Overview

Tiling theory provides a wonderful opportunity to illustrate both the beauty and utility of mathematics. It has all the relevant ingredients: there are stunning pictures; open problems can be stated without having to spend months providing the necessary background; and there are both deep mathematics and applications. Furthermore, tiling theory happens to be an area where many of the sub-fields of mathematics overlap. Tools can be applied from linear algebra, algebra, analysis, geometry, topology, and combinatorics. As such, it makes for an ideal capstone course for undergraduates or an introductory course for graduate students. This material can also be used for a lower-level course by skipping the more technical sections. In addition, readers from a variety of disciplines can read the book on their own to find out more about this intriguing subject. This book covers the necessary background on tilings and then delves into a variety of fascinating topics in the field, including symmetry groups, random tilings, aperiodic tilings, and quasicrystals. Although primarily focused on tilings of the Euclidean plane, the book also covers tilings of the sphere, hyperbolic plane, and Euclidean 3-space, including knotted tilings. Throughout, the book includes open problems and possible projects for students. Readers will come away with the background necessary to pursue further work in the subject.

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9781470474614

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Reviews

“In his book, Adams provides many fantastic hiking paths suitable for a wide range of readers. The paths are all walkable, and there is no need to bring ropes or carabiners. The hiking paths contain many scenic points where we can take rest and see interesting tilings. Occasionally along the path, the dimension leaps from 2 to 3. A hiker might notice that the metric system changes from Euclidean to hyperbolic. The paths are open-ended with the possibility that a hiker constructs a brand new path to a new scenic point.” - Keiko Kawamuro (University of Iowa), AMS Notices

Author Information

Colin Adams, Williams College, Williamstown, MA.

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