Introduction To Analysis, 3Rd Edition - ISBN:0131453335

Introduction To Analysis, 3Rd Edition

Date: 22 April 2011, 07:57

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The strongest point of the book is the exercises. They force you to reread and understand the proofs and they build a foundation for material that is to come.
Chapter 1 (2nd edition) need a complete rewrite. How can you obfuscate something as simple as the Archimedean property in all its forms? Chapter 8 on Euclidean spaces needs to be better integrated with what the student should know from the first linear algebra course.
The author's proofs are not clear and I found myself rewriting many of them in my own words or turning to other references.
The core chapters 2-7 and 11-13 are fine - especially if you buy the approach of doing analysis first in R and then doing it a second time in R^n. This may be especially appropriate in an environment where most of the students are future high school teachers and will only take 1 advanced calculus course.
There are an unusual number of typos in the second edition. They are no longer accessible on the author's website. But hey, the 3rd edition is available, just throw out the 2nd and get the latest.

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