
Explorations in Topology
Map Coloring, Surfaces and Knots
David Gay(Author)
Academic Press
Published on 7. August 2007
Book
Hardback
352 pages
978-0-12-370858-8 (ISBN)
Article exhausted; check for reprint
Description
Explorations in Topology 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.
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.
More details
Language
English
Place of publication
San Diego
United States
Publishing group
Elsevier Science Publishing Co Inc
Target group
College/higher education
Upper division, junior/senior mathematics majors and for high school mathematics teachers; mathematicians/mathematics educators interested/specializing in curriculum development.
Illustrations
Approx. 240 illustrations (250 in full color)
Dimensions
Height: 229 mm
Width: 152 mm
Weight
580 gr
ISBN-13
978-0-12-370858-8 (9780123708588)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
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08/2007
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11/2006
Academic Press
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Content
Preface vii
Chapter 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 Moebius 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
Chapter 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 Moebius 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