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Complex Analysis 3rd Edition

3.5 out of 5 stars 31 customer reviews
ISBN-13: 978-0070006577
ISBN-10: 0070006571
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Product Details

  • Series: International Series in Pure & Applied Mathematics (Book 7)
  • Hardcover: 336 pages
  • Publisher: McGraw-Hill Education; 3 edition (January 1, 1979)
  • Language: English
  • ISBN-10: 0070006571
  • ISBN-13: 978-0070006577
  • Product Dimensions: 6.3 x 1 x 9.1 inches
  • Shipping Weight: 2.5 pounds (View shipping rates and policies)
  • Average Customer Review: 3.5 out of 5 stars  See all reviews (31 customer reviews)
  • Amazon Best Sellers Rank: #726,876 in Books (See Top 100 in Books)

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Format: Hardcover
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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By A Customer on February 8, 2002
Format: Hardcover
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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Format: Hardcover
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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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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Format: Hardcover
This book is a classic on complex analysis. Unlike some "classics" in mathematics, it is quite accessible, for students at the appropriate level. In order to understand this book, one would need a solid background in mathematical analysis/advanced calculus, and probably one prior course in complex analysis.

This book is concise but reads rather quickly, at least compared to other books that are similarly dense. I think Ahlfors is a very good writer. Although this book seems thin, it covers a lot of material. I find the order of the material to be quite natural. I also like the problem sets...they are not too difficult for a book at this level, and they are very well-designed to help reinforce the basic ideas as well as explore deeper questions.

I think this book would make an outstanding textbook for a graduate course in advanced calculus. However, there are also a number of more modern textbooks on the subject (Greene & Krantz) that would also make equally good textbooks, so the choice of a book is more a question of personal taste than anything else. As a more introductory book on the same topic, I would recommend a number of books, including the one by Churchhill, or at a more intermediate level, the one by Gamelin, or the book by Stein and Shakarchi. There are other good complex analysis books out there too. The book by Hahn is also worth looking at--it is far more thorough than this book, although both the style of writing and the typesetting are a little less clear. Price-wise, however, these other books might offer more value for your money than this classic text.
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