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

John B Conway (Author)

Book Description

Publication Date: 1978 | ISBN-10: 0387903283 | ISBN-13: 978-0387903286 | Edition: 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

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: 6.1 x 0.8 x 9.2 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 3.8 out of 5 stars  See all reviews (13 customer reviews)
• Amazon Best Sellers Rank: #528,676 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

28 of 37 people found the following review helpful

1.0 out of 5 stars Should be avoided. December 4, 2007

By math student

Format:Hardcover

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....
- 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. Read more ›

3 of 3 people found the following review helpful

5.0 out of 5 stars A good read April 15, 2007

By From Detroit

Format:Hardcover|Amazon 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.

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.

2 of 2 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.

1 of 1 people found the following review helpful

3.0 out of 5 stars Poor typesetting October 1, 2012

By JL

Format:Hardcover|Amazon 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.

5.0 out of 5 stars Great book May 19, 2013

By E. Zanni

Format:Hardcover|Amazon 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.

11 of 17 people found the following review helpful

4.0 out of 5 stars a good book August 1, 2005

By Mohammad Alqudah

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.

17 of 28 people found the following review helpful

4.0 out of 5 stars A good book for a beginning graduate student. April 27, 2000

By C.M.

Format:Hardcover

I used this book in graduate school to help prepare for one of my Ph.D. qualifying exams. The text discusses beginning theory for functions of one complex variable. There are many examples, and the proofs are clearly stated.