Explorations in Topology, 1st Edition

  • Published By:
  • ISBN-10: 0124166407
  • ISBN-13: 9780124166400
  • DDC: 514
  • Grade Level Range: College Freshman - College Senior
  • 332 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013

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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.

Table of Contents

Front Cover.
Half Title Page.
Title Page.
Copyright Page.
1: Acme Does Maps and Considers Coloring Them.
2: Tours.
3: Maps Data.
4: Map Data and Map Coloring.
5: How to Color a Map with Four Colors.
6: Doughnuts.
7: The Möbius Strip.
8: New Worlds: Klein Bottles and Other Surfaces.
9: Surface Sums and Euler Numbers.
10: Classification of Surfaces.
11: Classification (Part II), Existence and Four-Space.
12: Coloring Maps on Surfaces.
13: Knots.
14: Projects.