Foundations of modern analysis (Pure and applied mathematics; a series of monographs and textbooks) 0th Edition

by Jean Alexandre Dieudonne (Author)

2 customer reviews

ISBN-13: 978-1124020341

ISBN-10: 1124020349

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Product Details

Series: Pure and applied mathematics; a series of monographs and textbooks
Hardcover: 361 pages
Publisher: Academic Press (1960)
Language: English
ISBN-10: 1124020349
ISBN-13: 978-1124020341
ASIN: B0006AWGOM
Product Dimensions: 9.1 x 6.6 x 1.1 inches
Shipping Weight: 1.6 pounds
Average Customer Review: 4.5 out of 5 stars See all reviews (2 customer reviews)
Amazon Best Sellers Rank: #908,699 in Books (See Top 100 in Books)
- #12437 in Books > Science & Math > Mathematics
- #146545 in Books > Textbooks

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10 of 10 people found the following review helpful

Great reference, terrible as class text book

By David Jimenez on July 21, 2010

Format: Hardcover Verified Purchase

When I was an undergrad, this was the book that my Analysis I teacher decided to use. I can tell you several things about the book, some good, some bad.

* The first good deed: It is very well organized. The topics have a very very natural and didactic order.
* Second: It has A LOT of results you may not find in one single Analysis book other than this. It is very exhaustive.
* Third, it is fairly easy to search, meaning, you will spend less time searching for the result you are looking for.

Now, the bad bad thing about it: If you are interested on proofs and techniques (as you normally are when you are taking a class in the topic), this is probably one of the worse books to study from. A typical proof in this book has two or three lines, with statements like "Apply theorem 2.3.9 and 2.5.23 to (4.8), and then, to that expression, apply corollary 3.8.11 and Lemma 4.3.10, obtaining the desired result". If you are really interested on the inner workings of the result you are proving, you have to go to each of those results, and try to figure out how they apply to your current situation. And of course, to understand the previous theorems, you will have to go and check their individual proofs, getting into a vicious cycle. Thus, as the chapter number increases, expect the number of results to check to increase at least quadratically proportional!

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9 of 9 people found the following review helpful

a great and unique book, deep and very rigorous for 1st yr grads

By mathwonk on January 6, 2012

Format: Hardcover

This book is simply outstanding. It contains more topics of interest in analysis that are hard to find than any other comparable introductory book I know. It is hard to read, but it is worth it. That is not a legitimate criticism of the book. If you cannot benefit from this book, then you were not ready for it. This is a book from the honors classes of the 1960's, when the high quality of the mathematics in a book or course were more important than how easy the author had made the discussion for "dummies". I have treasured this book for over 48 years, and actually own 2 or 3 copies, so I will have one at home, one at work, and one in my locker, as in "Stand and deliver". There is no other substitute for this book. E.g. try and find another beginning complex analysis discussion that includes a proof of the jordan curve theorem (not just for polygonal curves as in Hille). It does have limitations that one can differ with and criticize, such as the complete absence of diagrams, but these are choices by the author, who thinks it benefits the reader to do without them, (perhaps to create ones own). Just the exercises contain more useful material than many texts. This is a superb book, unlike any other I know of. (I am reviewing the hardback Academic Press edition. I bought my first copy in 1963.)

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