PDF Ebook Foundations Of Modern Analysis (Pure and Applied Mathematics), by J. Dieudonne
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Foundations Of Modern Analysis (Pure and Applied Mathematics), by J. Dieudonne
PDF Ebook Foundations Of Modern Analysis (Pure and Applied Mathematics), by J. Dieudonne
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FOUNDATIONS OF MODERN ANALYSIS. Enlarged and Corrected Printing J. DIEUDONNE This book is the first volume of a treatise which will eventually consist offour volumes. It is also an enlarged and corrected printing, essentially without changes, of my Foundations of Modern Analysis. 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 specialist monographs 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 birdseye view of his subject before he is launched onto the ocean of mathematical literature 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 the mathematicians 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, and certainly superfluous to rewrite the works of N. Bourbaki. I have therefore been 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 are therefore 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.
- Sales Rank: #625263 in Books
- Published on: 2008-11-04
- Original language: English
- Number of items: 1
- Dimensions: 8.50" h x 1.06" w x 5.51" l, 1.48 pounds
- Binding: Hardcover
- 412 pages
Most helpful customer reviews
0 of 0 people found the following review helpful.
Five Stars
By Ramon A. MataToledo
As described and on time.
11 of 12 people found the following review helpful.
Don't trust the company.
By Jonas Meyer
The same company put out a paperpack edition of this book that is also for sale on Amazon, and it is horrible. It was photocopied, badly, from an obviously used copy. They don't let you preview either one, and after having bought the other one I see the reason. Unless you have seen a hard copy of this exact printing to verify that it isn't a sham, do not buy this book.
However, I do like the book. Hopefully a legitimate reprinting will come out.
(I would appreciate comments and corrections from someone who has this printing.)
24 of 27 people found the following review helpful.
Not Recommended for Self-study
By Heraclitus Junior
This monograph is over 50 years old now and has been bettered in exposition by more recent efforts. Following the author's arguments in this book can sometimes be VERY difficult. His sentences are awkwardly constructed and it can take hours to unpack his proofs. Some of the proofs, though ingenious, are presented opaquely. It's almost as if Dieudonne was obfuscating matters on purpose!
Paradoxically, the exposition manages to be terse and rambling at the same time. Dieudonne seems averse to using clear cut theorem/proof-style headings and the book is highly inter-connected. Oftentimes, instead of repeating an equation that appeared hundreds of pages ago, he will simply put down a reference number. All in all, Foundations of Modern Analysis (FMA) makes for slow, painful reading and much of the difficulty is down to poor exposition rather than hard mathematics.
Obviously, this review is not meant as negative commentary on Dieudonne's mathematical ability. The book DOES contain a lot of really good material and some very clever proofs. This review is simply a warning to other students who are looking to learn the material on their own for the first time. FMA makes for a fine reference book, but it is far from the ideal textbook to buy and work off -- for that, I would recommend more modern, pedagogically palatable alternatives.
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