Explorations in Topology, 2nd Edition

Map Coloring, Surfaces and Knots

 
Explorations in Topology, 2nd Edition,David Gay,ISBN9780124166486
 
 
 

  

Elsevier

9780124166486

9780124166400

332

229 X 152

An innovative exploration into topology, empowering the reader with new approaches to problem solving and mathematical skills

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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

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.

Readership

Upper division, junior/senior mathematics majors and for high school mathematics teachers; mathematicians/mathematics educators interested/specializing in curriculum development.

David Gay

Affiliations and Expertise

Department of Mathematics, University of Arizona, Tucson, AZ, USA

Explorations in Topology, 2nd Edition

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

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Investigations, Questions, Puzzles, and More

Notes

References

2. Tours

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Investigations, Questions, Puzzles, and More

Notes

References

3. Maps Data

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Investigations, Questions, Puzzles, and More

Notes

References

4. Map Data and Map Coloring

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Investigations, Questions, Puzzles, and More

Notes

References

5. How to Color a Map with Four Colors

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Investigations, Questions, Puzzles, and More

Notes

References

6. Doughnuts

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Investigations, Questions, Puzzles, and More

Notes

References

7. The Möbius Strip

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Investigations, Questions, Puzzles, and More

Notes

References

8. New Worlds: Klein Bottles and Other Surfaces

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Investigations, Questions, Puzzles, and More

Notes

References

9. Surface Sums and Euler Numbers

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Investigations, Questions, Puzzles, and More

Notes

References

10. Classification of Surfaces

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Investigations, Questions, Puzzles, and More

Notes

References

11. Classification (Part II), Existence and Four-Space

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Investigations, Questions, Puzzles, and More

Notes

References

12. Coloring Maps on Surfaces

Investigations, Questions, Puzzles, and More

Notes

References

13. Knots

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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

Quotes and reviews

"...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

 
 
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