Geometry with an Introduction to Cosmic Topology

Format:

Book

Author/Creator:

Hitchman, Michael P., author.

Language:

English

Subjects (All):

Applied mathematics--Textbooks.

Applied mathematics.

Physical Description:

1 online resource

Place of Publication:

Department of Mathematics, McMinnville, Oregon Michael P. Hitchman 2020.

Language Note:

In English.

Summary:

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.

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

Notes:

Description based on print resource