Explorations in Topology: Map Coloring, Surfaces and Knots
Autor David Gayen Limba Engleză Paperback – 31 oct 2006
* 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"
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Specificații
Cuprins
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 Möbius 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
Recenzii
"...the tasks that are asked of the reader are challenging and require clear thinking. This text could be an exiting tool for self study or a non-traditional course that is not just based on lectures." --Zentralblatt MATH, Sep-14 "Each chapter ends with a section marked "Notes", typically about two pages long, which gives a somewhat broader perspective of the material covered in that chapter, typically placing each topic in historical context, and sometimes giving precise definitions and statements of theorems." --MAA.org, May 4, 2014