Aliprantis/burkinshaw analysis textbook

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Discussion Overview

The discussion revolves around the Aliprantis/Burkinshaw analysis textbook and its comparison to other standard analysis textbooks such as Baby Rudin, Apostol, and Bartle/Sherbert. Participants explore the appropriateness of Aliprantis/Burkinshaw for learning analysis, particularly for those at a beginner level.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants suggest that Aliprantis/Burkinshaw is at a higher level than Baby Rudin and may not be suitable for beginners.
  • One participant expresses a preference for Aliprantis, noting its orientation towards functional analysis but warns it may be too difficult for newcomers.
  • Another participant mentions that Baby Rudin is criticized for lacking intuition, which they believe is a significant drawback for those new to analysis.
  • Carothers is proposed as an alternative that may be more suitable for someone who has completed Spivak's calculus.
  • Berberian's books are mentioned as interesting, though one participant finds the introduction to analysis too easy.
  • Participants discuss the importance of reviewing several textbooks to determine which one aligns best with their learning style.
  • There is a question about whether the Aliprantis/Burkinshaw textbook serves as a good learning resource or is more of a reference, as suggested by some reviews.

Areas of Agreement / Disagreement

Participants express differing opinions on the suitability of the Aliprantis/Burkinshaw textbook for beginners, with some viewing it as too advanced while others appreciate its content. There is no consensus on the best textbook for learning analysis.

Contextual Notes

Participants reference various levels of prior mathematical experience, which may influence their perspectives on the textbooks discussed. The discussion highlights the subjective nature of textbook suitability based on individual learning preferences and backgrounds.

battousai
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does anyone have any experience of using this book? How does this compare to standard analysis textbooks ie. Baby Rudin, Apostol, Bartle/Sherbert etc.?
 
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yeah that one. So it's at the level of big Rudin?

basically I'm looking for a textbook to learn analysis from at the level of baby Rudin. But some people (micromass) hates the blue book for being too terse , and not giving intuition. I have the book, but I'm also looking for other options.
 
battousai said:
yeah that one. So it's at the level of big Rudin?

basically I'm looking for a textbook to learn analysis from at the level of baby Rudin. But some people (micromass) hates the blue book for being too terse , and not giving intuition. I have the book, but I'm also looking for other options.

I don't exactly hate baby Rudin because it is too terse. I hate it because it gives no intuition, there is a difference. Rudin likes to make things difficult (in my opinion) and it's not helpful to people new to analysis.

That said, I like Aliprantis quite a lot. It is more oriented towards functional analysis than other textbooks. But it is NOT a book suitable for beginners in analysis.

So, what is your experience in mathematics/analysis?? Did you ever complete a book at the level of Spivak's calculus??

Another book which is very interesting is Carothers. I think that book would be suitable for somebody who completed Spivak's calculus. Aliprantis might be too difficult.

Another nice book (which happens to be mathwonk's favorite) are the books by Berberian. However, I find it's introduction to analysis somewhat too easy. The other books are nice though.

I suggest you go to some sort of library and check out several analysis books. Read the first chapter and make some exercises. Then you can pick whichever you like best.
 
we did proofs in my multivariable calculus class, using williamson/trotter textbook. just finished with upper division linear algebra using friedberg/insel/spence. writing proofs isn't too much of a problem for me.

is this

https://www.amazon.com/dp/0521497566/?tag=pfamazon01-20

the book you're talking about? if so, what is good about this?
 
Yes, that's the book.
 
Is it a good book to learn analysis from? Or more of a reference (like some of the amazon reviews suggest)?
 

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