Mathematics Book Recommendations

[Shaun Culver]

Can anybody suggest books similar to these two:

https://www.amazon.com/dp/0521797071/?tag=pfamazon01-20

https://www.amazon.com/dp/981238555X/?tag=pfamazon01-20

I.O.W.:
Books that give the highlights of mathematics.

 

[Daverz]

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

 

[Shaun Culver]

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

Thank you! Good suggestion!

 

[Urkel]

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

 

[George Jones]

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".)

 

[redrzewski]

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

 

[Shaun Culver]

Does anybody who gave advice on functional analysis books have any advice for my original question? 'Daverz' gave a really good suggestion!