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Foundations of Modern Analysis Volume 1, by Jean Dieudonne
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Treatise on Analysis
- Sales Rank: #779136 in Books
- Published on: 1969-01-01
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x 6.50" w x 1.25" l,
- Binding: Hardcover
- 387 pages
Language Notes
Text: English (translation)
Original Language: French
Most helpful customer reviews
11 of 11 people found the following review helpful.
Great reference, terrible as class text book
By David Jimenez
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!
10 of 10 people found the following review helpful.
a great and unique book, deep and very rigorous for 1st yr grads
By mathwonk
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.)
19 of 38 people found the following review helpful.
Abstraction to its last consequences.
By Bernardo Vargas
I should be surprised to be the first reviewer of this book, but thinking it again I see the point. Dieudonné's books are just being displaced by more accesible and focused texts, instead of these authoritative Bourbaki-style treatises which are often too abstract to be useful. Bourbaki mathematics accomplished the mission of unifying and standarizing (more or less) the whole of mathematics, but once that was done, their work now turns out to be useless. The point is that when we tackle a problem, be it in pure or applied mathematics, we seldom need the high level of abstraction used by Bourbaki authors. Moreover, what we need are specific results to handle the details of our solututions, and Dieudonné pays almost no attention to them; he prefers to stay at the most general possible setting, making his treatment perspectiveless because he misses completely the goal of abstraction: To use its power when dealing with particular situations. That's why no one has reviewed Dieudonné before me: His books are read no more.
Nevertheless, undergraduate and graduate students may find it useful as a reference, but not as a course text because it presents no motivation to the topics treated and includes only a very short bibliography.
Its contents are: Set theory, real numbers, metric spaces, normed spaces, Hilbert spaces, spaces of continuous functions, differential calculus, analytic functions, existence theorems (for ODE's), and elementary spectral theory.
"Treatise on Analysis" consisted originally on this sole book. Later it was expanded to four and later on to nine.
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