Mathematics Book Recommendations

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Discussion Overview

The thread discusses recommendations for mathematics books, particularly those that highlight key concepts in mathematics, as well as books suitable for physics students studying Functional Analysis. The conversation includes inquiries about prerequisites for studying Functional Analysis and comparisons between various textbooks.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • Some participants seek books that provide highlights of mathematics, similar to two specific titles linked in the thread.
  • One participant mentions a book by Russian authors but does not provide details or personal experience with it.
  • A participant asks for recommendations for books on Functional Analysis for physics students, questioning the necessity of a strong background in real analysis.
  • Another participant suggests Reed and Simon's book as a classic, noting its level of rigor and useful end-of-chapter notes.
  • There is a mention of Kreyszig's book, which is described as pedagogically effective but not as rigorous as other texts mentioned.
  • One participant advises reviewing the first five chapters of Rudin's Real and Complex Analysis before studying Rudin's Functional Analysis, sharing their personal experience of transitioning from another analysis text.
  • A participant expresses a desire for advice on the original question regarding mathematics book recommendations, referencing a previous suggestion from another user.

Areas of Agreement / Disagreement

Participants express varying opinions on the necessity of a strong background in real analysis for studying Functional Analysis, and there is no consensus on the best books to recommend for either mathematics highlights or Functional Analysis.

Contextual Notes

Some suggestions depend on personal experiences and may not universally apply. The discussion reflects a range of perspectives on the prerequisites for Functional Analysis and the suitability of different textbooks.

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There's this one by some Russian authors. I haven't read it.
 
Daverz said:
There's this one by some Russian authors. I haven't read it.

Thank you! Good suggestion!
 
Gentlemen,
Sorry, rather than opening new thread, please let me post this question in this thread.
What book(s) would you recommend for physics student studying Functional Analysis?
Is strong background in real analysis a must prerequisite before doing Fuctional Analysis?
I observe Rudin's book is quite widely used, how about the one by Peter D. Lax?
Is it a good one? It seems it covers more topics than Rudin's does.
Any suggestion would be highly appreciated.

urkel
 
Urkel said:
Gentlemen,
Sorry, rather than opening new thread, please let me post this question in this thread.
What book(s) would you recommend for physics student studying Functional Analysis?
Is strong background in real analysis a must prerequisite before doing Fuctional Analysis?
I observe Rudin's book is quite widely used, how about the one by Peter D. Lax?
Is it a good one? It seems it covers more topics than Rudin's does.
Any suggestion would be highly appreciated.

urkel

https://www.amazon.com/dp/0125850506/?tag=pfamazon01-20 by Reed and Simon is a well-known classic. Don't be fooled by the title, this is a real mathematics at about the same level as Rudin. It has very interesting and useful end-of-chapter notes.

A background in real analysis certainly helps.

Even though several real analysis courses were prerequisites for the functional analysis course that I took, the textbook for this course, https://www.amazon.com/dp/0471504599/?tag=pfamazon01-20 by Kreyszig, does not really require analysis. This book is a pedagogical masterpiece (read the reviews!) that is very readable; a favourite of mine. It is, however, not quite at the level of the other books mentioned, and it does not contain a treatment of distributions (e.g., Dirac delta "functions".)
 
Last edited by a moderator:
I recommend going thru the first 5 chapters (at least) of Rudin's Real and Complex Analysis before tackling Rudin's Functional Analysis. I made the mistake of jumping from Royden's Real Analysis to Rudin's Functional Analysis (on self-study). Real and Complex Analysis provides some good examples and applications of some "basic" functional analysis.

I also like Hunter's Applied Analysis for motivation and examples while tackling Rudin.

http://www.math.ucdavis.edu/~hunter/book/pdfbook.html
 
Does anybody who gave advice on functional analysis books have any advice for my original question? 'Daverz' gave a really good suggestion!
 

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