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Title: The Shape of Space: How to Visualize Surfaces and Three-Dimensional Manifolds by Jeffrey R. Weeks ISBN: 0-8247-7437-X Publisher: Marcel Dekker Pub. Date: 01 August, 1985 Format: Hardcover List Price(USD): $55.00 |
Average Customer Rating: 5 (4 reviews)
Rating: 5
Summary: An Excellent Prolegomena to Elementary Topology.
Comment: I am trying to teach myself topology and find good elementary books in this subject rather slim in number. That is why I love this book. I can actually understand it. Weeks' clear prose and entertaining style make thinking about space an enjoyable activity in itself. I only wish a complete course could be written in this manner. Readers should not gain the impression that this even begins to scratch the surface of topology. It is more like an entertaining survey to motivate one into delving further into this wonderful subject.
By the way, I was suprised to realize that cosmologists have been confusing curvature with omega all this time. If something so fundamental can be mistaken how many other things in physics might be clearer with a sound topologic training?
Rating: 5
Summary: An explanation of how things can be twisted in space
Comment: Any author attempting to explain and visualize dimensions higher than three and/or the elliptic and hyperbolic geometries is engaged in a significant undertaking. In this book, Weeks does succeed in doing both but the reader is presented with a difficult task.
With 141 exercises and plenty of illustrations packed into 324 pages, it is short on explanation and the reader is forced to learn by problem solving. This is not to say that the exercises are poorly developed. On the contrary, they and the illustrations are very well done. However, doing an exercise after every few paragraphs does make the book a slow read, and in many cases it is necessary to understand a problem before the next material can be comprehended. Fortunately, complete solutions to all problems are given at the end of the book, but even so, a great deal of thought must be given to some of them before they are understood. As the book progressed, I found myself reading only fifteen to twenty-five pages on any given day. This necessitated a great deal of back-pedaling to previous illustrations and exercises, but it was the limit that I seemed able to comprehend at any given setting.
Beginning with Flatland (by A Square-actually Edwin A. Abbott) and going through the creation of manifolds, the presentation of the basic concepts, like all of the text, is very well written. It is just unfortunate that there is not more of it. For example, in Chapter 9 (concerning spheres), there are seven exercises and five and one-half pages of illustrations packed in twelve pages. Chapter 17 (describing bundles), has thirteen problems and seven and one-half pages of diagrams in a total of fifteen pages. Illustrations are valuable, but in this case they describe abstract phenomena not easily followed, and more words than usual are needed to explain precisely what is occurring.
And so, in conclusion, this book is highly recommended for those who wish to learn about the properties of manifolds and surfaces and are highly motivated to do so. But lacking that, the chances are very good that you will not make it beyond the midpoint.
Published in Journal of Recreational Mathematics, reprinted with permission.
Rating: 5
Summary: A must-read
Comment: As a high school student, many of the books regarding topology and manifolds are not always easy to follow. Jeffrey Weeks implements several illustrations and a simple yet poetic writing style to effectively portray worldy concepts to readers of all levels (even high scool students). It is obvious that he has a passion about his subject and has definitely inspired me to open my mind to mathematical ideas that had never found me before. I recommend this book to all readers!
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Title: Geometric Algebra for Physicists by Chris Doran, Anthony Lasenby, A. N. Lasenby ISBN: 0521480221 Publisher: Cambridge University Press Pub. Date: 01 July, 2003 List Price(USD): $95.00 |
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Title: On Quaternions and Octonions by John Horton Conway, Derek Alan Smith ISBN: 1568811349 Publisher: AK Peters, Ltd. Pub. Date: 01 January, 2003 List Price(USD): $29.00 |
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Title: A Course of Pure Mathematics by G.H. Hardy ISBN: 0521092272 Publisher: Cambridge University Press Pub. Date: 01 June, 1993 List Price(USD): $35.00 |
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Title: Linked: How Everything Is Connected to Everything Else and What It Means by Albert-Laszlo Barabasi ISBN: 0452284392 Publisher: Plume Books Pub. Date: 29 April, 2003 List Price(USD): $14.00 |
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Title: The Fabric of the Cosmos: Space, Time, and the Texture of Reality by Brian Greene ISBN: 0375412883 Publisher: Alfred A. Knopf Pub. Date: 01 February, 2004 List Price(USD): $28.95 |
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