- Hardcover: 330 pages
- Publisher: Springer; 2nd edition (1978)
- Language: English
- ISBN-10: 0387903283
- ISBN-13: 978-0387903286
- Product Dimensions: 6.1 x 0.9 x 9.2 inches
- Shipping Weight: 1.4 pounds (View shipping rates and policies)
- Average Customer Review: 20 customer reviews
- Amazon Best Sellers Rank: #494,974 in Books (See Top 100 in Books)
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Functions of One Complex Variable (Graduate Texts in Mathematics - Vol 11) (v. 1) 2nd Edition
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"This book presents a basic introduction to complex analysis in both an interesting and a rigorous manner. It contains enough material for a full year's course, and the choice of material treated is reasonably standard and should be satisfactory for most first courses in complex analysis. The approach to each topic appears to be carefully thought out both as to mathematical treatment and pedagogical presentation, and the end result is a very satisfactory book for classroom use or self-study." --MathSciNet
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Some of my complaints include, but are not limited to:
- No examples whatsoever; there may be one or two per chapter, jammed lamely into the body of the text
- The "expository prose" did nothing to elucidate the underlying mathematics; often Conway babbles for a while, then says something like "the proof is left to the reader". It came to a point last month where I simply just stopped reading the text and started to focus on just the theorems and proofs
- There were errors in some proofs, of omission and of commission. The two ugliest proofs I've ever seen in mathematics lie in this book: (1) a standard composition theorem for analytic functions done by cases (?) which ended with "the general case follows easily", and the argument was built upon sequences (?). In other books, the result is proved in three lines; (2) the Casorati-Weierstrass theorem: same sloppiness, but Wikipedia saved me with an elegant four-line proof. The open mapping theorem was almost incoherent; and a crucial part of it was left as an exercise. I managed to get this part from Adult Rudin with no problems, though.
- the exercises: some are actually fine, but many are obtuse, and obtusely stated. Ultimately - and this is a huge problem - one cannot trust whether or not exercises were written correctly, because of too much general and ubiquitous sloppiness.
- chapter 2 (mapping properties of analytic functions, mobius maps) is so poorly written i had to skip it entirely.
I have a whole list of complaints here on paper, that I collected while reading this book to expose when I reviewed it. It's simply not worth more time and effort to transcribe them.
Not the whole book is bad, the homotopy integral is treated fairly well (i guess), as are the earlier parts of complex integration, and isolated singularities. But all this stuff is elementary - the later chapters are what counts, and the two chapters following integration are a mess. I hate having to clean up SO MUCH of this book.
I recommend looking at Robert B. Ash's book, as it's only 15 dollars (and free online), compared to the 60 dollars which this book is, and more importantly he makes very wise comments regarding math pedagogy on his webpage. In contrast, Conway in his webpage is pictured drinking martinis; he was probably on his twelfth one when he began the writing of this book.
EDIT: i've been working through ash's online book from the start, and i notice the proofs are far more slick, yet far more intuitive. there are many more problems, and better, than in conway. plus there are hints and solutions - don't peek unless you really don't know where to start! ultimately i'm starting over somewhat. i can't pretend i know nothing after conway, but i've abandoned his book completely. i wasted a graduate semester on conway's garbage.