- Paperback: 616 pages
- Publisher: Clarendon Press; Reprint edition (February 18, 1999)
- Language: English
- ISBN-10: 0198534469
- ISBN-13: 978-0198534464
- Product Dimensions: 9 x 1.3 x 6.1 inches
- Shipping Weight: 1.9 pounds (View shipping rates and policies)
- Average Customer Review: 71 customer reviews
- Amazon Best Sellers Rank: #34,532 in Books (See Top 100 in Books)
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Visual Complex Analysis Reprint Edition
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"Visual Complex Analysis is a delight, and a book after my own heart. By his innovative and exclusive use of the geometrical perspective, Tristan Needham uncovers many surprising and largely unappreciated aspects of the beauty of complex analysis." --Roger Penrose
"Tristan Needham's Visual Complex Analysis will show you the field of complex analysis in a way you almost certainly have not seen before. Drawing on historical sources and adding his own insights, Needham develops the subject from the ground up, drawing us attractive pictures at every step of the way. If you have time for a year course, full of fascinating detours, this is the perfect text; by picking and choosing, you could use it for a variety of shorter courses. I am tempted to hide the book from my own students, in order to appear more clever for popping up with crisp historical anecdotes, great exercises, and pictures that explain things like that mysterious 2*pi that crops up in integrals. Whether you use Visual Complex Analysis as a text, a resource, or entertaining summer reading, I highly recommend it for your bookshelf."--American Mathematical Monthly
"Delivers what its title promises, and more: an engaging, broad, thorough, and often deep, development of undergraduate complex analysis and related areas. . .A truly unusual and notably creative look at a classical subject." --American Mathematical Monthly
"One of the saddest developments in school mathematics has been the downgrading of the visual for the formal. I'm not lamenting the loss of traditional Euclidean geometry, despite its virtues, because it too emphasised stilted formalities. But to replace our rich visual intuition by silly games with 2 x 2 matrices has always seemed to me to be the height of folly. It is therefore a special pleasure to see Tristan Needham's 'Visual Complex Analysis' with its elegantly illustrated visual approach. Yes, he has 2 x 2 matrices--but his are interesting." --New Scientist
"Committed to the exclusive use of geometrical arguments and content to pay the price of 'an initial lack of rigour', he has produced a radically new text. The author writes "as though [he] were explaining the ideas directly to a friend". This informal style is excellently judged and works extremely well."--Mathematical Review
"This is a book in which the author has been willing to make himself available as our teacher. His own voice enters in a rather charming way....I recommend Visual Complex Analysis, as something to read and enjoy, to share with students, and perhaps to inspire other books in which the voice of the author is vividly present to teach and explain."--American Mathematical Monthly
From the Author
The book recently won First Prize in the National Jesuit Book Award Contest for the best mathematics or computer science book published in 1994, 1995, or 1996. --This text refers to an out of print or unavailable edition of this title.
Top customer reviews
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I am not a professional, just a wannabee, but with a math/physics background of sorts and a particular interest in complex analysis.
I have gone through or tried to go through a lot of math books, and this one is outstanding in it's clear presentation of fascinating ideas and visualizations.
I tend to put those little sticky book marks on pages of books where an intriguing idea is that I want to be sure to go back and think about more. While many of my books end up with too many markers to be practical, this book has outdone them all as I have markers on nearly every single page!
If you are here it means you are considering getting this book and you are probably concerned about the price. Never mind the price, if you are interested in complex analysis it is worth every penny and more. You will be thrilled if you go ahead and get it and use it. I know I am.
The only negative: As always with most books with exercises, there should be a detailed solution manual. I know this complicates things for those taking classes, but for those of us doing self study for the joy of it, because we love this stuff, it would be so wonderful if there was always a detailed solution manual for when we get stuck. I do also think solution manuals would help students overall. After all, tests usually count for more than homework and if someone is lazy and just copying answers they will not do well on the tests. Having solutions handy could help students spend more time doing exercises, even extra exercises, do more work and avoid excessive frustration or giving up. I believe a good solutions manual helps everyone and makes the world a better (and much more pleasant) place.
The book presents fundamental ideas of complex analysis in a quick and esoteric manner. There is no proving of a single statement in the book. Mathematics to me has always been about what you can PROVE (for those who think otherwise, consider that it made front page news when Fermat's theorem was nearly proven albeit in hyperbolic space).
I am not a connoisseur of math books, but it would appear from other ratings that Needham has perhaps written other books of value. However, this has no bearing on the incredibly poor nature of this book.
Unless you have a deep background in complex math or wish to be completely baffled, avoid this book at all costs.
As for my copy, I would be more than willing to part with it for a 50 cent soda.
I plan on buying a more traditional Complex Analysis text to give what I know about Complex Analysis a foundation, which is not something I think I should have to do after a quality semester course.
I applaud the author's effort to visually describe the complex plane: in particularly complex multiplication and integration. He also goes into great detail on Mobius transformations and other geometric concepts. However, I think that he missed the opportunity to describe complex differentials completely. While he speaks of analytic functions being "everywhere aplitwist," he doesn't describe the nature of differentials at analytic points: namely, the differential remains the same, regardless of which path we take from the point. This much more clearly explains the rigidity of analytic functions (along with theorems like FTC, maximum modulus, etc. which follow directly from this rigidity).
I believe that he forsakes his own thesis in describing the argument principle in generic topological arguments. These arguments are far more involved than they need to be.
More than anything, I dislike how he uses results that haven't been proved. It is quite annoying to use Cauchy's Theorem throughout the book, not proving it till very late.
All that said, this is an overall great book that will get you thinking about the concepts. His writing style is very skillful, and, obviously, he provides a lot of figures to help get his point across. It is definitely worth adding to your library, but I think that you will need at least one other text to completely grasp the subject. (I personally recommend Gamelin's book.)