Explorations in Topology - 1st Edition

Explorations in Topology

1st Edition

Map Coloring, Surfaces and Knots

Authors: David Gay
Imprint: Academic Press
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This book 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 Index


Academic Press
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About the Author

David Gay

Affiliations and Expertise

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