12 of 12 people found the following review helpful:
5.0 out of 5 stars
A must-read, May 12, 2000
This review is from: The Shape of Space: How to Visualize Surfaces and Three-Dimensional Manifolds (Monographs and Textbooks in Pure and Applied Mathematics, Vol. 96) (Hardcover)
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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11 of 11 people found the following review helpful:
5.0 out of 5 stars
Topology at its entertaining and intuitive best., May 7, 1999
By A Customer
This review is from: The Shape of Space: How to Visualize Surfaces and Three-Dimensional Manifolds (Monographs and Textbooks in Pure and Applied Mathematics, Vol. 96) (Hardcover)
It's been many years since I read this book. But it was terrific, and I cannot praise it too highly. I have to believe that anyone from a bright junior higher to a scientific Nobel laureate, if not versed in the subject, can read this book with pleasure and profit. This book is light and easy to work through, but rich in content. It will carry you along with almost no effort while introducing you to exotic things from Klein bottles to periodic and curved spaces. The line diagrams filling the book are crystal clear and add charm all by themselves. This book could only be created by someone who loves the subject and loves to teach. All hats off to Jeffrey Weeks! -- no bones about it, he has produced a masterpiece of math education. I doubt that topology has ever been presented in a more winsome way.
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11 of 12 people found the following review helpful:
5.0 out of 5 stars
An explanation of how things can be twisted in space, November 23, 2000
This review is from: The Shape of Space: How to Visualize Surfaces and Three-Dimensional Manifolds (Monographs and Textbooks in Pure and Applied Mathematics, Vol. 96) (Hardcover)
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.
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