Western State College of Colorado

The Hat Game was first introduced in 1998 as a recreational puzzle.  It was not until after the puzzle spread to mathematicians across the country that it was realized that the puzzle had connections to coding theory.  This presentation will discuss the relationship between the game and Hamming Codes.  We will show how these codes can be used to find an optimal strategy for the Hat Game.

Students and faculty use Hamming codes in a simulated Hat Game.

Geometrician Paulus Gerdes has been studying the properties of pictograms and ideograms of the Tchokwe people in the Lunda region of Angola, Africa since the mid 1980s. He discovered that these designs had mathematical properties that generated a new class of designs. In honor of his source of inspiration he named the class Lunda-designs This presentation explores different aspects of the Lunda-design such as constructing Lunda-designs in general, constructing Lunda-design magic squares, and exploring a subset of the Lunda-design called the Liki-design.

The Central Limit Theorem is one of the most amazing theorems in all of probability and statistics.  Without this important theorem complex problems would be impossible to figure out unless much work was put into solving these problems.  The Central Limit Theorem was not completely proven until the mid-1900s, and it was then that this theorem put statistics and probability on the map.  Mathematicians started to look at this field as important and one in need of further discovery.  This theorem appears to be simple, but the proof itself is harder than one might imagine.  This theorem is so remarkable that one can use the result throughout probability to make complex problems appear easy.

Eigenvalues and eigenvectors provide a very useful characterization of the linear transformation associated with square matrices. One traditionally uses the derminant and Gaussian elimination to find eigenvalues and eigenvectors. In this talk we describe an alternative technique which can compute eigenvalues and eigenvectors without calculating determinants.

The board game RISK is one of the simpler strategy games, and is therefore useful in developing mathematical solutions to strategic scenarios. In this talk we answer two question of interest to RISK players by using Markov Chains.

Q1. If you attack a territory with your armies, what is the probability that you will capture this territory?

Q2. If you engage in a war, how many armies should you expect to lose depending on the number of armies your opponent has on that territory?