Geometry with an Introduction to Cosmic Topology

Michael P. Hitchman

Digital versions HTML and PDF
Source available     No
Exercises Yes
Answers No
License CC-BY-SA
  • 212 pages (PDF) and 8 chapters for a one semester course, an advanced reading course, or for independent study
  • Print version available for about $11.
  • Originally published by Jones and Bartlett in 2009
  • Activity guide using Sage and Geogebra
  • MAA Review calls it “a masterfully written textbook.”
  • For more information and to download PDF or to access HTML

From the preface:

   Geometry with an Introduction to Cosmic Topology offers an introduction to non-Euclidean geometry through the lens of questions that have ignited the imagination of stargazers since antiquity. What is the shape of the universe? Does the universe have an edge? Is it infinitely big?

   This text is intended for undergraduate mathematics and physics majors who have completed a multivariable calculus course and are ready for a course that practices the habits of thought needed in advanced courses of the undergraduate mathematics curriculum. The text is also particularly suited to independent study, with essays and other discussions complementing the mathematical content in several sections.


  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