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Customer Reviews (6)

I wish the first half were there.
This book is a translation of the second half of two part book on the differential calculus and the author refers occasionally to the first book. Although the book is very good it would have been better if Dover had a translation of the first part (which is more elementary). I ended up buying the pair of books combined into one volume as a second hand French book (the editor is Hermann).
The first volume is really a very good introduction.
However you could probably use Tom Apostol's book to prepare for this book, but you'll be spending a lot of money.

A classic on this topic
''Differential Forms'' by H. Cartan is a classic evergreen book.

I found it a perennial source of inspiration.

No Illustrations
Don't be fooled by the lovely cover. This is a geometry book with no illustrations. I found it quite dense, with a formula in nearly every second sentence. I think it requires quite a bit of preparation to understand and provides no intuition whatsoever. Not for the faint of heart.

Typical good french book
When you skim through the table of contents you get excited about the way the book starts (with multilinear and alternating forms in vector spaces) and amazed about how far it goes (Stokes and Frobenius Theorems, calculus of variations, mechanics and differential geometry with moving frames).

Of course, the style is french formal. Not dry. You can tell that if you were a professional mathematician you would benefit pretty much from these writings. He uses sharp mathematical terms like Banach space, topological terms without being pedantic. But the formality level doens't close the subject hermetically from mere mortals.

The prose is good and it could get you all the way up through the subject. Another good reference for these subject is do Carmo's differential forms and Arnold's Mathematical Methods of Classical Mechanics which dedicates 40 pages explaining the subject aiming the application in Hamiltonian mechanics.

What is prerequisite before reading this book?
I bought this book a week ago and spent one and half hour for quick overview.

I'm studying intermediate Calculus with linear algebra.
Well, my impression was it's very difficult to read.
There are very few examples with solution, all the context written without diagrams.

... Read more

Product Description
Noted mathematician offers basic treatment of theory of analytic functions of a complex variable, touching on analytic functions of several real or complex variables as well as the existence theorem for solutions of differential systems where data is analytic. Also included is a systematic, though elementary, exposition of theory of abstract complex manifolds of one complex dimension. Topics include power series in one variable, holomorphic functions, Cauchy’s integral, more. Exercises. 1973 edition.
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Customer Reviews (5)

Horrible
The first time I ordered this book I received the wrong book and then following the instructions on the invoice returned it.Then I reordered and should have received the book by now, but have not!And I need this book for my work!I am thoughly discusted by the extremely poor service I have gotten here and am thinking I should do business with some other book company from now on -- any other book company!

Sincerely,
Dr. Dennis P. Allen, Jr.

my favorite intro to complex analysis
This is a masterful treatment of the subject, including power series, integration, the homotopy version of cauchy's theorem, residue calculus, differential equations, harmonic functions, and intro to riemann surfaces.

i confess i do not recognize the book i read from the first review here however, as mine begins with formal power series and has rather little on several complex variables.I have both the 1963 hardback and the recent dover reprint and they are identical, but i have not seen the french version.

It is sobering that after 2 years not one person has even reacted to this review.Are todays students totally clueless about what books to learn from?I have a phd in math and am an internationally known researcher in math.give yourself a break and give my suggestions a try.how much do you have to lose on a book of this price?

if you doubt me i would recall that this was the book of choice at harvard in 1965 by the great john torrance tate.

a translation of a classic
This elegant little book by Henri Cantan covers both complex functions on one and several variables, and in that way (by the inclusion of several variables) it differs and stands out from most other books on complex variables at the beginning US-graduate level. It is a translation of an original French language version. I can recommend both the original and the translation. It is readable, and the exercises are plenty and excellent. Thanks to Dover, the translation is now readily available and cheap.

Cartan's book starts with complex numbers, power series, and a review of the standard complex functions of one variable, e.g., the exponential, and the complex logarithm. Then follow holomorphic functions, Taylor and Laurent expansions, singularities, Cauchy's theorems, residues, analytic continuation, lots of examples, and beautifully illustrated. Included are also geometric topics, elementary complex geometry, Mobius transformations, automorphisms, transformation groups, differential forms, harmonic and analytic functions, Riemann surfaces, and infinite products, and a brief chapter on conformal mappings.

The book is divided pretty evenly between one and several variables, with the second half being several variables. However each part can be read pretty much independently of the other.

The book in its French edition was published first in the 1950ties, and the first English edition in 1963, and then starting 1995 reprinted by Dover. It is suitable as a text for a course or as a supplement in a standard beginning graduate course in complex function theory. While it contains the standard elements in such a course, we note that a systematic treatment of power series comes relatively late, in Chapter 10, beginning on page 195 (halfway into the book.) Some readers might want to begin with that.

Of other Dover titles on the same subject, but considerably more elementary we recommend the books by Fisher, Volkovyskii et al, Silverman, Schwerdtfeger, and Flanigan. These books however only cover the case of a single variable. Review by Palle Jorgensen, August 5, 2006.

A good introduction
At first the book appeared to be too difficult. Indeed, it is designed for students with some familiarity with Algebra and Topology. However, the more I read the book, the better it appeared. It's chapter on integration is one of the best I've seen. It doesn't seem to cover much, but the addition of some facts from several variables is in very good taste.

Good and affordable.
Cartan's book on complex analysis is not brand new, but that does not matter as the subject itself has been "stabilized" for a long period of time. It is indeed good to see that this "lovely" book being available at the modest price of [price]. The fact that the author was among the founders of Bourbaki may intimidate some would-be readers, but you don't have to be worried. The treatment of the subject is no pedantic and quite accessible for beginners. ... Read more

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When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made, Cartan and Eilenberg tried to unify the fields and to construct the framework of a fully fledged theory. The invasion of algebra had occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras. This book presents a single homology (and also cohomology) theory that embodies all three; a large number of results is thus established in a general framework. Subsequently, each of the three theories is singled out by a suitable specialization, and its specific properties are studied.

The starting point is the notion of a module over a ring. The primary operations are the tensor product of two modules and the groups of all homomorphisms of one module into another. From these, "higher order" derived of operations are obtained, which enjoy all the properties usually attributed to homology theories. This leads in a natural way to the study of "functors" and of their "derived functors."

This mathematical masterpiece will appeal to all mathematicians working in algebraic topology. ... Read more

Customer Reviews (3)

Old - Antiquated
Yes, this is a landmark book and yes this book has served many a fine mathematician but, let's be honest here, this book is out dated.Since the creation of this book there have been both advances within the field and the core terminology has been agreed upon.Why read a text, especially as an introduction, whose notation and basic terminology is extinct?Yes, it is nice to go back and read the works of the masters, the pioneers and wrap yourself up in a nice warm blanket of original and new thought.Whereas, if your trying to learn the subject matter for your own benefit or for research reasons, then I would not recommend this text.For those of you who are new to the field, my suggestion is to stay far away from this text.Try L.R. Vermani's text or Rotmans text instead.For those of you who are not new to the field then I am sure you already own your own copy, so enjoy.Finally, a word about the 3-stars.Sure this text deserves 5 stars for being well written, for being a landmark text and for many other reasons but, this texts hay day has gone and went.It is time to give up the old and bring in the up to date and more relavent texts such as Weibel's.In general, save your time and your money.

A landmark, that's it.
As the title of the series suggests, this is another "landmark" inbooks of mathematics. In fact, this was the only book on homological algebra for a certain period of time. I don't think this is a fungus, but with other modern good textbooks available (Weibel, for example) I am not inclined to give it "five stars".

H. Cartan and S. Eilenberg are the authors
I believe this is volume #19 of the Princeton Math. Ser.entitled Homological Algebra. The authors are H. Cartan and S. Eilenberg. H. Cartan is one of E. Cartan's sons. ... Read more

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Les achats comprennent une adhésion à l'essai gratuite au club de livres de l'éditeur, dans lequel vous pouvez choisir parmi plus d'un million d'ouvrages, sans frais. Le livre consiste d'articles Wikipedia sur : Laurent Schwartz, Jean-Pierre Serre, Nicolas Bourbaki, Alexandre Grothendieck, Henri Cartan, André Weil, Éléments de Mathématique, Alain Connes, Szolem Mandelbrojt, Roger Godement, Jean Dieudonné, Séminaire Nicolas Bourbaki, Adrien Douady, Bourbakisme, Charles Ehresmann, Claude Chevalley, Pierre Samuel, Armand Borel, Jean-Christophe Yoccoz, Yves Colin de Verdière, René de Possel, Joseph Oesterlé, Jean Delsarte, Pierre Cartier. Non illustré. Mises à jour gratuites en ligne. Extrait : Nicolas Bourbaki est un mathématicien imaginaire, sous le nom duquel un groupe de mathématiciens francophones, formé en 1935 à Besse-et-Saint-Anastaise (Besse-en-Chandesse à l'époque) en Auvergne sous l'impulsion d'André Weil, a commencé à écrire et éditer des textes mathématiques à la fin des années 1930. L'objectif premier était la rédaction d'un traité d'analyse. Le groupe s'est constitué en association, l'Association des amis de Nicolas Bourbaki, le 30 août 1952. Sa composition a évolué avec un renouvellement constant de générations. Sous le nom Nicolas Bourbaki fut publiée une présentation cohérente des mathématiques, appuyée sur la notion de structure, dans une série d'ouvrages sous le titre Éléments de mathématique. Cette œuvre est à ce jour inachevée. Elle a eu une influence sur l'enseignement des mathématiques et sur l'évolution des mathématiques du siècle. Toutefois, elle connaît de nombreuses critiques : incompatibilité entre le formalisme retenu et la théorie des catégories, , manque d'exemples, incompréhension des étudiants, etc. L'activité du groupe cependant a dépassé la rédaction d'ouvrages, par exemple avec l'organisation des séminaires Bourbaki. Le nom de famille Bourbaki était le nom emprunté par Raoul Husson en 1923 lor...http://booksllc.net/?l=fr ... Read more

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This digital document, covering the life and work of Henri (Paul) Cartan, is an entry from Contemporary Authors, a reference volume published by Thompson Gale. The length of the entry is 1636 words. The page length listed above is based on a typical 300-word page. Although the exact content of each entry from this volume can vary, typical entries include the following information:

• Place and date of birth and death (if deceased)
• Family members
• Education
• Professional associations and honors
• Employment
• Writings, including books and periodicals
• A description of the author's work
• References to further readings about the author