Geometry with an Introduction to Cosmic Topology 2018th Edition by Michael Hitchman ISBN 9781717134813 1717134815

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Product details: 

ISBN 10:  1717134815

ISBN 13: 9781717134813

Author:  Michael P. Hitchman
Motivated by questions in cosmology, the 2018 edition of Geometry with an Introduction to Cosmic Topology follows the Erlangen program to develop hyperbolic, elliptic, and Euclidean geometry – three possibilities for the global geometry of the universe.

The text uses Mobius transformations in the extended complex plane to define and investigate these three candidate geometries, thereby providing a natural setting in which to express results common to them all, as well as results that encapsulate key differences. With these geometries in hand, the text then explores the interplay between the shape of a space and the type of geometry it admits.

It is written to be suitable for a one semester course in geometry or as a guide to independent study, with over 200 exercises and several essays on topics such as the history of geometry, parallax and curvature, and research aimed at determining the shape of the universe.

Table of contents: 

1. An Invitation to Geometry

2. The Plane and Complex Numbers

3. Transformations

4. Geometry

5. Hyperbolic Geometry

6. Elliptic Geometry

7. Geometry on Surfaces

8. Cosmic Topology

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Tags: Michael Hitchman, an Introduction, Cosmic Topology