Explorations in Topology Map Coloring, Surfaces And Knots

This book 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 chapters 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 materialGay, David is the author of 'Explorations in Topology Map Coloring, Surfaces And Knots', published 2006 under ISBN 9780123708588 and ISBN 0123708583.