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Textbook

Topology of Surfaces, Knots, and Manifolds

ISBN: 978-0-471-35544-1
176 pages
January 2001, ©2001
Topology of Surfaces, Knots, and Manifolds (0471355445) cover image

Description

Topology of Surfaces, Knots, and Manifolds offers an intuition-based and example-driven approach to the basic ideas and problems involving manifolds, particularly one- and two-dimensional manifolds. A blend of examples and exercises leads the reader to anticipate general definitions and theorems concerning curves, surfaces, knots, and links-the objects of interest in the appealing set of mathematical ideas known as "rubber sheet geometry." The result is a text that is accessible to a broad range of undergraduate students, yet still provides solid coverage of the mathematics underlying these topics.

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Table of Contents

Introduction and Intuitive Ideas

Manifolds

Classification of Compact Surfaces

Putting More Structure on Surfaces

Graphs and Topology

Knot Theory

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The Wiley Advantage

  • A student-friendly writing style provides a clear exposition of concepts.
  • Mathematical results are presented accurately and main definitions, theorems, and remarks are clearly highlighted for easy reference.
  • Carefully selected exercises, some of which require hands-on work or computer-aided visualization, reinforce the understanding of concepts or further develop ideas.
  • Extensive use of illustrations helps the students develop an intuitive understanding of the material.
  • Frequent historical references chronicle the development of the subject and highlight connections between topology and other areas of mathematics.
  • Chapter summary sections offer a review of each chapter's topics and a transitional look forward to the next chapter.
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