Explorations in Topology: Map Coloring, Surfaces and Knots

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David Gay provides his readers with 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 helps readers connect with the material and "learn by doing". Explorations in Topology is ideal for use in an introductory course for junior or senior mathematics majors and high school mathematics teachers; it is also a great resource for mathematicians/mathematics educators interested in curriculum development and original approaches to the teaching of advanced undergraduate mathematics.

This innovative text includes several user-friendly features, including end-of-chapter Investigations that give the reader opportunities to work on a variety of open-ended, non-routine problems, and make conjectures from which theorems emerge. The Notes sections in each chapter provide historical background, introduce standard terminology, and make connections with mainstream mathematics. The final chapter of Projects provides opportunities for continued involvement in research.

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Editorial Reviews

From the Publisher
"...the tasks that are asked of the reader are challenging and require clear thinking. This text could be an exiting tool for self study or a non-traditional course that is not just based on lectures."—Zentralblatt MATH, Sep-14

"Each chapter ends with a section marked "Notes", typically about two pages long, which gives a somewhat broader perspective of the material covered in that chapter, typically placing each topic in historical context, and sometimes giving precise definitions and statements of theorems."—MAA.org, May 4, 2014

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Product Details

  • ISBN-13: 9780123708588
  • Publisher: Elsevier Science
  • Publication date: 11/15/2006
  • Pages: 352
  • Product dimensions: 9.00 (w) x 6.00 (h) x 0.94 (d)

Table of Contents

Preface     vii
Acknowledgments     xi
Acme Does Maps and Considers Coloring Them     1
Acme Adds Tours     27
Acme Collects Data from Maps     49
Acme Collects More Data, Proves a Theorem, and Returns to Coloring Maps     73
Acme's Solicitor Proves a Theorem: the Four-Color Conjecture     89
Acme Adds Doughnuts to Its Repertoire     103
Acme Considers the Mobius Strip     125
Acme Creates New Worlds: Klein Bottles and Other Surfaces     149
Acme Makes Order Out of Chaos: Surface Sums and Euler Numbers     177
Acme Classifies Surfaces     205
Acme Encounters the Fourth Dimension     225
Acme Colors Maps on Surfaces: Heawood's Estimate     253
Acme Gets All Tied Up with Knots     271
Where to Go from Here: Projects     313
Index     331
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