Explorations in Topology

This book gives students a rich experience with low-dimensional topology, enhance formal and topological course, empower them with the future, more formal topology course. The innovative idea-solving process, presents the development of ideas in a natural way. The end-of-chapter Investigations give a reader the opportunity 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 emerge from these experiences. The end-of-chapter Notes provide historical background, and introduce combinations with mainstream mathematics. The final chapter of the topic 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 the storyline, and students have become involved
* The text models the problem-solving process, and the reader with the material

Preface vii
Chapter 1: Acme Does Maps and Considers Coloring Them
Chapter 2: Acme Adds Tours
Chapter 3: Acme Collects Data from Maps
Chapter 4: Acme Collects More Data, Proves and Theorem, and Returns to Coloring Maps
Chapter 5: Acme's Solicitor Proves and Theorem: the Four-Color Conjecture
Chapter 6: Acme Adds Donuts to Its Repertoire
Chapter 7: Acme Considers the Möbius Strip
Chapter 8: Acme Creates New Worlds: Klein Bottles and Other Surfaces
Chapter 9: Acme Makes Order Out of Chaos: Surface Sums and Euler Numbers
Chapter 10: Acme Classifies Surfaces
Chapter 11: Acme Encounters the Fourth Dimension
Chapter 12: Acme Colors on Surfaces: Heawood's Estimate
Chapter 13: Acme Gets All Tied Up with Knots
Chapter 14: Where to Go from Here: Projects
index