Advanced Calculus/Real Analysis Book

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Discussion Overview

The discussion revolves around recommendations for supplemental textbooks for an advanced calculus course, specifically aimed at providing detailed explanations and step-by-step examples. The context includes the needs of a student preparing for graduate studies in mathematics.

Discussion Character

  • Homework-related
  • Technical explanation

Main Points Raised

  • One participant expresses a need for a more accessible textbook alongside Goldberg's Methods of Real Analysis, seeking detailed explanations and examples.
  • Another participant recommends a book by Thomson, Bruckner, and Bruckner, highlighting its affordability and availability for preview and download.
  • A different participant suggests two Dover publications by Georgi Shilov and Maxwell Rosenslicht, praising Dover's reputation for quality and affordability in mathematics texts.
  • Another recommendation includes "Analysis: With an Introduction to Proof" by Steven Lay, noted for its clarity in proofs and techniques, along with "Elementary Analysis: The Theory of Calculus" by Kenneth Ross as good introductory texts.

Areas of Agreement / Disagreement

Participants generally agree on the need for supplemental texts but present multiple competing recommendations without a consensus on a single best option.

Contextual Notes

Participants provide various suggestions based on personal experiences and preferences, which may reflect differing definitions of what constitutes a suitable supplemental text.

tarheelborn
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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.
 
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I recommend

https://www.amazon.com/dp/143484367X/?tag=pfamazon01-20 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):

http://classicalrealanalysis.com/TBB.aspx"

Caution: the same authors also published a graduate-level book called "Real Analysis."
 
Last edited by a moderator:
Thank you so much!
 
Two books published by Dover that are, in my opinion, excellent for your purpose are

https://www.amazon.com/dp/0486689220/?tag=pfamazon01-20 by Georgi Shilov

and
https://www.amazon.com/dp/0486650383/?tag=pfamazon01-20 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:
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.
 
Thanks for all your help!
 

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