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Complex Analysis [Hardcover]

by Lars Ahlfors
3.3 out of 5 stars  See all reviews (26 customer reviews)

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Book Description

January 1, 1979 0070006571 978-0070006577 3
A standard source of information of functions of one complex variable, this text has retained its wide popularity in this field by being consistently rigorous without becoming needlessly concerned with advanced or overspecialized material. Difficult points have been clarified, the book has been reviewed for accuracy, and notations and terminology have been modernized. Chapter 2, Complex Functions, features a brief section on the change of length and area under conformal mapping, and much of Chapter 8, Global-Analytic Functions, has been rewritten in order to introduce readers to the terminology of germs and sheaves while still emphasizing that classical concepts are the backbone of the theory. Chapter 4, Complex Integration, now includes a new and simpler proof of the general form of Cauchy's theorem. There is a short section on the Riemann zeta function, showing the use of residues in a more exciting situation than in the computation of definite integrals.

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Complex Analysis + Real and Complex Analysis (International Series in Pure and Applied Mathematics) + Principles of Mathematical Analysis (International Series in Pure and Applied Mathematics)
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Product Details

  • Series: International Series in Pure and Applied Mathematics (Book 7)
  • Hardcover: 336 pages
  • Publisher: McGraw-Hill Science/Engineering/Math; 3 edition (January 1, 1979)
  • Language: English
  • ISBN-10: 0070006571
  • ISBN-13: 978-0070006577
  • Product Dimensions: 9.3 x 6 x 1 inches
  • Shipping Weight: 2.5 pounds (View shipping rates and policies)
  • Average Customer Review: 3.3 out of 5 stars  See all reviews (26 customer reviews)
  • Amazon Best Sellers Rank: #461,718 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
45 of 47 people found the following review helpful
4.0 out of 5 stars $143?!?! February 8, 2002
By A Customer
This is a classic complex analysis text, a pleasure to read and covering all the usual topics. The prerequisites are modest; ideally, one will be familiar with the material in Rudin's "Princples of Mathematical Analysis," but a good, mathematically oriented calculus course (Spivak's "Calculus" is beautiful) is quite sufficient.
That said, the price tag is ridiculous. It was bad enough at $90 (judging by previous reviewers, that was back in the ancient days of 2001). The last edition of this book is dated 1979. It's used in graduate courses all around the world. That means that used copies are not hard to come by.
For $143, one can buy a used copy of Ahlfors, and *new* copies of Conway's and Needham's complex analysis books, and still have pocket change left. That's the course I would recommend.
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64 of 69 people found the following review helpful
3.0 out of 5 stars A classic at an obscene price January 21, 2006
This book has for decades been THE classic graduate level text in Complex Analysis. It is important to point out that it is not for beginners. To learn complex analysis from the ground up, my own recommendations are the book by Saff & Snider or the somewhat dated, but delightfully conversational book by Stewart and Tall.

Not only does this book require some previous understanding of Complex Analysis, but it also requires that mysterious ability called "mathematical maturity" - the ability to fill in omitted steps and details when following an argument. But, for a person posessing the prerequisites, this is a fine book.

However, any review of this book would be incomplete if it didn't address the issue of price. Advanced math books are all expensive, it is true. But this book is a particularly egregious case of price-gouging. For one thing, the book was written many years ago, so the publisher is not trying to recover any recent high cost of paying the author for his work. Secondly, the book is only something like 336 pages long (much shorter, for example, than a mystery novel by Elizabeth George). It comes out to about 40 cents per page!

Math students, as a rule, are not wealthy people. The price of this book is simply offensive. You can save more than 25% off the price of this book and get BOTH volumes of the Conway book, "Functions of One Complex Variable". I'm not thoroughly familiar with that Conway book, but I've browsed it online. It seems to be well written and has more material (in the two volumes together) than this (Ahlfors) book has. Furthermore, just in principle, I don't think a publisher should be rewarded for this kind of unwarranted greed and price-gouging. Refuse to buy this until the price becomes more reasonable.
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18 of 21 people found the following review helpful
4.0 out of 5 stars why 4 stars and not five? November 2, 2004
I was a (French)graduate student in France some 25 years ago and I would have been delighted to use this book if translated in French; I had to rely on Cartan's book which is a very good book too but which takes for granted that one already knows quite a lot on complex numbers, series, convergence and topology...As a substitute to Cartan, there was a translation of Rudin's real and complex analysis which begins with measure theory...Anyway, it is very difficult to learn this subject in any book without advice from instructors and attending lectures.

There could be more worked examples in this book but it is not a self teaching book (neither is Cartan's...which is very similar in essence to Ahlfors but more narrow minded). For a more "basic" book in the subject, see Marsden's Basic complex analysis but proofs are often mixed up with exercises...which does not suit everybody. My final point is the following: this book contains much more stuff to work at or to think about than its French counterpart; moreover,in this book, efforts are made to avoid formalism (Bourbaki?). US maths students are very lucky indeed. But the book is certainly too expensive.
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14 of 16 people found the following review helpful
5.0 out of 5 stars A Classic Masterpiece June 14, 2000
By Eze
This book has been, since its first edition in 1953, the standard textbook for rigorously learning complex analysis, and not without a reason. The wonderful theory of this branch of mathematics is appropriately emphasized and thoroughly constructed, leading to more general and precise results than most textbooks. While the constant appearance of new texts on the field can only help appreciate the subject from a different perspective, few give you such a deep and serious treatment like this gem.
Postscript: An earlier reviewer claims that Ahlfors never defines the set of complex numbers, while this is indeed done in the fourth through sixth pages in a much more analytical way than generally found elsewhere. It is quite possible to dislike this author's style or approach (or anybody's for that matter), but it would be difficult to charge Ahlfors with being sloppy with his writing.
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12 of 14 people found the following review helpful
5.0 out of 5 stars Excellent exposition of the Riemann method. August 26, 1999
By A Customer
Format:Hardcover|Verified Purchase
This classic is a brilliant exposition of the Riemann (geometrical) method of complex analysis as opposed to the Weierstrassian (power series) method. The latter approach is done well by Whittaker & Watson or Henrici. Ahlfors book is the best I know of for the geometrical approach. It is written for senior undergraduates or graduate students majoring in mathematics.
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31 of 41 people found the following review helpful
1.0 out of 5 stars Total Garbage January 18, 2010
First, a little about my background. I have no problems with many "classic" books in mathematics, even some that I believe should have been retired years ago on the grounds that (pedagogically) better books in the field have since been developed. Rudin's "Principles of Mathematical Analysis" is excellent because it is so organized, rigorous and elegant, though I don't personally think it's best for an introductory analysis course. Royden's "Real Analysis", older than I am, is serviceable and likely still has a place in the world. As for complex analysis, I think Conway's "Functions of One Complex Variable" and Lang's "Complex Analysis" are books that deserve to be called classics in the field and ought to enjoy wider circulation than they actually do. A couple years ago I worked through the Conway text on my own up to Cauchy's Theorem and found it pleasant. Now, at last, I'm taking a graduate-level complex analysis course, and oh what a crying shame: we're using this ancient travesty by Ahlfors.

Look, I don't mind terse proofs, or what some code-name "elegant" proofs. Like I said, I really like Rudin, and no one is terse if Rudin isn't. I can fill in the gaps in a terse but organized proof just fine, and I can also fill in the gaps in intuitive "hand-waving" proofs like the kind you'll find in Hatcher's "Algebraic Topology". But Ahlfors often manages terseness without elegance and hand-waving without intuition. It's breath-taking -- how does he do it? He couldn't have typed the book in the dark because there are very few typos, so it must be some special skill one acquires through life-long study of the Obscure Arts.

It's true what others say: the exercises often seem to have little to do with whatever Ahlfors was rambling on about in the sub-subsection they're found in.
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Most Recent Customer Reviews
2.0 out of 5 stars Why all the Negative Reviews?
I am sorry that I have to write such a negative review about a classic book in mathematics. I eat, sleep, and breathe mathematics and enjoyed just about every other course I took... Read more
Published 3 months ago by Mathematician
2.0 out of 5 stars It's really not that amazing
I used this book when I took a graduate-level complex analysis course. I ended up using this book along with Gamelin's complex analysis text, which I like much more. Read more
Published 3 months ago by budding mathematician
1.0 out of 5 stars A famous mathematician does not mean he is a good teacher
Of course, Ahlfor is a great mathematician, he was the one of the two men to receive the the first Fields Medal. Read more
Published on July 20, 2011 by Wan Koon Yat
1.0 out of 5 stars Printing Quality is Very LOW!
I just got it that is sold directly by Amazon yesterday. It seems printing quality is very low. And the second page of this book,

which says

copyright 1979,... Read more
Published on May 19, 2011 by Chris
5.0 out of 5 stars Excellent book
The book from the seller was in great shape and unlike some sellers, was shipped in time and the product particularly was in mint condition
Published on September 28, 2009 by Ramaswamy Meyyappan
2.0 out of 5 stars A Poor Choice for a Complex Analysis Class
I feel the need to update my review. I have looked at many complex analysis books in depth. These include Palka, Saff, Karunakaran, Hauser, Conway, and Wunsch. Read more
Published on May 3, 2008 by Jason Broadway
5.0 out of 5 stars Classic book on complex analysis: one of the best, but overpriced
This book is a classic on complex analysis. Unlike some "classics" in mathematics, it is quite accessible, for students at the appropriate level. Read more
Published on December 25, 2007 by Alexander C. Zorach
2.0 out of 5 stars pedgogically worthless
I'm not sure why the other reviews are so positive. The book is very thorough and rigorous I'm sure, but the explanations are terrible. Read more
Published on June 9, 2006 by Fei Erde
5.0 out of 5 stars A Classic
Another classic text from graduate school (text for class taught by P.L. Duren) providing a background in introductory complex analysis. Read more
Published on June 17, 2004 by ktrmes
5.0 out of 5 stars A good and valuable intro to Complex Analysis
I picked up this book as a text to my complex functions class. The topics presented in the book is the classic need-to-know materials for undergraduates (complex functions,... Read more
Published on February 27, 2004 by bal gombak
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