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The Shape of Space: Textbooks in Mathematics

Autor Jeffrey R. Weeks
en Limba Engleză Hardback – 24 dec 2019
The Shape of Space, Third Edition maintains the standard of excellence set by the previous editions. This lighthearted textbook covers the basic geometry and topology of two- and three-dimensional spaces—stretching students’ minds as they learn to visualize new possibilities for the shape of our universe.
Written by a master expositor, leading researcher in the field, and MacArthur Fellow, its informal exposition and engaging exercises appeal to an exceptionally broad audience, from liberal arts students to math undergraduate and graduate students looking for a clear intuitive understanding to supplement more formal texts, and even to laypeople seeking an entertaining self-study book to expand their understanding of space.
Features of the Third Edition:
  • Full-color figures throughout
  • "Picture proofs" have replaced algebraic proofs
  • Simpler handles-and-crosscaps approach to surfaces
  • Updated discussion of cosmological applications
  • Intuitive examples missing from many college and graduate school curricula

About the Author:
Jeffrey R. Weeks is a freelance geometer living in Canton, New York. With support from the U.S. National Science Foundation, the MacArthur Foundation and several science museums, his work spans pure mathematics, applications in cosmology and—closest to his heart—exposition for the general public.
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Specificații

ISBN-13: 9781138062276
ISBN-10: 1138062278
Pagini: 364
Ilustrații: 194
Dimensiuni: 156 x 234 x 17 mm
Greutate: 1.18 kg
Ediția:3
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Textbooks in Mathematics


Public țintă

Undergraduate Core

Cuprins

Part I Surfaces and Three-Manifolds
Flatland
Gluing
Vocabulary
Orientability
Classification of Surfaces
Products
Flat Manifolds
Orientability vs. Two-Sidedness
Part II Geometries on Surfaces
The Sphere
The Hyperbolic Plane
Geometries on Surfaces
Gauss-Bonnet Formula and Euler Number
Part III Geometries on Three-Manifolds
Four-Dimensional Space
The Hypersphere
Hyperbolic Space
Geometries on Three-Manifolds I
Bundles
Geometries on Three-Manifolds II
Part IV The Universe
The Universe
The History of Space
Appendix A: Answers
Appendix B: Bibliography
Appendix C: Conway’s ZIP Proof

Notă biografică

Jeffrey R. Weeks is a free-lance geometer living in Canton, New York. With support from the U.S. National Science Foundation, the MacArthur Foundation and several science museums, his work spans pure mathematics, applications in cosmology and—closest to his heart—exposition for the general public.

Descriere

The Shape of Space, Third Edition maintains the standard of excellence set by the previous editions. This lighthearted textbook covers the basic geometry and topology of two- and three-dimensional spaces—stretching students’ minds as they learn to visualize new possibilities for the shape of our universe.