Where to go next? did the intro to analysis

In summary, the individual has completed an introductory course in analysis and is looking to advance their knowledge on their own. They are considering three options for further study: Fleming's "Functions of Several Variables," Kreyzig's "Introductory Functional Analysis," and Spivak's "Calculus on Manifolds." After receiving suggestions, they have decided to start with Kreyzig's book as it seems more accessible. They hope to eventually be able to master Spivak's book, but acknowledge it may take some time.
  • #1
octol
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Ok I've done an introductary course in analysis using the first 2/3 of Parzynski and Zipse - Introduction to Mathematical Analysis. This (I think) is about equivalent to Rudin up and including chap 7 (series of functions).

I probably won't have time to take any more classes in mathematics as I'm more of a theoretical physicist, but I'd still try to advance my knowledge in analysis a bit on my own. The problem is I don't know in which direction I should continue.

So far I'm considering one of the following options:

1) Fleming - Functions of Several Variables

2) Kreyzig - Introductory Functional analysis

3) Spivak - Calculus on Manifolds

The criteria is that it can't be too big a step up as I'm not a mathematician and I'll be studying on my own. Kreyzig looks very nice from that aspect, while Spivak seems scary.

Anybody has any suggestions?
 
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  • #2
I have all of the books that you listed as options, but I have none of them with me right now.

It might be useful to study, in some book, the material in chapter 9 of Blue Rudin. This stuff is probably covered in both Fleming and Spivak. Even though Spivak is a wonderful book, Fleming's treatment is probably more accessible.

Kreyzig was the text for a course that I took, and I think it would make a great self-study text. Studying Kreyzig would give you a good grounding (Better than many physicsts receive!) in the mathematics that underlies quantum theory.
 
  • #3
Thanks for the help. So I will probably start by reading Kreyszig, it doesn't seem as scary as the others. At least one day I hope I'll be able to master the book by Spivak, but that day seems far away...
 

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