The Tiling Book: An Introduction to the Mathematical Theory of Tilings - Softcover

Colin Adams (author)

Softcover

ISBN 10: 1470474611 ISBN 13: 9781470474614

Publisher: American Mathematical Society, 2022

Synopsis

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.

About this title

About the Author

Colin Adams, Williams College, Williamstown, MA.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2022
• ISBN 10: 1470474611
• ISBN 13: 9781470474614
• Binding: Paperback
• Language: English
• Number of pages: 298