Topology of Surfaces, Knots, and Manifolds | 
 enlarge | Author: Stephan C. Carlson
Publisher: Wiley
Category: Book
Buy New: $60.85
New (14) Used (6) from $48.95
Rating:  3 reviews
Sales Rank: 1919974
Media: Hardcover
Edition: International student edition
Pages: 176
Number Of Items: 1
Shipping Weight (lbs): 0.9
Dimensions (in): 9.4 x 6.4 x 0.5
ISBN: 0471355445
Dewey Decimal Number: 514
EAN: 9780471355441
Publication Date: January 1, 2001
Availability: Usually ships in 1-2 business days
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Product Description
Topology of Surfaces, Knots, and Manifolds offers an intuition-based and example-driven approach to the basic ideas and problems involving manifolds, particularly one- and two-dimensional manifolds. A blend of examples and exercises leads the reader to anticipate general definitions and theorems concerning curves, surfaces, knots, and links--the objects of interest in the appealing set of mathematical ideas known as "rubber sheet geometry." The result is a book that provides solid coverage of the mathematics underlying these topics.
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| Customer Reviews:
 No math library is complete without this book March 15, 2001
Michael S. McClendon (Edmond, OK United States)
8 out of 11 found this review helpful
This book presents the topology of surfaces, manifolds and knots in a manner that is reachable for undergraduate students with only a knowledge of calculus. Some linear algebra might be helpful. The text is written in a style that is easy to follow and there are superfluous examples. The exercises in the text are well thought out and are not extremely difficult. The exercises complement the text very well. The text makes clear a lot of difficult concepts such as isotopic surfaces as opposed to homeomorphic surfaces. I particularly enjoyed the manner in which the topology of knots was explained. After reading this text, the reader should be able to better visualize the projective plain and even the Klein bottle as it exists in 4-dimensional space. I have not read a text on topology that I enjoyed reading as much since Munkres. This text is a must have for any topologist.
Fun, but not very substantive. May 9, 2002
Carey Allen (San Francisco Bay Area)
2 out of 3 found this review helpful
This is a relatively fun romp through some very interesting concepts, but it lacks rigor. The book could have been much stronger if the author had simply developed some of the basic concepts (compactness, connectedness, homeomorphisms, homotopy, etc) rather than do a little hand-waving around a nice illustration. As it stands, this book is only 140 pages long, and does not develop any of its topics (manifolds, surfaces, graphs, knots) adequately. This book is far too weak to serve as a good text. Kinsey's TOPOLOGY OF SURFACES is much stronger, and costs less. Or look as something like Gamelin's INTRO TO TOPOLOGY. Or even Schaum's outline GENERAL TOPOLOGY, which deals with the basics, but is highly readable and rigorous.
 Very Misleading Title, Quite Thin, No Rigor, and Overpriced June 8, 2001
8 out of 9 found this review helpful
This book is subtitled "A First Undergraduate Course" but is certainly below undergraduate level. A high school student could easily follow this--which might be a good thing in certain cases--but the rigor is lacking. In fact, there is barely a hint of any rigor whatsoever. It is mostly intuitive arguments and the author often says things like "but we won't bother worrying about mathematical technicalities". It does get you to be able to visualize certain things well, but the visualization techniques can be found in other books also. The book is very thin and a quick read--hardly worth the money they are trying to get for it. If you're really at the undergraduate level and want to learn some topology, try something like Mendelson's "Introduction to Topology" by Dover or one of the excellent topology books in the series "Undergraduate Texts in Mathematics" by Springer. Munkres is also a classic. If you're not an undergraduate in a math related field and just want to know about the ideas behind topology or perhaps see some visualization techniques, try something like "The Shape of Space" by Weeks. Overall I was very disappointed with this text. If you could purchase this book for under $20 it might be worth it, but even then I think the other books I quoted are better in both price and substance.
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