Geometry with an Introduction to Cosmic Topology
by Michael P. Hitchman
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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 the habits of thought needed in advanced courses of the undergraduate mathematics curriculum. The text is also suited to independent study, with essays and discussions throughout.
Mathematicians and cosmologists have expended considerable amounts of effort investigating the shape of the universe, and this field of research is called cosmic topology. Geometry plays a fundamental role in this research. Under basic assumptions about the nature of space, there is a simple relationship between the geometry of the universe and its shape, and there are just three possibilities for the type of geometry: hyperbolic geometry, elliptic geometry, and Euclidean geometry. These are the geometries we study in this text. 
Book Description
Geometry with an Introduction to Cosmic Topology approaches 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 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 the habits of thought needed in advanced courses of the undergraduate mathematics curriculum. The text is also suited to independent study, with essays and discussions throughout.
Mathematicians and cosmologists have expended considerable amounts of effort investigating the shape of the universe, and this field of research is called cosmic topology. Geometry plays a fundamental role in this research. Under basic assumptions about the nature of space, there is a simple relationship between the geometry of the universe and its shape, and there are just three possibilities for the type of geometry: hyperbolic geometry, elliptic geometry, and Euclidean geometry. These are the geometries we study in this text.
This open book is licensed under a Creative Commons License (CC BY-SA). You can download Geometry with an Introduction to Cosmic Topology ebook for free in PDF format (3.2 MB).
Table of Contents
Chapter 1
An Invitation to Geometry
Chapter 2
The Complex Plane
Chapter 3
Transformations
Chapter 4
Geometry
Chapter 5
Hyperbolic Geometry
Chapter 6
Elliptic Geometry
Chapter 7
Geometry on Surfaces
Chapter 8
Cosmic Topology
Book Details
Title
Geometry with an Introduction to Cosmic Topology
Subject
Science and Mathematics
Publisher
Self-publishing
Published
2020
Pages
238
Edition
1
Language
English
ISBN13 Digital
9781717134813
ISBN10 Digital
1717134815
PDF Size
3.2 MB
License
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