A polytope exchange transformation is a (discontinuous) map from a polytope to itself that is a translation wherever it is defined. The 1-dimensional examples, interval exchange transformations, have been studied fruitfully for many years and have deep connections to other areas of mathematics, such as Teichmuller theory. This book introduces a general method for constructing polytope exchange transformations in higher dimensions and then studies the simplest example of the construction in detail. The simplest case is a 1-parameter family of polygon exchange transformations that turns out to...

In Really Big Numbers, mathematician and author, Richard Evan Schwartz, leads math lovers of all ages on an innovative and strikingly illustrated journey through the infinite number system. You Can Count on Monsters is a unique teaching tool that takes maths lovers on a journey designed to motivate kids to learn the fun of factoring and prime numbers.

This book introduces a simple dynamical model for a planar heat map that is invariant under projective transformations. The map is defined by iterating a polygon map, where one starts with a finite planar $N$-gon and produces a new $N$-gon by a prescribed geometric construction. One of the appeals of the topic of this book is the simplicity of the construction that yet leads to deep and far reaching mathematics. To construct the projective heat map, the author modifies the classical affine invariant midpoint map, which takes a polygon to a new polygon whose vertices are the midpoints of the...

Pay a visit to the Infinite Farm! In Life on the Infinite Farm, mathematician and award-winning children's book author Richard Schwartz teaches about infinity and curved space through stories of whimsical farm animals. Join Gracie, the shoe-loving cow with infinitely many feet, Hammerwood, the gum-loving crocodile with an endless mouth, and their friends as they navigate the challenges that come with being infinitely large. Children as young as 5 will enjoy the lighthearted illustrations and the fanciful approach to infinity. Older students (and even adult professional mathematicians) will...