Explorations in Topology

Explorations in Topology

Map Coloring, Surfaces and Knots

2nd Edition - December 4, 2013

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  • Author: David A. Gay
  • eBook ISBN: 9780124166400

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Description

Explorations in Topology, Second Edition, provides students a rich experience with low-dimensional topology (map coloring, surfaces, and knots), enhances their geometrical and topological intuition, empowers them with new approaches to solving problems, and provides them with experiences that will help them make sense of future, more formal topology courses. The book's innovative story-line style models the problem-solving process, presents the development of concepts in a natural way, and engages students in meaningful encounters with the material. The updated end-of-chapter investigations provide opportunities to work on many open-ended, non-routine problems and, through a modified "Moore method," to make conjectures from which theorems emerge. The revised end-of-chapter notes provide historical background to the chapter's ideas, introduce standard terminology, and make connections with mainstream mathematics. The final chapter of projects provides ideas for continued research. Explorations in Topology, Second Edition, enhances upper division courses and is a valuable reference for all levels of students and researchers working in topology.

Key Features

  • Students begin to solve substantial problems from the start
  • Ideas unfold through the context of a storyline, and students become actively involved
  • The text models the problem-solving process, presents the development of concepts in a natural way, and helps the reader engage with the material

Readership

Upper division, junior/senior mathematics majors and for high school mathematics teachers; mathematicians/mathematics educators interested/specializing in curriculum development.

Table of Contents

  • Dedication

    Preface

    To the Reader

    Format of the Chapters

    Overview of the Chapters

    Success in the Course for Which the Book Is Designed

    Instructor’s Manual

    Acknowledgments

    1. Acme Does Maps and Considers Coloring Them

    Scene 1

    Scene 2

    Scene 3

    Scene 4

    Investigations, Questions, Puzzles, and More

    Notes

    References

    2. Tours

    Scene 1

    Scene 2

    Scene 3

    Scene 4

    Investigations, Questions, Puzzles, and More

    Notes

    References

    3. Maps Data

    Scene 1

    Scene 2

    Scene 3

    Scene 4

    Scene 5

    Investigations, Questions, Puzzles, and More

    Notes

    References

    4. Map Data and Map Coloring

    Scene 1

    Scene 2

    Scene 3

    Investigations, Questions, Puzzles, and More

    Notes

    References

    5. How to Color a Map with Four Colors

    Scene 1

    Investigations, Questions, Puzzles, and More

    Notes

    References

    6. Doughnuts

    Scene 1

    Scene 2

    Scene 3

    Scene 4

    Investigations, Questions, Puzzles, and More

    Notes

    References

    7. The Möbius Strip

    Scene 1

    Scene 2

    Scene 3

    Scene 4

    Investigations, Questions, Puzzles, and More

    Notes

    References

    8. New Worlds: Klein Bottles and Other Surfaces

    Scene 1

    Scene 2

    Scene 3

    Investigations, Questions, Puzzles, and More

    Notes

    References

    9. Surface Sums and Euler Numbers

    Scene 1

    Scene 2

    Scene 3

    Scene 4

    Investigations, Questions, Puzzles, and More

    Notes

    References

    10. Classification of Surfaces

    Scene 1

    Scene 2

    Scene 3

    Investigations, Questions, Puzzles, and More

    Notes

    References

    11. Classification (Part II), Existence and Four-Space

    Scene 1

    Scene 2

    Scene 3

    Scene 4

    Investigations, Questions, Puzzles, and More

    Notes

    References

    12. Coloring Maps on Surfaces

    Investigations, Questions, Puzzles, and More

    Notes

    References

    13. Knots

    Scene 1

    Scene 2

    Scene 3

    Scene 4

    Investigations, Questions, Puzzles, and More

    Notes

    References

    14. Projects

    Project Ideas

    I Map Coloring

    II Surfaces

    III Surfaces and Maps

    IV Three-Space

    V Knots and Links

    VI Miscellaneous

    Resources

    References

    Communicating Project Results

Product details

  • No. of pages: 332
  • Language: English
  • Copyright: © Elsevier 2013
  • Published: December 4, 2013
  • Imprint: Elsevier
  • eBook ISBN: 9780124166400

About the Author

David A. Gay

Affiliations and Expertise

Department of Mathematics, University of Arizona, Tucson, AZ, USA

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