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Explorations in Topology - 1st Edition - ISBN: 9780123708588, 9780080492667

Explorations in Topology

1st Edition

Map Coloring, Surfaces and Knots

Author: David Gay
eBook ISBN: 9780080492667
Paperback ISBN: 9781493300884
Imprint: Academic Press
Published Date: 15th November 2006
Page Count: 352
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Explorations in Topology gives students a rich experience with low-dimensional topology, enhances their geometrical and topological intuition, empowers them with new approaches to solving problems, and provides them with experiences that would help them make sense of a future, more formal topology course.

The innovative story-line style of the text models the problems-solving process, presents the development of concepts in a natural way, and through its informality seduces the reader into engagement with the material. The end-of-chapter Investigations give the reader opportunities to work on a variety of open-ended, non-routine problems, and, through a modified "Moore method", to make conjectures from which theorems emerge. The students themselves emerge from these experiences owning concepts and results. The 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 opportunities for continued involvement in "research" beyond the topics of the book.

Key Features

  • Students begin to solve substantial problems right 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


Upper division, junior/senior mathematics majors and for high school mathematics teachers; individuals who are interested in innovative approaches to the teaching of advanced undergraduate mathematics; mathematicians/mathematics educators interested/specializing in curriculum development.

Table of Contents

Chapter 1: Acme Does Maps and Considers Coloring Them
Chapter 2: Acme Adds Tours
Chapter 3: Acme Collects Data from Maps
Chapter 4: Acme Collects More Data, Proves a Theorem, and Returns to Coloring Maps
Chapter 5: Acme’s Solicitor Proves a Theorem: the Four-Color Conjecture
Chapter 6: Acme Adds Doughnuts to Its Repertoire
Chapter 7: Acme Considers the Möbius Strip
Chapter 8: Acme Creates New Worlds: Klein Bottles and Other Surfaces
Chapter 9: Acme Makes Order Out of Chaos: Surface Sums and Euler Numbers
Chapter 10: Acme Classifies Surfaces
Chapter 11: Acme Encounters the Fourth Dimension
Chapter 12: Acme Colors Maps on Surfaces: Heawood’s Estimate
Chapter 13: Acme Gets All Tied Up with Knots
Chapter 14: Where to Go from Here: Projects


No. of pages:
© Academic Press 2006
15th November 2006
Academic Press
eBook ISBN:
Paperback ISBN:

About the Author

David Gay

Affiliations and Expertise

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

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