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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 geometric… Read more
LIMITED OFFER
Immediately download your ebook while waiting for your print delivery. No promo code needed.
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.
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
DG