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๐Ÿ“

The Shape of Space

โœ Scribed by Jeffrey R. Weeks


Publisher
Chapman and Hall/CRC
Year
2019
Tongue
English
Leaves
365
Series
Textbooks in Mathematics
Edition
3
Category
Library

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โœฆ Synopsis


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 spacesโ€•stretching studentsโ€™ 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 andโ€•closest to his heartโ€•exposition for the general public.

โœฆ Table of Contents


Contents
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
Acknowledgments
PART I Surfaces and Three-Manifolds
1. Flatland
2. Gluing
3. Vocabulary
4. Orientability
5. Classification of Surfaces
6. Products
7. Flat Manifolds
8. Orientability vs. Two-Sidedness
PART II Geometries on Surfaces
9. The Sphere
10. The Hyperbolic Plane
11. Geometries on Surfaces
12. The Gauss-Bonnet Formula and the Euler Number
PART III Geometries on Three-Manifolds
13. Four-Dimensional Space
14. The Hypersphere
15. Hyperbolic Space
16. Geometries on Three-Manifolds I
17. Bundles
18. Geometries on Three-Manifolds II
PART IV The Universe
19. The Universe
20. The History of Space
Appendix A Answers
Appendix B Bibliography
Appendix C Conwayโ€™s ZIP Proof
Index


๐Ÿ“œ SIMILAR VOLUMES


The Shape of Space
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โœ Jeffrey R. Weeks ๐Ÿ“‚ Library ๐Ÿ“… 2019 ๐Ÿ› Chapman and Hall/CRC ๐ŸŒ English

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