Explorations in Topology

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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 would help them make sense of a future, more formal topology course. The innovative story-line style of the text models the problem-solving process, presents the development of concepts in a natural way, and through its engaging informality seduces the reader into meaningful encounters with the material. The updated end-of-chapter Investigations give the reader opportunities to work on many open-ended, non-routine problems and, through a modified "Moore method, " to make conjectures from which theorems emerge. The students emerge from these experiences owning concepts and results. The revised end-of-chapter Notes provide historical background to the chapter's ideas, introduces standard terminology, and makes connections with mainstream mathematics. The final chapter of projects provides opportunities for continued involvement in "research" beyond the topics of the book. Explorations in Topology, Second Edition, will enhance an upper division course or prove a valuable reference for all levels of students and researchers working in topology.