Which Analysis Textbook to Start With? Dover Pubs Advice

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Discussion Overview

The discussion revolves around selecting appropriate textbooks for self-studying analysis, with a focus on various titles published by Dover Publications. Participants share their experiences and recommendations regarding the difficulty level and content of different analysis texts.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant expresses uncertainty about which analysis textbook to start with and lists several Dover titles, seeking suggestions on the order of study and recommendations for better alternatives.
  • Another participant, familiar with Kolmogorov & Fomin, suggests that it may not be suitable for beginners and questions the appropriateness of Shilov's functional analysis book for someone new to the subject.
  • A different participant proposes that the first three listed books appear more elementary and suggests starting with the easiest one among them, emphasizing the importance of personal understanding over the quality of the books.
  • One participant inquires about the suitability of Apostol's "Mathematical Analysis" as an introductory text for self-study, noting a positive experience with Apostol's calculus book.
  • A participant who read Shilov's "Elementary Real and Complex Analysis" found it easy to understand but was disappointed by its lack of depth in certain topics, suggesting it could still be a helpful resource for beginners.
  • Another participant endorses Apostol's book as an excellent high-level introduction to analysis, referencing its historical use in a Harvard course.
  • One participant shares their experience with Arthur Mattuck's book, suggesting it is readable and proposes collaboration in learning with others.

Areas of Agreement / Disagreement

There is no clear consensus on which textbook is the best starting point for self-study, as participants express differing opinions on the suitability of various texts and their own experiences with them.

Contextual Notes

Participants' recommendations depend on their individual backgrounds and experiences with analysis, which may influence their views on the difficulty and appropriateness of the suggested textbooks.

Who May Find This Useful

Individuals interested in self-studying analysis, particularly those seeking recommendations for textbooks at various levels of difficulty.

Knissp
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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:
https://www.amazon.com/dp/0486650383/?tag=pfamazon01-20
Intro to Real Analysis:
https://www.amazon.com/dp/0486612260/?tag=pfamazon01-20
Elementary Real/Complex Analysis:
https://www.amazon.com/dp/0486689220/?tag=pfamazon01-20
Elementary Functional Analysis:
https://www.amazon.com/dp/0486689239/?tag=pfamazon01-20
Elements of the Theory of Functions and Functional Analysis:
https://www.amazon.com/dp/0486406830/?tag=pfamazon01-20

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?
 
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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?
 
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.
 
Sorry for the thread hijack.

Would Apostol's book "mathematical analysis" be a good intro for a beginner wanting to self-study analysis?
 
I ask because I can get the book at my library, and I liked his Calculus book a lot.
 
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/dp/0387952977/?tag=pfamazon01-20
 
Last edited by a moderator:
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.
 
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! =)

Cheers,
 

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