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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 | |
Table of Contents provided by Publisher. All Rights Reserved. |