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Complex Analysis 3rd Edition
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Top Customer Reviews
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.
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.
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.
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.
Most Recent Customer Reviews
Classic 1st year graduate text which emphasizes treatment by the methods of elementary topology. An approach you should feel comfortable with if you used Rudin's Principles 3rd... Read morePublished 18 months ago by Paul A. Bonyak
His style takes some getting used to.
The top of every chapter might seem like an informal invitation- but don't let him seduce you too far there! Read more
Opinions on this book seem split down the middle. On one side, it is a classic and contains many great topics regarding a fascinating field of mathematics. Read morePublished 21 months ago by mojambo
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 morePublished on January 13, 2014 by Mathematician
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 morePublished on January 7, 2014 by budding mathematician
Of course, Ahlfor is a great mathematician, he was the one of the two men to receive the the first Fields Medal. Read morePublished on July 20, 2011 by Wan Koon Yat
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,
copyright 1979,... Read more
First, a little about my background. I have no problem with many "classic" books in mathematics, even some that I believe should have been retired years ago on the grounds that... Read morePublished on January 18, 2010 by Linear Functional