Colloquia

Dr. P.Mezo: Images of Symmetry

1:00-2:00, MacPhail Room (Herzberg 4351)

What makes an object symmetrical? We will give a mathematical answer to this question in the context of group theory. We will then classify beautiful symmetries appearing in both nature and artifacts. No mathematical background is required.

Dr. Dave Amundsen: Chaos - From Order to Disorder and Back

1:00-2:00, MacPhail Room (Herzberg 4351)

The notion of chaos is generally associated with disorder and lack of predictability. In mathematics the theory of chaos indeed applies to systems ostensibly with these characteristics, however beneath this there lies discernible structure which can be analyzed and quantified. This in turn leads to useful concepts and techniques which may be applied to systems where such behaviour is observed, such as fluid flow, finance, and meteorology. With the help of visualization packages such as MATLAB, I will demonstrate how chaotic behaviour arises in certain simple models, and how it can in turn be characterized and understood. This talk will be geared to a general audience and no prior knowledge of nonlinear dynamics will be assumed.

Dr. Brett Stevens: Scheduling the Video Game Olympics Using Geometry

1:00-2:00, MacPhail Room (Herzberg 4351)

Every year at The University of Mary Washington a computer science professor holds a Video Game Olympics. The general structure has been fairly consistent: There are n² participants in the tournament. At any given moment, these participants are in groups of size n, in one of n distinct rooms, competing against one another. Each room contains a single video game. After the players finish a round, they all gather their belongings and leave the room in order to move on to a new room to play the next round. At the end of the evening, every player will have played every game on time. Equivalently, every participant will have visited every room exactly once. We wish to balance the tournament as much as possible meaning that we would like the most possible pairs of people to play against each other and correspondingly, reduce the number of times a pair plays against each other more than once. What are the best tournaments we can construct? Answering this question will introduce us to finite geometries, a beautiful subject which connects to algebra and discrete mathematics.

Dr. Angello Mingerelli: The History of Zero and Finance Through the Middle Ages

1:00-2:00, MacPhail Room (Herzberg 4351)

Blackjack and Ramanajan

1:00-2:00, MacPhail Room (Herzberg 4351)

Blackjack

Speaker: Steven Wu

Billions are poured into a gambling industry annually that is designed for the house edge to rake in profits. A New York Times bestseller written by Edward O. Thorp resulted from the phenomenon discovered that flipped the odds of one casino game, Blackjack, in favor to the player. After a brief overview on the rules of how to play, features that distinguish it as capable of a positive expectation for the player, I will detail the pertinent mathematics that explain how each unique rule, from doubling down to the option of taking insurance, affects the expectation of the game. After describing what constitutes "Basic Strategy", I will show how Thorp manipulated the probabilities using card counting to produce a winning strategy that swept the nation through use of examples of certain game scenarios.

The Story of Srinivasa Ramanujan

Speaker: Arthur Mehta

The talk will be split into two segments. The first segment will consist of a brief telling of the one of the most romantic stories in the history of mathematics: the story of Srinivasa Ramanujan. Ramanujan was a self-taught Indian mathematician who was born into poverty. After years of obscurity his talent was finally recognized by G.H Hardy, a prominent mathematician at Trinity College, Cambridge. The discovery of Ramanujan eventually resulted with him traveling to England to work alongside Hardy. This led to one of the most productive mathematical partnerships of the 20th century, and resulted in works contributing to a wide variety of areas, including Number Theory, Analytic Combinatorics, Infinite Fractions and Infinite Series. This segment will be followed by a segment devoted to examining a select set of works completed by Ramanujan. These works will include a look at Ramanujan's work on Highly Composite Numbers: his contribution to determining the number of partitions of a given number. Lastly we will examine a host of intriguing identities, infinite series and infinite fractions produced by Ramanujan.