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Geometry with an Introduction to Cosmic Topology

(1 review)

Michael P. Hitchman, Linfield College

Pub Date: 2018

ISBN 13: 978-1717134813

Publisher: Independent

Language: English

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Reviewed by Katherine Brandl, Associate Professor, Centenary College of Louisiana on 12/3/19

This book is jam-packed with material, and includes some history of the subject along with some of the basics before venturing into more advanced mathematics. My students tend to need a little more of the basics. I generally need to do some review... read more


Table of Contents

  • 1 An Invitation to Geometry
  • 2 The Complex Plane
  • 3 Transformations
  • 4 Geometry
  • 5 Hyperbolic Geometry
  • 6 Elliptic Geometry
  • 7 Geometry on Surfaces
  • 8 Cosmic Topology

About the Book

Motivated by questions in cosmology, the open-content text Geometry with an Introduction to Cosmic Topology uses Mobius transformations to develop hyperbolic, elliptic, and Euclidean geometry - three possibilities for the global geometry of the universe.

The text, written for students who have taken vector calculus, also explores the interplay between the shape of a space and the type of geometry it admits. Geometry is suitable for a semester course in non-Euclidean geometry or as a guide to independent study, with over 200 exercises and several essays on topics including the history of geometry, parallax and curvature, and research aimed at determining the shape of the universe.

About the Contributors


Michael P. Hitchman