- Series: Graduate Texts in Mathematics (Book 103)
- Hardcover: 489 pages
- Publisher: Springer; 4th edition (July 30, 2003)
- Language: English
- ISBN-10: 0387985921
- ISBN-13: 978-0387985923
- Product Dimensions: 6.1 x 1.1 x 9.2 inches
- Shipping Weight: 1.8 pounds (View shipping rates and policies)
- Average Customer Review: 10 customer reviews
- Amazon Best Sellers Rank: #574,126 in Books (See Top 100 in Books)
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Complex Analysis (Graduate Texts in Mathematics) 4th Edition
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"The very understandable style of explanation, which is typical for this author, makes the book valuable for both students and teachers."
EMS Newsletter, Vol. 37, Sept. 2000
"A highly recommendable book for a two semester course on complex analysis."
Top customer reviews
I completed a year of Complex Analysis back in graduate school and had the misfortune of using Alfors book which is a terrible book. I had to purchase a supplementary book by Speigal to understand the basics. I wish I had got a hold of Langs book then.
I will start out by saying what I like about this book: most of it. This book provides a lot of topological flavour to complex variables, which I find very helpful. To someone who thinks topologically, many of the proofs in this book will seem more intuitive than in other texts. This is particularly true when you get into more advanced material.
Overall, the writing is very clear. Lang is excellent at providing motivation, especially as you get farther along in this book. Unlike some of his other books, he can't be criticized as moving too fast in this book.
Now the bad: the book starts out very slow, painfully so. It seems the first chunk of the book is aimed at teaching rigorous complex analysis to someone whose background in analysis is weak. Lang repeats all of the basic theorems about limits, differentiation, convergence, etc. in full detail. However, the material picks up eventually, and by the end of the book it's moving fast enough that anyone who enjoyed the first part will have trouble understanding the later material. This book covers a lot more material than most undergrad books on the subject, so I suppose it lives up to the GTM title.
Bottom line: I don't like the choice or order of topics in initial chapters. Some of the "new" material specific to complex variables is mixed in with old results common to basic analysis on the real line. Anyone with a good background in analysis will be frustrated trying to find what they need to learn. Also, Lang confuses the logic of the subject by working with the terms "analytic" and "holomorphic" separately for a great deal of time before showing their equivalence. His definitions, terminology, and development don't line up with many other authors, and he has not convinced me that his choice of development was justified...because most of the stuff I like in this book comes after the first few chapters. However, if you can get past these hurdles, you'll find that this is a pretty great book that has a lot to offer.