Explorations in Topology
Map Coloring, Surfaces and Knots
- 1st Edition - November 15, 2006
- Author: David Gay
- Language: English
Explorations in Topology gives students a rich experience with low-dimensional topology, enhances their geometrical and topological intuition, empowers them with new approache… Read more
Explorations in Topology gives students a rich experience with low-dimensional topology, enhances their geometrical and topological intuition, empowers them with new approaches to solving problems, and provides them with experiences that would help them make sense of a future, more formal topology course.
The innovative story-line style of the text models the problems-solving process, presents the development of concepts in a natural way, and through its informality seduces the reader into engagement with the material. The end-of-chapter Investigations give the reader opportunities to work on a variety of open-ended, non-routine problems, and, through a modified "Moore method", to make conjectures from which theorems emerge. The students themselves emerge from these experiences owning concepts and results. The 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 opportunities for continued involvement in "research" beyond the topics of the book.
- Students begin to solve substantial problems right 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
Upper division, junior/senior mathematics majors and for high school mathematics teachers; mathematicians/mathematics educators interested/specializing in curriculum development.
1. Acme Does Maps and Considers Coloring Them
2. Acme Adds Tours
3. Acme Collects Data from Maps
4. Acme Collects More Data, Proves a Theorem, and Returns to Coloring Maps
5. Acme’s Solicitor Proves a Theorem. the Four-Color Conjecture
6. Acme Adds Doughnuts to Its Repertoire
7. Acme Considers the Möbius Strip
8. Acme Creates New Worlds. Klein Bottles and Other Surfaces
9. Acme Makes Order Out of Chaos. Surface Sums and Euler Numbers
10. Acme Classifies Surfaces
11. Acme Encounters the Fourth Dimension
12. Acme Colors Maps on Surfaces. Heawood’s Estimate
13. Acme Gets All Tied Up with Knots
14. Where to Go from Here. Projects
2. Acme Adds Tours
3. Acme Collects Data from Maps
4. Acme Collects More Data, Proves a Theorem, and Returns to Coloring Maps
5. Acme’s Solicitor Proves a Theorem. the Four-Color Conjecture
6. Acme Adds Doughnuts to Its Repertoire
7. Acme Considers the Möbius Strip
8. Acme Creates New Worlds. Klein Bottles and Other Surfaces
9. Acme Makes Order Out of Chaos. Surface Sums and Euler Numbers
10. Acme Classifies Surfaces
11. Acme Encounters the Fourth Dimension
12. Acme Colors Maps on Surfaces. Heawood’s Estimate
13. Acme Gets All Tied Up with Knots
14. Where to Go from Here. Projects
- Edition: 1
- Published: November 15, 2006
- Language: English
DG
David Gay
Affiliations and expertise
Department of Mathematics, University of Arizona, Tucson, AZ, USA