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Visual Complex Analysis [Paperback]

Tristan Needham
4.1 out of 5 stars  See all reviews (19 customer reviews)
List Price: CDN$ 88.50
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Book Description

Jan. 1 1999 0198534469 978-0198534464 Reprint
Now available in paperback, this successful radical approach to complex analysis replaces the standard calculational arguments with new geometric ones. With several hundred diagrams, and far fewer prerequisites than usual, this is the first visual intuitive introduction to complex analysis. Although designed for use by undergraduates in mathematics and science, the novelty of the approach will also interest professional mathematicians.

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Product Description


`...one very fine recent example of mathematical graphics at a high level is Needham's Visual Complex Analysis.' Notices of the AMS

From the Publisher

numerous line drawings

Inside This Book (Learn More)
First Sentence
Four and a half centuries have elapsed since complex numbers were first discovered. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Customer Reviews

Most helpful customer reviews
4 of 4 people found the following review helpful
5.0 out of 5 stars Gee, a math book that really teaches, how unusual April 22 2003
I tried to learn complex analysis from Ahlfors, I wouldn't recommend you try it although it is a good book. The problem is there are certain subtleties in complex variables that are NOT obvious. There are few authors of math books that remember that we do not know these subtleties. I could go on a tirade about the general state of math literature for hours, but my only remark here is that in my view most authors seem to be trying to impress someone other than the students, maybe other professors ? Anyhow, this book is a definite departure from this nonsense. There are 12 chapters each with many exercises. The first couple of chapters have over forty and since I try to do them all, well ... If you read this book carefully and do the execises you WILL know this subject. You could teach it. You don't see Thm followed by Proof. What you do see is a clear presentation of the ideas with PICTURES and EXPLANATIONS that you can understand, of course you really find out about that "understand" part when you get to the exercises. The biggest problem I had was getting out of the old way of thinking and into a more geometric way of thinking. Couldn't recommend it more highly. Another author who writes to teach is Victor Bryant. His book Yet Another Introduction to Analysis is great for a highschool senior or 1st year college. (He is with me on the state of math literature.) Also, Hans Schwerdtfeger's book Geometry of Complex Numbers goes well with Needham and is very cheap ! I'm surprised Needham didn't include it in the bibliography. It's a little gem and covers some of the same material.
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3 of 3 people found the following review helpful
What a great book this is!
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.
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2 of 2 people found the following review helpful
5.0 out of 5 stars Best math book I've read in years! Sept. 29 2002
I have recently finished reading this book cover-to-cover and, in spite of having worked
in mathematical physics for 40 years, feel compelled to gush like a teenager. It is mighty
therapy for a generation raised on conciseness, abstruseness, abstraction and Bourbaki.
Possibly one cause for this sorry state of affairs (there are others, but I'm in a generous mood!)
is the vast mass of knowledge that has to be mastered by modern devotees. But, like any fashion, this
one has taken on a life of its own. A friend who works at MIT recently showed a book to a young post-doc,
claiming it was a "friendly" introduction to such-and-such. Without even glancing at the evidence, the
hot-shot replied that if it was all that friendly, it couldn't possibly be any good!
Needham takes you back to an earlier sensibility, naive and profound in equal measure,
tackling problems leisurely with nothing but your own intuition and a few simple facts
from geometry. Following his guidance, you understand the solution several times from
different angles and come out with that intoxicating feeling of "owning" the entire
thing, not as a means to an end (publishing, accolades, ...) but as a thing of beauty. It's
hard to believe, but early masters like Newton actually managed to understand vast and
complex fields of science in this very tactile way. That art, largely lost, has been revived
lately by a select few including Needham and Chandrasekhar (Newton's Principia for the
Common Reader, Clarendon Press, 1997). I've made a complete mess of my copy: margin notes,
sketches, ... and probably a few drool marks. Let's hope this starts a movement. If there is a way
to save American math education, this has got to be it! Thanks, Tristan.
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Most recent customer reviews
4.0 out of 5 stars Lots of material, great pictures but too chatty
I purchased this book as a reference and because of it's coverage on Mobius Transformations, which is great! My qualms are with the other parts of the book, however. Read more
Published on March 2 2004
3.0 out of 5 stars Decent Book for Graduate work but not good main text
I used this book in an introductory Complex Variables course in a top 20 ranked US college. I enjoyed the authors clear explaination of material and clearly british sense of... Read more
Published on Oct. 2 2003 by Christopher G. Moore
5.0 out of 5 stars Where do I send the 50-cent soda for the book?!
This book does an exceptional job of giving a hands-on person an opportunity to "see" what is happening in complex analysis. Read more
Published on Aug. 21 2003 by Chip Smith
5.0 out of 5 stars excellent book on this subject
i am not a philisopher like some reviewers here...this book is really wonderful and even better.
the subject is very clearly explained in a very educational manner. Read more
Published on Aug. 8 2003 by Ahmed Morsi
1.0 out of 5 stars A barely tolerable door stop
I bought this book in conjuction with a class on complex mathematics I took at a university. Within two classes I had abandoned all hope of actually learning something and by... Read more
Published on Aug. 6 2003
5.0 out of 5 stars A great marvel
This is a marvelous presentation of the subject. After looking at many analysis books which require a great deal of coffee to accompany them, I was surprised to find a book that... Read more
Published on June 25 2003 by Dima
3.0 out of 5 stars Hm.......
Th merits of this book has been well talked by others, I have few to add to. My question is, in order to distinguish the text, does the author distort the history of the subject? Read more
Published on June 8 2003
5.0 out of 5 stars What a beauty!
This is one hell of a book. Needham explains the geometrical concept of complex numbers and functions in a highly visual way. Read more
Published on Nov. 26 2002 by "jayjina"
5.0 out of 5 stars One book to read...
If somebody ask you to choose one book, because you are going to live the rest of your live in Mars, choose this one.
Published on Oct. 16 2002 by Juan Gustavo Sanchez
1.0 out of 5 stars S
this is a masterpiece by needham yet it lacks the educational interest that was shown in his other books . Read more
Published on May 10 2002
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