Explorations in Topology: Map Coloring, Surfaces and Knots / Edition 2

by David Gay

Overview

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.

Product Details

ISBN-13:	9780124166486
Publisher:	Elsevier Science
Publication date:	12/10/2013
Edition description:	2nd ed.
Pages:	332
Product dimensions:	6.00(w) x 9.10(h) x 1.00(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

What People are Saying About This

From the Publisher

An innovative exploration into topology, empowering the reader with new approaches to problem solving and mathematical skills

Editorial Reviews

"...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

From the Publisher