Explorations in Topology: Map Coloring,
- Author: Gay
- Publisher: Elservier
- Publish Date: 2017-10-30
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.
| Author | Gay |
|---|---|
| Publish Date | Oct 30, 2017 |
| Table Of Content | Dedication Preface To the Reader Format of the Chapters Overview of the Chapters Success in the Course for Which the Book Is Designed Instructor’s Manual Acknowledgments 1. Acme Does Maps and Considers Coloring Them Scene 1 Scene 2 Scene 3 Scene 4 Investigations, Questions, Puzzles, and More Notes References 2. Tours Scene 1 Scene 2 Scene 3 Scene 4 Investigations, Questions, Puzzles, and More Notes References 3. Maps Data Scene 1 Scene 2 Scene 3 Scene 4 Scene 5 Investigations, Questions, Puzzles, and More Notes References 4. Map Data and Map Coloring Scene 1 Scene 2 Scene 3 Investigations, Questions, Puzzles, and More Notes References 5. How to Color a Map with Four Colors Scene 1 Investigations, Questions, Puzzles, and More Notes References 6. Doughnuts Scene 1 Scene 2 Scene 3 Scene 4 Investigations, Questions, Puzzles, and More Notes References 7. The Möbius Strip Scene 1 Scene 2 Scene 3 Scene 4 Investigations, Questions, Puzzles, and More Notes References 8. New Worlds: Klein Bottles and Other Surfaces Scene 1 Scene 2 Scene 3 Investigations, Questions, Puzzles, and More Notes References 9. Surface Sums and Euler Numbers Scene 1 Scene 2 Scene 3 Scene 4 Investigations, Questions, Puzzles, and More Notes References 10. Classification of Surfaces Scene 1 Scene 2 Scene 3 Investigations, Questions, Puzzles, and More Notes References 11. Classification (Part II), Existence and Four-Space Scene 1 Scene 2 Scene 3 Scene 4 Investigations, Questions, Puzzles, and More Notes References 12. Coloring Maps on Surfaces Investigations, Questions, Puzzles, and More Notes References 13. Knots Scene 1 Scene 2 Scene 3 Scene 4 Investigations, Questions, Puzzles, and More Notes References 14. Projects Project Ideas I Map Coloring II Surfaces III Surfaces and Maps IV Three-Space V Knots and Links VI Miscellaneous Resources References Communicating Project Results |