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Foundations of Mathematical Analysis
This classroom-tested volume offers a definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. Upper-level undergraduate students with a background in calculus will benefit from its teachings, along with beginning graduate students seeking a firm ...more
Paperback, 448 pages
Published May 20th 2010 by Dover Publications
(first published August 6th 2002)
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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.
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 ...more
Jan 13, 2008 Scott Neal Reilly rated it really liked it · review of another edition
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.