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Functions of One Complex Variable (Graduate Texts in Mathematics - Vol 11) (v. 1) [Hardcover]

John B Conway
3.9 out of 5 stars  See all reviews (14 customer reviews)

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Book Description

1978 0387903283 978-0387903286 2nd

"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." --MATHSCINET


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Functions of One Complex Variable (Graduate Texts in Mathematics - Vol 11) (v. 1) + Functions of One Complex Variable II (Graduate Texts in Mathematics, Vol. 159)
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Editorial Reviews

Review

"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

Product Details

  • Hardcover: 330 pages
  • Publisher: Springer; 2nd edition (1978)
  • Language: English
  • ISBN-10: 0387903283
  • ISBN-13: 978-0387903286
  • Product Dimensions: 9.6 x 6.3 x 0.8 inches
  • Shipping Weight: 1.4 pounds (View shipping rates and policies)
  • Average Customer Review: 3.9 out of 5 stars  See all reviews (14 customer reviews)
  • Amazon Best Sellers Rank: #625,301 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
5 of 5 people found the following review helpful
5.0 out of 5 stars A Classic under Attack July 24, 2012
By Bill Ed
Format:Hardcover
I find myself in the strange position of defending a classic text which has been widely used for several decades. I find the book to be superbly organized and written. It is the text I used in graduate school, and I have used it on at least two occasions when teaching a second course in complex analysis. My students never shared any complaints with me, and it has been my favorite complex analysis text for over 3 decades.

I'd conjecture that Professor Conway couldn't care less that a few low-ball ratings here of his text have brought the average rating score down far from where it would otherwise be, but for some reason it does bother me.
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29 of 40 people found the following review helpful
1.0 out of 5 stars Should be avoided. December 4, 2007
Format:Hardcover|Verified Purchase
I concur with the reviewer Sidhant. I had tons of frustrations with this book this semester - it's so annoying. I just finished and reviewed Munkres' topology book, and Sterling Berberian's Fundamentals of Real Analysis, and the difference between these books and Conway's is (respectively) like the difference between say Bach and pure cacophony: cymbals, screeches, sirens, horns, etc.

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.
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3 of 3 people found the following review helpful
5.0 out of 5 stars A good read April 15, 2007
Format:Hardcover|Verified Purchase
We're using this book for my graduate level complex analysis course, and over all, I'm pleased with it. Aside from some goofy notation (i.e., an empty box to represent the empty set?), it's pretty well written. The pace of the text isn't too fast or too slow, and there are plenty of exercises of a varying degree of difficulty to help you learn the material. Another nice feature is the price; one can find it for less than $50, so it'll make a nice reference book even if it wasn't assigned for a class.
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7 of 9 people found the following review helpful
5.0 out of 5 stars Excellent Book March 11, 2009
By SL2C
Format:Hardcover
I have used this book back in my college days. I am amazed to see such a low rating on this book. This is one of the best books on complex analysis.
Mind you this is a Graduate Text in Mathematics. So it is intended to cover lot of ground using clear logical path. I agree to some extent that this book does not have lot of examples but a GTM is supposed to be like that. The way I used/read this book is to supplement it with other books on the topic. The proofs of theorems in this book are complete without any errors.

If you are a graduate student and want to learn complex analysis, this is the best book available out there.
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2 of 2 people found the following review helpful
3.0 out of 5 stars Poor typesetting October 1, 2012
By JL
Format:Hardcover|Verified Purchase
This book is reasonably concise, and its minimalistic exposition is not suitable for people taking a first course in complex analysis. By comparison, I find the book by Palka more readable if that's what you're looking for. Unfortunately, every even numbered page looks like it came from an inkjet printer low on ink. You usually come to expect more than that from a Springer book.
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5.0 out of 5 stars Great book May 19, 2013
Format:Hardcover|Verified Purchase
Functions of One Complex Variable Vol. I is a well-organized textbook preseting basic principles and concepts of Complex Analysis. The text is full of examples, which helps a lot the reader to consolidate some notions and aspects of the theory. Moreover, Conway invited the reader to explore further the results presented through a vast number of exercises in the end of each section. Personally, I only have one bad comment: the exercises do not have many comments or hints. This is very unappealing for the self-taught student of other fields, such as Engineering or Physics.
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11 of 17 people found the following review helpful
4.0 out of 5 stars a good book August 1, 2005
Format:Hardcover
An ideal text for a first-year graduate students in mathematics studying Compex Analysis. And this depend how the professor present the material. The exposition is complete and very clear, including a lot of optional material for the curious. which could be very useful to those preparing for a qualifying exam in analysis at the PhD level. Overall, recommend text.
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