Explorations in Topology

Explorations in Topology

Map Coloring, Surfaces and Knots

1st Edition - November 15, 2006

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  • Author: David Gay
  • eBook ISBN: 9780080492667

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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

  • Preface
    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

Product details

  • No. of pages: 352
  • Language: English
  • Copyright: © Academic Press 2006
  • Published: November 15, 2006
  • Imprint: Academic Press
  • eBook ISBN: 9780080492667

About the Author

David Gay

Affiliations and Expertise

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

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