Game theory is a fascinating and interdisciplinary branch of mathematics that looks at situations in which “players” must chose among several different actions to achieve the best possible outcome. Originally developed as a tool in economics, game theory is now used to explore many different fields, including politics, psychology, biology, ecology and philosophy, as well as to analyze standard recreational games. In this course, we will explore the basic ideas of game theory and some of its many applications, including the Prisoner’s Dilemma and its relationship to the Cold War, evolutionary theory and popular culture. We will also look at the role of mathematics in social choice theory. Social choice theory asks: are there reasonable and fair ways to select a president; measure the power that individuals have within organizations; or divide up assets in a divorce settlement. Arrow’s famous Impossibility Theorem says that it is impossible to design an election system that is fair all the time. We will study this result using simple geometric tools and try to understand the many paradoxes inherent in voting theory.