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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
This text develops non-Euclidean geometry and geometry on surfaces at a level appropriate for undergraduate students who have completed a multivariable calculus course and are ready for a course in which to practice habits of thought needed in advanced courses of the undergraduate mathematics curriculum. The text uses Mobius transformations in the extended complex plane to define and investigate these three candidate geometries, thereby providing a natural setting in which to express results common to them all, as well as results that encapsulate key differences. With these geometries in hand, the text then explores the interplay between the shape of a space and the type of geometry it admits. The text is also suited to independent study.
Title: Geometry with an Introduction to Cosmic Topology by Mike Hitchman Publisher: Michael Hitchman Year: 2017 Pages: 238 Type: PDF Language: English ISBN-10 #: 1717134815 ISBN-13 #: 978-1717134813 License: CC BY 4.0 Amazon: Amazon
The author Michael P. Hitchman is a mathematics professor at Linfield University in Oregon. He studies shapes and space, and how they relate to the universe. He specializes in geometry and is interested in how it connects to the shape of the universe.
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