1
    I am currently taking an advanced calculus course and, for the most part, I really like it. However, I believe I could benefit from a supplemental textbook. My class uses Goldberg's Methods of Real Analysis. I would like to be able to find a text that offers more detailed explanations and, particularly, step-by-step examples to show the theorems. I suppose I need a "for dummies" version of advanced calculus. I am an older student, attempting to refresh/learn enough to get into graduate school in mathematics. Thanks for your help.
  2. jcsd
  3. Oct 8, 2009 #2


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    I recommend

    https://www.amazon.com/Elementary-Real-Analysis-Brian-Thomson/dp/143484367X/" by Thomson, Bruckner, and Bruckner.

    You can preview parts of it using the "look inside" feature at Amazon to see if it's what you are after. The price is pretty good at $27 for a paperback, or you can download a full PDF version here for a token charge (I think it was literally one dollar, with substantial chunks available for free):


    Caution: the same authors also published a graduate-level book called "Real Analysis."
    Last edited by a moderator: May 4, 2017
  4. Oct 8, 2009 #3
    Thank you so much!
  5. Oct 10, 2009 #4
    Two books published by Dover that are, in my opinion, excellent for your purpose are

    https://www.amazon.com/Elementary-C...sr_1_1?ie=UTF8&s=books&qid=1255201897&sr=1-1" by Georgi Shilov

    https://www.amazon.com/Introduction-Analysis-Maxwell-Rosenlicht/dp/0486650383/ref=pd_sim_b_5" by Maxwell Rosenslicht.

    Also, if you plan on pursuing pure math, Dover is a fantastic publisher offering many cheap, well-written texts that are far better than many texts put out by publishers for 5-10x the price. To see their math catalogue, go to http://store.doverpublications.com/by-subject-science-and-mathematics-mathematics.html".

    Best of luck!
    Last edited by a moderator: May 4, 2017
  6. Oct 10, 2009 #5
    Analysis: With an Introduction to Proof by Steven Lay
    This book is an excellent starter to analysis. It gives many proofs that are extremely clear, and has quite a big chunk devoted to techniques of proof.

    Elementary Analysis: The Theory of Calculus by Kenneth Ross

    These are great introductory books that don't have an ego.
  7. Oct 12, 2009 #6
    Thanks for all your help!
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