Geometry with an Introduction to Cosmic Topology
Michael P. Hitchman, Linfield College
Copyright Year: 2018
Last Update: 2020
Publisher: Michael P. Hitchman
Conditions of Use
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
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.
I have not come across any errors in the text.
This text has an interesting perspective on geometry that is both modern and timeless.
The language is clear and understandable for a typical mathematics major or minor.
The language and notation are consistent throughout.
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.
The text is well organized. Material in the later chapters builds on material in earlier chapters.
There are no problems with the interface.
I have not found any grammatical errors.
This is not really relevant for a geometry text.
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