Introduction to Topology Pure and Applied

Learn the basics of point-set topology with the understanding of its real-world application to a variety of other subjects including science, economics, engineering, and other areas of mathematics. Introduces topology as an important and fascinating mathematics discipline to retain the readers interest in the subject. Is written in an accessible way for readers to understand the usefulness and importance of the application of topology to other fields. Introduces topology concepts combined with their real-world application to subjects such DNA, heart stimulation, population modeling, cosmology, and computer graphics. Covers topics including knot theory, degree theory, dynamical systems and chaos, graph theory, metric spaces, connectedness, and compactness.A useful reference for readers wanting an intuitive introduction to topology.

Colin Adams is the Thomas T. Read Professor of Mathematics at Williams College. He received his PhD from the University of Wisconsin–Madison in 1983. He is particularly interested in the mathematical theory of knots, their applications, and their connections with hyperbolic geometry. He is the author of The Knot Book, an elementary introduction to the mathematical theory of knots and co-author with Joel Hass and Abigail Thompson of How to Ace Calculus: The Streetwise Guide, and How to Ace the Rest of Calculus: the Streetwise Guide, humorous supplements to calculus. He has authored a variety of research articles on knot theory and hyperbolic 3-manifolds. A recipient of the Deborah and Franklin Tepper Haimo Distinguished Teaching Award from the Mathematical Association of America (MAA) in 1998, he was a Polya Lecturer for the MAA for 1998-2000, and is a Sigma Xi Distinguished Lecturer for 2000-2002. He is also the author of mathematical humor column called "Mathematically Bent" which appears in the Mathematical Intelligencer.

Robert Franzosa is a professor of mathematics at the University of Maine. He received his Ph.D from the University of Wisconsin–Madison in 1984. He has published research articles on dynamical systems and applications of topology to geographic information systems. He has been actively involved in curriculum development and in education outreach activities throughout Maine. He is currently co-authoring a text, Algebraic Models in Our World, which is targeted for college-level general-education mathematics audiences. He was the recipient of the 2003 Presidential Outstanding Teaching Award at the University of Maine.

Introduction
What is Topology?
Example Applications
Euclidean Space
Operations on Sets
Functions
Relations
Topological Spaces
Open Sets and the Definition of a Topology
Basis for a Topology
RNA Phenotype Spaces
Closed Sets
Interior, Closure, and Boundary
Interior and Closure of Sets
Limit Points
The Boundary of a Set
An Application to Geographic Information Systems
Creating New Topological Spaces
The Subspace Topology
The Product Topology
Configuration Spaces for Physical Systems
The Quotient Topology
Continuous Functions and Homeomorphisms
Continuity
Homeomorphisms
The Forward Kinematics Map in Robotics
Metric Spaces
Metrics
Metrics and Information
Properties of Metric Spaces
Connectedness
A First Approach to Connectedness
Distinguishing Topological Spaces Via Connectedness
The Intermediate Value Theorem
Path Connectedness
Automated Guided Vehicles
Compactness
Open Coverings and Compact Spaces
Compactness in Euclidean Space
Compactness and Calculus
Limit Point Compactness
The One-Point Compactification
Dynamical Systems and Chaos
Degree Theory
Fixed Points
Knot Theory
Manifolds
Embeddings
Graph Theory
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Introduction to Topology Pure and Applied

Summary

Author Biography

Table of Contents

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