Explorations in topology map coloring, surfaces, and knots
1. Acme does maps and considers coloring them2. Tours -- 3. Maps data -- 4. Map data and map coloring -- 5. How to color a map with four colors -- 6. Doughnuts -- 7. The Möbius strip -- 8. New worlds: Klein bottles and other surfaces -- 9. Surface sums and Euler numbers -- 10. Classification of surf...
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
London u.a.
Elsevier
2014
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| Ausgabe: | 2. ed. |
| Schriftenreihe: | Elsevier insights series
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| Schlagworte: | |
| Online Zugang: | Verlagsangaben Inhaltstext |
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Tag hinzufügen | Zusammenfassung: | 1. Acme does maps and considers coloring them2. Tours -- 3. Maps data -- 4. Map data and map coloring -- 5. How to color a map with four colors -- 6. Doughnuts -- 7. The Möbius strip -- 8. New worlds: Klein bottles and other surfaces -- 9. Surface sums and Euler numbers -- 10. Classification of surfaces -- 11. Classification (Part II), existence and four-space -- 12. Coloring maps on surfaces -- 13. Knots -- 14. Projects. 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 will help them make sense of future, more formal topology courses. The book's innovative story-line style models the problem-solving process, presents the development of concepts in a natural way, and engages students in meaningful encounters with the material. The updated end-of-chapter investigations provide opportunities to work on many open-ended, non-routine problems and, through a modified "Moore method," to make conjectures from which theorems emerge. The revised 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 ideas for continued research. Explorations in Topology, Second Edition, enhances upper division courses and is a valuable reference for all levels of students and researchers working in topology. Upper division, junior/senior mathematics majors and for high school mathematics teachers; mathematicians/mathematics educators interested/specializing in curriculum development.-- 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 will help them make sense of future, more formal topology courses. The book's innovative story-line style models the problem-solving process, presents the development of concepts in a natural way, and engages students in meaningful encounters with the material. The updated end-of-chapter investigations provide opportunities to work on many open-ended, non-routine problems and, through a modified "Moore method," to make conjectures from which theorems emerge. The revised 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 ideas for continued research. Explorations in Topology, Second Edition, enhances upper division courses and is a valuable reference for all levels of students and researchers working in topology. Upper division, junior/senior mathematics majors and for high school mathematics teachers; mathematicians/mathematics educators interested/specializing in curriculum development.-- |
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| Beschreibung: | XIII, 315 S. Ill., zahlr. graph. Darst. |
| ISBN: | 0124166482 0-12-416648-2 9780124166486 978-0-12-416648-6 |