Thirty minutes before the talk coffee and cookies will be
Bear Hall 211 at 2:30.
Title: Card Shuffling as a Dynamical System
Speaker: Russ Herman
How does a magician know that the eighth card in a deck of 50 cards
returns to it original position after only three perfect
shuffles? How many perfect shuffles will return a full deck of
cards to their original order? What is a "perfect" shuffle?
In this talk we will review some of the history and mathematics of the
perfect shuffle. We will explore models of the perfect shuffle of a
deck of arbitrary size, leading to a discrete dynamical system. In
particular, we will look at the dynamics of the doubling map and the
logistic map as a way of introducing standard notions from nonlinear
dynamics, such as fixed points, periodic orbits, symbolic dynamics and
chaos. This talk will be at a level accessible by undergraduates and is
meant as an introduction to discrete dynamical systems via card