Explorations in Topology: Map Coloring, Surfaces and Knots

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9781493300884: 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 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

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About the Author:

David Gay joined Intel Research in Berkeley in 2001 where he has been a designer and the principal implementer of the nesC language, the C dialect used to implement the TinyOS sensor network operating system, and its applications. He has a diploma in Computer Science from the Swiss Federal Institute of Technology in Lausanne and a Ph.D. from the University of California, Berkeley.

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