- Series: Chapman & Hall/CRC Pure and Applied Mathematics (Book 249)
- Hardcover: 408 pages
- Publisher: CRC Press; 2 edition (December 12, 2001)
- Language: English
- ISBN-10: 0824707095
- ISBN-13: 978-0824707095
- Product Dimensions: 6.2 x 0.9 x 9.2 inches
- Shipping Weight: 1.4 pounds (View shipping rates and policies)
- Average Customer Review: 4.9 out of 5 stars See all reviews (14 customer reviews)
- Amazon Best Sellers Rank: #457,990 in Books (See Top 100 in Books)
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The Shape of Space (Chapman & Hall/CRC Pure and Applied Mathematics) 2nd Edition
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Top Customer Reviews
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.Read more ›
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.
This book is well written with many illustrations and exercises to help you get an intuitive understanding of 3 Dimensional manifolds. This helped me a lot in my second year Analysis class as I had an intuitive notion of manifolds taught in class.
At the same time the book is easy enough for high school students who always wondered what a Mobius strip or a Klein bottle was but did not find any books on it. This book would make Topology interesting for everyone. I give it a five star rating.
This book is an ideal introduction to topology for beginners with little or no mathematical background. It introduces topological manifolds (especially 2- and 3-manifolds) and their applications to cosmology and the shape of space. It is filled with diagrams, examples and exercises with full solutions at the end of the book.
The book assumes almost no knowledge of mathematics or physics, and is thus suitable for high-school and beginning college students. It is a must read for students contemplating a career in pure mathematics or theoretical physics, and who want to get a taste of the applications of pure mathematics to the physical world.
For those wishing to go a step further on the subject of the shape of space, the author published a paper (Nature 425, 593 - 595, 09 October 2003) claiming that the universe is a dodecahedral 3-manifold, based on cosmic microwave background measurements. This book may be a nice introduction for this paper and for subsequent papers that will surely ensue, trying to describe the shape of space.
Most Recent Customer Reviews
Excellent introduction to 2 and 3 dimension geometry, including 3-manifolds and the shape of the universe.Published 20 months ago by Daniel P. Evans
I can't give him five stars as good as Jeffery Weeks is, because the book doesn't even mentions Bianchi's manifold types. Read morePublished on October 13, 2008 by Roger Bagula
This is a great book for anyone who is interest in Mathematical Topology and Cosmology Topology. This book does not require a reader to have strong mathematics knowledge. Read morePublished on August 5, 2007 by 亚马逊客户
I have a bachelors degree in Math.
As Feynman said, what we really mean by math is careful reasoning. Read more
This text is non-intimidating as an introduction to topology. Weeks carefully guides the reader through the building blocks of torii, Moebius strips, projective planes, and other... Read morePublished on July 5, 2007 by Shawn Gardner
This is a painless way to learn some advanced topology--or at least to gain insight. It's almost a picture book. Read morePublished on November 25, 2006 by C. Dunn
This is a very good book for people whom have a light background in math. It is a readable book and great introduction into manifolds and torus. Read morePublished on February 19, 2006 by Edward J. Koslowska