Foundations of Modern Analysis by J. Dieudonne (PDF)

Description

In this text, the whole structure of analysis is built up from the foundations. The only things assumed at the outset are the rules of logic and the usual properties of the natural numbers, and with these two exceptions all the proofs in the text rest on the axioms and theorems proved earlier. Nevertheless this treatise (including the first volume) is not suitable for students who have not yet covered the first two years of an undergraduate honours course in mathematics. A striking characteristic of the elementary parts of analysis is the small amount of algebra required. Effectively all that is needed is some elementary linear algebra (which is included in an appendix at the end of the first volume, for the reader’s convenience). However, the role played by algebra increases in the subsequent volumes, and we shall finally leave the reader at the point where this role becomes preponderant, notably with the appearance of advanced commutative algebra and homological algebra. As reference books in algebra we have taken R. Godement’s “Abstract Algebra,” and S. A. Lang’s “Algebra” which we shall possibly augment in certain directions by means of appendices. As with the first volume, I have benefited greatly during the preparation of this work from access to numerous unpublished manuscripts of N. Bourbaki and his collaborators. To them alone is due any originality in the presentation of certain topics.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Some pages are blurry, badly printed. Otherwise its a good book.

⭐As described and on time.

⭐I had problems with this product because I get in bad condition, I requested the change but I got too bad. But the Amazon store interested behaved and timely response to my request, which was satisfied with his answer for this reason I will continue buying from Amazon.

⭐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.

⭐The book is a pleasure to read, and I recommend it to anyone who is learning analysis. However, this version is xeroxed from a used copy of the 1969 corrected printing. For the most part it is attractive enough and it is almost always clear enough to read, but there are a few pages with xeroxed pen marks or page-edge lines, a few where the text is slightly distorted, and worst of all a few that are actually difficult to read because of how badly they were copied. I recommend it only if you can get it very cheap.

⭐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.)

⭐Starting from the basic concepts of sets and numbers, through metric spaces to normed vector spaces over the complex or real numbers, to Banach and Hilbert spaces. Dieudonne gives us an exposition of the differential calculus and complex variable theory in their most modern and abstract forms. The derivative and higher derivatives are given in their full generality as is Cauchy’s formula and the theory of residues. This is not a book for a beginner, but ideally for the mathematically mature with some prior knowledge of these subjects.

⭐This is one of my favorite books, I do have Russian translation of this book and it was very tempting to have English original, unfortunately the quality of the binding is very poor, this is hard cover version. After couple days of using this book I had noticed snapping sound, while I opening and closing this book. Further investigation had detected that part of the binding had unglued and snapping against hard cover.

⭐IL TESTO IN ALCUNE PAGINE E’ TAGLIATO MALE. AD ESEMPIO PAG 355 E’ ILLEGGIBILEDas Wichtigste habe ich schon zur deutschen Übersetzung geschrieben. Zu dieser speziellen Ausgabe kann ich nur sagen, Seitenlayout und Druck sind schrecklich, es wirkt als wären es Fotokopien, bei denen der innere Rand zu klein gewählt wurde.中古品を購入したものなので、レビューする資格があるか微妙ですが。送られてきた商品には、海外のレビューにあるようにあきらかにコピー機を使用したとおぼしきページが存在します。コピー中の歪みはもちろん、ページナンバーへの書き込みの写り込み、ページの切れ、そのうえ、印刷ミスと思える不鮮明なページも複数あります。森毅の訳本を手に入れて、なんとか前半は判読できましたが…。こちらが本家、とのレビューもありますが、まごうことなき「海賊版」のような感じです。奥付には初版のらしきページ、最後のページにはprinted in U.S.Aとかあり、アメリカでの印刷ミスのような感じもしますが、なんだか妙です。学生が友達の本をコピーして、装丁しなおしたような感じの本です。内容は、数学（数学を通した文化全体？）にたいするすぐれた批評、革命をめざしたもので、二十世紀の「熱さ」を感じさせる良書だとは思います。が、二十一世紀の現在、プリントミスで読書ストレスが生じるのは納得できないような気もします。中古品とはいえ、2千円以上出費しているので、あまりいい気分がしませんでした。やがて、二十世紀を代表するであろう、すぐれた本であることは明らかでしょうから、新品ではきちんとした「商品」として流通することを希望してやみません。

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