Explorations in Topology: Map Coloring, Surfaces and Knots

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.

Students begin to solve substantial problems from the startIdeas unfold through the context of a storyline, and students become actively involvedThe text models the problem-solving process, presents the development of concepts in a natural way, and helps the reader engage with the material

CHAPTER 1: ACME makes maps and considers coloring them
CHAPTER 2: ACME adds tours to its services
CHAPTER 3: ACME collects data from maps
CHAPTER 4: ACME gathers more data, proves a theorem, and returns to coloring maps
CHAPTER 5: ACME’s lawyer proves the four color conjecture
CHAPTER 6: ACME adds doughnuts to its repertoire
CHAPTER 7: ACME considers the Möbius strip
CHAPTER 8: ACME creates new worlds --- Klein bottle and other surfaces
CHAPTER 9: ACME makes order out of chaos --- surface sum and Euler numbers
CHAPTER 10: ACME classifies surfaces
CHAPTER 11: ACME encounters the fourth dimension
CHAPTER 12: ACME colors maps on surfaces --- Heawood’s estimate
CHAPTER 13: ACME gets all tied up with knots
CHAPTER 14: Where to go from here --- Projects