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Function Theory of One Complex Variable (Graduate Studies in Mathematics, 40) 2nd Edition
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Top Customer Reviews
However, if it was ever true that the devil is in the details, then this certainly applies to a mathematics book. I found the present book to be rather disappointing in this respect. I probably shouldn't have been surprised as Krantz has acquired some notoriety as a mass producer of math books. Few of the proofs can be called polished, and occasionally there are minor gaps (usually easy to fix, though) in the arguments. Cross references are often done awkwardly; sometimes, essentially the same argument is presented several times at different places without clarifying comment, setting the reader's head spinning unnecessarily.
The quality of the writing gets successively worse as we approach the end of the book. For example, I cannot shake off the suspicion that the treatment of the analytic continuation of Riemann's zeta function in Ch. 15 was hastily copied, with errors, from some other book; definitely, very little can be taken at face value here and the authors manage to completely obscure the main point behind the procedure used (which is essentially Riemann's original argument). Curiously, the following (final) Ch. 16 is independent of Ch.Read more ›
However, after reading a bit further I was disappointed to find it severely flawed. It seems that the beginning was written very carefully, but by the middle chapters it becomes unforgivably sloppy. It is riddled with errors of a kind that don't belong in the second edition of anything, and more importantly, the presentation is disorganized and uneven. Most of the proofs are inelegant and could be shortened considerably; many of them contain completely unnecessary statements that serve no apparent purpose, formal or intuitive, and it seems as though the authors simply didn't put much thought into cleaning them up. The prose similarly contains a lot of hemming and hawing and little material of use. The presence of elementary material alongside advanced topics is incongruous.Read more ›
The level of the book is elementary, especially for a graduate text, and I appreciate the authors for making honest and reasonable claims about the accessibility of their book. This book would probably even work well for someone who has not had a prior course in complex analysis, such as senior undergraduates. Some of the more advanced topics are presented in clearer ways in this book than I have seen elsewhere.
This book has a wealth of exercises, and the difficulty level is somewhat inconsistent. Some of the exercises are outright inane--possibly inappropriate for a graduate-level text, but useful for rote practice. Others are more interesting. I appreciate, however, the inclusion of more elementary exercises: many graduate texts have the problem of not including enough such exercises, which can make it hard for students to master the fundamentals. This book avoids this pitfall.
The best part about this book is the prose. This book is well-written and is a pleasure to read. Theorems and results are well-motivated, and necessary nuances are effectively communicated through the text.Read more ›
Most Recent Customer Reviews
I had this textbook during my first experience with Complex Analysis (or variables for that matter!). For most of the semester I had to use other books to understand HW problems. Read morePublished on May 5, 2014 by C. J. Fessler
The hardcover, and the book itself are good. We use it as a textbook; the content is sort of hard yet sufficient motivation is provided.Published on January 17, 2014 by Chin-Hung Lin
This book has great exercises, and covers all of the important stuff. If you plan on reading it cover to cover it is a great choice since it has solid, readable prose that... Read morePublished on March 6, 2011 by Jon