Michael P. Hitchman

Digital versions PDF and HTML (online)
Source available     No
Exercises Yes
Answers No
License Copyright by author: all rights reserved; you can print copies for personal use
  • 177 pages (PDF) and 8 chapters for a one semester course, an advanced reading course, or for independent study
  • Print version soon to be available
  • Originally published by Jones and Bartlett in 2009
  • Supplementary Geometer’s Sketchpad activities available
  • 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.

Contents

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