Overview

"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.* 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"

Full Product Details

Author:   David Gay (Department of Mathematics, University of Arizona, Tucson, AZ, USA)
Publisher:   Elsevier Science Publishing Co Inc
Imprint:   Academic Press Inc
Dimensions:   Width: 15.20cm , Height: 2.10cm , Length: 22.90cm
Weight:   0.570kg
ISBN:  

9780123708588

ISBN 10:   0123708583
Pages:   352
Publication Date:   07 August 2007
Audience:   College/higher education ,  Tertiary & Higher Education
Replaced By:   9780124166486
Format:   Hardback
Publisher's Status:   Out of Print
Availability:   In Print  
Limited stock is available. It will be ordered for you and shipped pending supplier's limited stock.

Table of Contents

Preface vii 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

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