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Introduction to Topology Pure and Applied

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ISBN-10: 0131848690

ISBN-13: 9780131848696

Edition: 2008

Authors: Colin Adams, Robert Franzosa

List price: $209.80
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Description:

For juniors and seniors of various majors, taking a first course in topology. This book introduces topology as an important and fascinating mathematics discipline. Students learn first the basics of point-set topology, which is enhanced by the real-world application of these concepts to science, economics, and engineering as well as other areas of mathematics. The second half of the book focuses on topics like knots, robotics, and graphs. The text is written in an accessible way for a range of undergraduates to understand the usefulness and importance of the application of topology to other fields.
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Book details

List price: $209.80
Copyright year: 2008
Publisher: Prentice Hall PTR
Publication date: 6/18/2007
Binding: Hardcover
Pages: 512
Size: 7.00" wide x 9.50" long x 1.25" tall
Weight: 2.354
Language: English

Colin Adams is the Thomas T. Read Professor of Mathematics at Williams College. His books include "The Knot Book", "Riot at the Calc Exam and Other Mathematically Bent Stories", and "How to Ace Calculus: The Streetwise Guide". He is the humor columnist for the "Mathematical Intelligencer".

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