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?

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.

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!

Before reading this book, I had very little knowledge what a mutual fund was, and had even less knowledge how to invest in them. This book explains step by step the different types of funds (small cap, mid cap, growth, blend, index, etc.) in a very easy-to-read format. It also recommends investment strategies for people at all stages of their life, and explains why certain funds may work better for people than others. After reading this book, I feel much more confident picking the right fund, and knowing how to react to market swings. A definite A+.

I would highly recommend this book to anyone interested in learning about mutual fund investing. Unlike other books on the subject I have read, the author details how loads and high expenses can devastate investment returns.

But this book can also be quite serious, although it may take someone with an extensive math background to see this. The book seems aimed primarily at high-schoolers, but graduate students in topology can definitely benefit from reading it.

Weeks starts out by explaining surfaces and the quotient space descriptions of the torus and klein bottle. Later chapters describe 3-manifolds, fibre bundles(!), and the 8 geometries relevant to Thurston's geometrization conjecture. The focus of the book is on applying these concepts to investigating the shape of our spatial universe. This is a particularly apt goal, given that many times in the book the reader is asked to imagine living in various kinds of spaces.

He has a very good set of exercises designed to increase one's visualization powers. For example, in the chapter on 3-manifolds, he has the reader color various covering space pictures of 3-manifolds like the 3-torus, according to some specifications; this really helps one understand how covering maps work.

As someone who was familiar with topology before reading the book, I can say that the book has definitely increased my understand of 3-manifolds, which is more than I can say for most topology books. In particular, I found the material on fibre bundles very enlightening.

What is the universe as a whole shaped like? Does it curve back on itself? Does it meet itself at the other side without curving? Is its Flatland analogy a plane, or a sphere, or a doughnut, or a Klein bottle? What other, stranger geometries become possible with the added dimension? And if the universe has one of these exotic shapes, how could astronomers ever know for sure?

Jeffrey Weeks, a MacArthur ("genius grant") fellow and a consultant to NASA on cosmological observations, believes that there's no reason why a liberal arts student or a high schooler shouldn't be able to have a solid understanding of the answers to these questions, even though some of them are at the edge of research in cosmology and three-manifolds, and others have traditionally not been part of the math curriculum before graduate school.

The math is presented at an elementary level, but it is genuine mathematics. Readers in the intended audience must be prepared to roll up their sleeves; there are exercises, and there are formulas, and their minds will be stretched. But there are no prerequisites other than a little first-year algebra, and the discussion stays at a vividly concrete level, with a plethora of diagrams to aid the swelling imagination. High schoolers will benefit from some guidance getting through it; it's appropriate for undergraduate self-study.

More mathematically sophisticated readers, even those who've taken a course in algebraic topology or differentiable manifolds, will find the book a lively read, but will still probably learn a thing or two. I, for one, was startled to be shown a Moebius strip that was two-sided! (The trick is to embed it in a non-orientable three-space.)

The payoff is in the final two chapters, which detail programs of astronomical observation that could well tell us the precise topology and geometry of the universe, and explain just how they would do it. One chapter is devoted to a technique based on correlating distances between galactic clusters, and the other to a statistical search for correlated arcs of great circles in the cosmic microwave background. Both observations will probably be completed within the next decade. It's an exciting prospect.

Buyers note: I believe the Amazon characterization of this as a paperback is in error. I bought the second edition in hardcover at the same list price. In its (successful) attempt to avoid intimidation, it uses a large typeface, so it would fill out some 200 pages in a more typical math format.

I am an Instructor of Esthetics, and I have also had the privilege of working withJeffrey Bruce during the 1980's.
While the book's photos and colors may be a bit dated, the information and how-to's in this book are timeless.
Perfect for the woman who needs easy to understand instructions, step by step guidance, all with a delightfully
devilish sense of humour.
Well worth the read.

I found the way David Madden portrayed the life of James Agee to be quite extraordinary. He really did a great job of mentioning and explaining all the life changing events that happend in Agee's life. This book was a great help for me to write my report on James Agee. I really learned a lot about a wonderful novelist. Not only was he a novelist but a poet, journalist, film critic, and social activist. This book revealed everything about him and made understanding him a lot easier for me.