Explorations in topology : map coloring, surfaces, and knots
著者
書誌事項
Explorations in topology : map coloring, surfaces, and knots
（Elsevier insights）
Elsevier, 2014
2nd ed
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注記
Includes bibliographical references
内容説明・目次
内容説明
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.
目次
CHAPTER 1: ACME makes maps and considers coloring themCHAPTER 2: ACME adds tours to its servicesCHAPTER 3: ACME collects data from maps CHAPTER 4: ACME gathers more data, proves a theorem, and returns to coloring mapsCHAPTER 5: ACME's lawyer proves the four color conjectureCHAPTER 6: ACME adds doughnuts to its repertoireCHAPTER 7: ACME considers the Moebius stripCHAPTER 8: ACME creates new worlds --- Klein bottle and other surfacesCHAPTER 9: ACME makes order out of chaos --- surface sum and Euler numbersCHAPTER 10: ACME classifies surfacesCHAPTER 11: ACME encounters the fourth dimensionCHAPTER 12: ACME colors maps on surfaces --- Heawood's estimateCHAPTER 13: ACME gets all tied up with knotsCHAPTER 14: Where to go from here --- Projects
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