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Foundations of modern analysis (Pure and applied mathematics; a series of monographs and textbooks): Dieudonne, J.: 9781124020341: Amazon.com: Books

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

by J. Dieudonne (Author)

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FOUNDATIONS OFMODERN ANALYSISEnlarged and Corrected PrintingJ. DIEUDONNEThis book is the first volume of a treatise which will eventually consist offour volumes. It is also an enlarged and corrected printing, essentiallywithout changes, of my Foundations of Modern Analysis, published in1960. Many readers, colleagues, and friends have urged me to write a sequelto that book, and in the end I became convinced that there was a place fora survey of modern analysis, somewhere between the minimum tool kitof an elementary nature which I had intended to write, and specialistmonographs leading to the frontiers of research. My experience of teachinghas also persuaded me that the mathematical apprentice, after taking the firststep of Foundations, needs further guidance and a kind of general birdseyeview of his subject before he is launched onto the ocean of mathematicalliterature or set on the narrow path of his own topic of research.Thus I have finally been led to attempt to write an equivalent, for themathematicians of 1970, of what the Cours dAnalyse of Jordan, Picard,and Goursat were for mathematical students between 1880 and 1920.It is manifestly out of the question to attempt encyclopedic coverage, andcertainly superfluous to rewrite the works of N. Bourbaki. I have thereforebeen obliged to cut ruthlessly in order to keep within limits comparable tothose of the classical treatises. I have opted for breadth rather than depth, inthe opinion that it is better to show the reader rudiments of many branchesof modern analysis rather than to provide him with a complete and detailedexposition of a small number of topics.Experience seems to show that the student usually finds a new theorydifficult to grasp at a first reading. He needs to return to it several times beforehe becomes really familiar with it and can distinguish for himself whichare the essential ideas and which results are of minor importance, and onlythen will he be able to apply it intelligently. The chapters of this treatise arevi PREFACE TO THE ENLARGED AND CORRECTED PRINTINGtherefore samples rather than complete theories: indeed, I have systematically tried not to be exhaustive. The works quoted in the bibliography willalways enable the reader to go deeper into any particular theory.However, I have refused to distort the main ideas of analysis by presentingthem in too specialized a form, and thereby obscuring their power andgenerality. It gives a false impression, for example, if differential geometryis restricted to two or three dimensions, or if integration is restricted to Lebesgue measure, on the pretext of making these subjects more accessible orintuitive.On the other hand I do not believe that the essential content of the ideasinvolved is lost, in a first study, by restricting attention to separable metrizabletopological spaces. The mathematicians of my own generation were certainlyright to banish, hypotheses of countability wherever they were not needed: thiswas the only way to get a clear understanding.

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ISBN-10

1124020349
ISBN-13

978-1124020341
Edition

First Edition
Publisher

Academic Press
Publication date

January 1, 1960
Language

English
Print length

361 pages

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Foundations of Modern Analysis (Pure and Applied Mathematics, 10)
J. Dieudonne

Hardcover
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Foundations of Modern Analysis
J Dieudonne

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Product details

ASIN ‏ : ‎ B0006AWGOM
Publisher ‏ : ‎ Academic Press
Publication date ‏ : ‎ January 1, 1960
Edition ‏ : ‎ First Edition
Language ‏ : ‎ English
Print length ‏ : ‎ 361 pages
ISBN-10 ‏ : ‎ 1124020349
ISBN-13 ‏ : ‎ 978-1124020341
Item Weight ‏ : ‎ 8.1 ounces

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Curatica
Too Difficult for American Readers
Reviewed in the United States on February 9, 2022

The public in America understands 4x4" studs and should be given numbers to crunch, not principles. And objects to see, not abstractions. A good book for the wrong audience.

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mathwonk
a great and unique book, deep and very rigorous for 1st yr grads
Reviewed in the United States on January 7, 2012
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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David Jimenez
Great reference, terrible as class text book
Reviewed in the United States on July 21, 2010
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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15 people found this helpful

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Bernardo Vargas
Abstraction to its last consequences.
Reviewed in the United States on May 3, 2000
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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Foundations of modern analysis (Pure and applied mathematics; a series of monographs and textbooks) First Edition

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Too Difficult for American Readers

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

Great reference, terrible as class text book

Abstraction to its last consequences.

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

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Top reviews from the United States

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5.0 out of 5 stars Too Difficult for American Readers

5.0 out of 5 stars a great and unique book, deep and very rigorous for 1st yr grads

4.0 out of 5 stars Great reference, terrible as class text book

3.0 out of 5 stars Abstraction to its last consequences.

Too Difficult for American Readers

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

Great reference, terrible as class text book

Abstraction to its last consequences.