Customer Reviews

Real Analysis and Foundations, Second Edition (Studies in Advanced Mathematics)

5 star:		(1)
4 star:		(1)
3 star:		(1)
2 star:		(0)
1 star:		(0)

 

 

I have studied Real Analysis from both this book and Bartle and Sherbert. Personally, I like both for different reasons and could recommend both.

Krantz, in my opinion is very good at providing a means to developing a geometric intuition, as he introduces basic point set topology very early and uses it throughout the text (this is a strength of Baby Rudin as well). I feel that Krantz's proofs are not as complicated as those in Bartle and Sherbert, and thus are much easier to follow. I feel that this book is easy to understand and includes a helping or two of complex analysis as a bonus.

Now, I would not be an honest person if I did not mention the mistakes in this book. Yeah, Krantz makes a few significant errors. They are sprinkled around so, just watch for them. I don't recall Bartle and Sherbert having as many.

Now, to contrast with Bartle and Sherbert. I feel that Krantz is lacking in its teaching of analysis techniques- Bartle and Sherbert achieve this well. Their proofs are much more complicated, but in that complication you learn a lot about how to DO analysis. Point set topology is mainly introduced in the last chapter so you lack that power through out the book (a poor choice of writing style in my opinion) but the machinery you develop in this book beats Krantz into the ground. Bartle and Sherbert is lacking a little on conceptual development in my opinion (but does have some strengths over Krantz even on this front).

Neither book is perfect, both are incomplete. As I said before, I could easily recommend both without reservation. I do recommend getting a copy of Rudin's Principles of Real Analysis as a supplementary text to either book. Rudin's book is very difficult for most undergraduates (It was very hard for me the first time I looked through it) but EXCELLENT. Given the choice, personally, I would have chosen Krantz because I felt that I understood analysis better after working through it. But having read Bartle and Sherbert first well prepared me for Krantz! Moral of the story: read both (if time permits).

To summarize:
1) Go with Krantz for concepts and to UNDERSTAND analysis
2) Go with Bartle and Sherbert for techniques and to DO analysis
3) Go with Walter Rudin to MASTER (undergraduate) real analysis after one of the other two! (Unless you go to Berkeley or Harvard and are really smart- then just jump straight to Rudin)

The Krantz text- while it covers many of the topics of real analysis- its notation is not concise. I would look elsewhere.

This book is an excellent text for understanding the foundations of Analysis. I have used this book as a suplement for several math classes. It is a good refrence tool for math majors.