Real Analysis (Baby Rudin vs Apostol)

Click For Summary

Discussion Overview

The discussion centers around the comparison of two real analysis textbooks: Apostol's Mathematical Analysis and Rudin's Principles of Mathematical Analysis. Participants share their experiences with these texts, exploring their strengths and weaknesses, and consider how to effectively use them in conjunction for self-study in real analysis.

Discussion Character

  • Exploratory
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses difficulty with Rudin's proof, suggesting that it may not be suitable as a sole textbook and considers using Apostol as a supplement.
  • Another participant recommends Strichartz for a more verbose approach, while also mentioning Abbott's Understanding Analysis as a potential resource.
  • A participant shares their experience with Abbott's book, finding it well-written but too slow-paced for their needs, and expresses skepticism about Strichartz as well.
  • Some participants inquire about the best way to use Rudin and Apostol together, debating whether to learn theory from Apostol and solve problems from Rudin.
  • Carothers' book is suggested as an alternative to Rudin, noted for its gentler exposition and broader coverage, although it lacks multivariable analysis.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach to studying real analysis using these texts. There are multiple competing views regarding the effectiveness of each book and how they might be used together.

Contextual Notes

Some participants express uncertainty about the pacing and depth of various textbooks, indicating that personal learning styles may significantly influence their preferences. There are also unresolved questions about the best strategies for integrating the two texts.

Who May Find This Useful

Individuals interested in self-studying real analysis, particularly those considering different textbooks and their approaches to learning the material.

Falgun
Messages
77
Reaction score
45
I am currently trying to self study Real analysis . I have completed Hubbard's Multivariable book & Strang's Linear algebra book. I have Apostol's Mathematical Analysis & Baby Rudin . I started with rudin yesterday and was making excellent headway until I encountered a theorem about 15 pages in. After some difficulty I managed to prove it but when I saw rudin's proof I was completely baffled. He did in three lines what took me a page . I am still trying to understand the proof as of now. But I am beginning to feel rudin might not be as good as a sole textbook. I am considering using apostol's book as a supplement.
How does it compare to Rudin?

Does anyone have any suggestions about using apostol & rudin in conjunction?

Feel free to recommend other resources and tips to learn analysis.Thanks in advance.
 
Physics news on Phys.org
I know that people have issues with it, but if you feel that a verbose approach would work better for you, take a look at Strichartz.

Many people recommend Abbott Understanding Analysis.
 
caz said:
I know that people have issues with it, but if you feel that a verbose approach would work better for you, take a look at Strichartz.

Many people recommend Abbott Understanding Analysis.
I flipped through a pdf of abbott before I tried rudin but I didn't find it all that satisfying. Sure, the writing's excellent and very easy to read but I felt the pace was too slow. As for strichartz I don't think it will suit me for the same reason.

What are your thoughts on Apostol's Analysis book?

I was more hoping you would tell me how to use Rudin & Apostol together?
Like should I get the theory from apostol & problems from rudin or what?
 
I like Rudin a lot, but another option is Carothers' book. It's maybe a gentler read and has good exposition and problems from what I've looked at. I think it also covers more than Rudin (though it doesn't do any multivariable analysis from what I remember).
 
Infrared said:
I like Rudin a lot, but another option is Carothers' book. It's maybe a gentler read and has good exposition and problems from what I've looked at. I think it also covers more than Rudin (though it doesn't do any multivariable analysis from what I remember).
Sure I'll check it out.
 

Similar threads

Real Analysis Textbook Recommendation
  • · Replies 2 ·
Replies
2
Views
3K
Analysis Is Baby Rudin a good choice for first my Real Analysis textbook?
  • · Replies 9 ·
Replies
9
Views
6K
Analysis Study plan for Functional Analysis - Recommendations and critique
  • · Replies 13 ·
Replies
13
Views
5K
Analysis What are some recommended analysis textbooks that complement Rudin's PMA?
  • · Replies 1 ·
Replies
1
Views
3K
Analysis Readability of Rudin's Real and Complex Analysis
  • · Replies 5 ·
Replies
5
Views
4K
Apostol Analysis vs Shilov Analysis
  • · Replies 9 ·
Replies
9
Views
5K
Analysis Supplements to Complex Analysis of Rudin-RCA?
  • · Replies 7 ·
Replies
7
Views
3K
Calculus Why "Transition Books (Apostol, Spivak)" are necessary?
  • · Replies 12 ·
Replies
12
Views
7K
Calculus Multivariable Calculus, Hubbard and Hubbard and Lang's
  • · Replies 2 ·
Replies
2
Views
4K
Analysis Which book will suit the following course syllabus (introductory analysis)?
  • · Replies 5 ·
Replies
5
Views
2K