Explorations in Topology
Map Coloring, Surfaces and Knots
- 2nd Edition - December 4, 2013
- Latest edition
- Author: David Gay
- Language: English
Explorations in Topology, Second Edition, provides students a rich experience with low-dimensional topology (map coloring, surfaces, and knots), enhances their geometric… Read more
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Description
Description
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.
Key features
Key features
- Students begin to solve substantial problems 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
Readership
Readership
Table of contents
Table of contents
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
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Scene 4
Investigations, Questions, Puzzles, and More
Notes
References
2. Tours
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Scene 2
Scene 3
Scene 4
Investigations, Questions, Puzzles, and More
Notes
References
3. Maps Data
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Scene 2
Scene 3
Scene 4
Scene 5
Investigations, Questions, Puzzles, and More
Notes
References
4. Map Data and Map Coloring
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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
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Scene 2
Scene 3
Scene 4
Investigations, Questions, Puzzles, and More
Notes
References
7. The Möbius Strip
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Scene 2
Scene 3
Scene 4
Investigations, Questions, Puzzles, and More
Notes
References
8. New Worlds: Klein Bottles and Other Surfaces
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Scene 2
Scene 3
Investigations, Questions, Puzzles, and More
Notes
References
9. Surface Sums and Euler Numbers
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Scene 2
Scene 3
Scene 4
Investigations, Questions, Puzzles, and More
Notes
References
10. Classification of Surfaces
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Scene 2
Scene 3
Investigations, Questions, Puzzles, and More
Notes
References
11. Classification (Part II), Existence and Four-Space
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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
Review quotes
Review quotes
"...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
Product details
Product details
- Edition: 2
- Latest edition
- Published: October 30, 2018
- Language: English
About the author
About the author
DG