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· 45 ratings · 5 reviews

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Overall decent and mostly clear exposition, as one should expect with any math book. The main issue for me is that many of the definitions and proofs presented in this book are unmotivated, leaving the reader asking "why did we just do that?!" after each step. Also the graphics are kinda cheesy (I just couldn't convince myself that point on a certain drawing of a parabola looks differentiable!), and the language can get quite stale, unlike Spivak's writing. Overall decent and mostly clear exposition, as one should expect with any math book. The main issue for me is that many of the definitions and proofs presented in this book are unmotivated, leaving the reader asking "why did we just do that?!" after each step. Also the graphics are kinda cheesy (I just couldn't convince myself that point on a certain drawing of a parabola looks differentiable!), and the language can get quite stale, unlike Spivak's writing. ...more

May 09, 2009 Ben rated it really liked it

We used this text book for a functional analysis class I took. It has a pretty good and very rigorous treatment of real and functional analysis. The class mostly focused on metric spaces and this book does a good job covering topics like completeness, Cauchy sequences, compactness, connectnessed, and other topical matter that starts with the letter "C." The latter half of the book covers integration, including the Lebesgue integral, but we did not follow the book's treatment, which is fairly ort We used this text book for a functional analysis class I took. It has a pretty good and very rigorous treatment of real and functional analysis. The class mostly focused on metric spaces and this book does a good job covering topics like completeness, Cauchy sequences, compactness, connectnessed, and other topical matter that starts with the letter "C." The latter half of the book covers integration, including the Lebesgue integral, but we did not follow the book's treatment, which is fairly orthodox, of building the Lebesgue integral using measure theory. Instead showed integral must exist as a continuous extension of the Riemann integral using density and completion arguments studied earlier on the book. So, I can not actually comment on the book's treatment of the Lebesgue integral, but I suspect it is done well.

I would like to note that is not an advanced calculus book, as another reviewer described it. At least not in any meaningful sense. Yes it deals with calculus and a lot of the topics covered in a calculus book in a more rigorous fashion, but it is really an advanced real analysis or introductory functional analysis book.

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Jan 13, 2008 Scott Neal Reilly rated it really liked it

Recommends it for: the most serious of math geeks and advanced calculus professors looking for a good textbook

I was looking for something a bit more abstract than this book gave me, but that's more my fault for picking a book from a catalog than flipping through it at a bookstore first. This is a fine advanced calculus college textbook with all the proofs that I recall from my advanced calculus course from days of old. It's clear and well-organized but very proof-based with minimal glue to hold it all together. In this way, it would be a fine class textbook. I was looking for something a bit more abstract than this book gave me, but that's more my fault for picking a book from a catalog than flipping through it at a bookstore first. This is a fine advanced calculus college textbook with all the proofs that I recall from my advanced calculus course from days of old. It's clear and well-organized but very proof-based with minimal glue to hold it all together. In this way, it would be a fine class textbook. ...more

Mar 17, 2009 Stephen rated it it was amazing

This has been such a critical book in my mathematical development. I find myself often referring back to this book as a source to fill in holes, and referring it to colleagues as a good book to do so