- 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: 4.4 out of 5 stars See all reviews (67 customer reviews)
- Amazon Best Sellers Rank: #44,870 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.
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Top Customer Reviews
Needham's book is unique in its clear explanation of how the rich properties of analytic functions all follow from the "ampli-twist" concept of complex differentiation. In my class, I use this crucial, geometrical idea from the first mention of the derivative, where it goes hand in hand with the concept of conformal mapping (which is often at the back of introductory texts, but which I think should appear near the beginning). Perhaps the most delighful section of Needham's book is the one where he uses the same ampli-twist concept to give a very intuitive, unified proof of Cauchy's theorem, Morera's theorem, and the fact that a loop integral of the conjugate gives 2i times the area enclosed. The book also contains many clever and challenging problems, which are appropriate to give students to help them "think outside the box", as it were.
The most amazing thing about Needham's book is that it is sure to delight and edify both beginners and experts alike with its simple, geometrical explanations. This is all the more impressive because geometry in mathematics education is more traditionally a vehicle to teach rigorous proofs rather than intuitive understanding.
This is a book that any math afficionado must have, and will undoubtedly savor. I frankly don't understand those reviewers who have given this book fewer than five stars. In fact, five stars wouldn't seem to be enough here. This book is among the best math books one will ever find! What else would one want from a such book? It is exciting, friendly, creative, often funny, crystal clear, fresh, deep, and unfailingly courteous to the reader--a quality not always found in math texts.
Additionally, this book succeeds on another level -- it is just plain beautiful. Math, to be great, must be beautiful, while books about great math too often are not. This book is truly beautiful, even artful. The author has taken great care to create beauty here.
I intially bought this book, because as an ex-mathematician whose analysis skills were getting rusty I wanted to revisit complex analysis. This book certainly succeeded in brushing up those old skills, but it also deepened them. The book has marvelous insights and geometric drawings that demonstrate in a clever way the links between complex analysis and other branches of math and physics. How could one not love the lovely and intricate drawings that depict, say, loxodromic transformations on a sphere, or the eye-popping diagrams of rotations in hyperbolic space? They're fabulous! Even the problem sets are delightful.
As a side note, some of the historical glosses about mathematicians are also very lively, and are another source of pleasure here.
On the dust jacket is the blurb--"If you must buy only one math book this year, this is the one to buy." I have to agree. I bought a couple dozen math books last year, and this one outshines the rest. I can't recommend it highly enough, even if you already feel comfortable with complex analysis.
I encourage my fellow readers to pick this up, and see how beautiful a math book can be.
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.)