Introduction to Tiling Theory

About this Course

About the Course

In this course, Professor Colin Adams (Williams College) explores tiling theory. In the first mini-lecture, we think about tilings found in everyday life and give the mathematical definition of a tiling. In the second mini-lecture, we learn how to generate complex monohedral tiles and think about tiling symmetries. In the third mini-lecture, we discuss the number of possible tiling patterns that can be made with differently shaped prototiles and then introduce random tilings. In the fourth mini-lecture, we explore uniform tilings and coronas. In the fifth mini-lecture, we discuss applications of aperiodic tilings to quasicrystals.

About the Lecturer

Colin Adams is the Thomas T. Read Professor of Mathematics at Williams College in in Williamstown, MA. His research interests are primarily in hyperbolic 3-manifolds and knot theory. He has often collaborated and published his research with students from SMALL, an undergraduate summer research program at Williams College. Professor Adams is the author of The Knot Book (1984), which has been praised for its accessible approach to advanced topics in knot theory. He has also written a comic book called Why Knot? (2004) that introduces knot theory to a more general audience. He has written and collaborated on many other books, including How to Ace Calculus: The Streetwise Guide (1998) and Zombies & Calculus (2014). He also writes Mathematically Bent, a column of math humour for The Mathematical Intelligencer, a mathematical journal published bySpringer. Professor Adams was awarded the Deborah and Franklin Tepper Haimo National Distinguished Teaching Award by the Mathematical Association of America in 1998 and the Robert Foster Cherry Great Teacher Award from Baylor University in 2003.