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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
---|---|---|---|---|---|
Searching... | 30000010328442 | QA611 G39 2014 | Open Access Book | Book | Searching... |
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Summary
Summary
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.
Table of Contents
Chapter 1 ACME makes maps and considers coloring them |
Chapter 2 ACME adds tours to its services |
Chapter 3 ACME collects data from maps |
Chapter 4 ACME gathers more data, proves a theorem, and returns to coloring maps |
Chapter 5 ACME's lawyer proves 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 bottle and other surfaces |
Chapter 9 ACME makes order out of chaos - surface sum 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 |