
Geometry with an Introduction to Cosmic Topology - 2018 Edition
Michael P. Hitchman, Linfield College
Copyright Year:
Last Update: 2024
ISBN 13: 9781717134813
Publisher: Michael P. Hitchman
Language: English
Formats Available
Conditions of Use
Attribution-ShareAlike
CC BY-SA
Reviews





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
Reviewed by Katherine Brandl, Associate Professor, Centenary College of Louisiana on 12/3/19
Comprehensiveness
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 of the geometry they learned in high school and a refresher on proofs. When I've used this book in the past I have supplemented with material from other texts.
Content Accuracy
I have not come across any errors in the text.
Relevance/Longevity
This text has an interesting perspective on geometry that is both modern and timeless.
Clarity
The language is clear and understandable for a typical mathematics major or minor.
Consistency
The language and notation are consistent throughout.
Modularity
As math texts go it is actually quite modular. While many sections rely on information from previous sections, some of the chapters can be used on their own. In the past I have used this text to supplement another text. I could also imagine using this as the main text, possibly supplementing with another text.
Organization/Structure/Flow
The text is well organized. Material in the later chapters builds on material in earlier chapters.
Interface
There are no problems with the interface.
Grammatical Errors
I have not found any grammatical errors.
Cultural Relevance
This is not really relevant for a geometry text.
Table of Contents
- Front Matter
- An Invitation to Geometry
- The Complex Plane
- Transformations
- Geometry
- Hyperbolic Geometry
- Elliptic Geometry
- Geometry on Surfaces
- Cosmic Topology
- List of Symbols
- References
- Index
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
Author
Michael P. Hitchman, Linfield College