Explorations in Topology
Map Coloring, Surfaces and Knots
(Sprache: Englisch)
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...
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Produktdetails
Produktinformationen zu „Explorations in Topology “
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.
Klappentext zu „Explorations in Topology “
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
Inhaltsverzeichnis zu „Explorations in Topology “
Preface viiChapter 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 a Theorem, and Returns to Coloring Maps
Chapter 5: Acme's Solicitor Proves a Theorem: 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 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 Maps on Surfaces: Heawood's Estimate
Chapter 13: Acme Gets All Tied Up with Knots
Chapter 14: Where to Go from Here: Projects
Index
Bibliographische Angaben
- Autor: Gay
- 2007, 352 Seiten, 240 farbige Abbildungen, Maße: 15,2 x 23,4 cm, Kartoniert (TB), Englisch
- Verlag: Academic Press
- ISBN-10: 0123708583
- ISBN-13: 9780123708588
Sprache:
Englisch
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