This course is principally a study of the calculus of functions of two or more variables, but also includes the study of vectors, vector-valued functions and their derivatives. The course covers limits, partial derivatives, multiple integrals, and includes applications in physics. Credit cannot be granted for both this course and MATH-221.

This course introduces sample spaces and events, axioms of probability, counting techniques, conditional probability and independence, distributions of discrete and continuous random variables, joint distributions (discrete and continuous), the central limit theorem, descriptive statistics, interval estimation, and applications of probability and statistics to real-world problems. A statistical package such as Minitab or R is used for data analysis and statistical applications.

Classical game theory models conflict and cooperation between rational decision-making agents with hidden parameters. Topics include matrix games, Nash equilibria, the minimax theorem, prisoner’s dilemma, and cooperative games. Applications can include adaptive or statistical decision theory, artificial intelligence (online learning, multi-agent systems), biology (evolutionary games, signaling behavior, fighting behavior), economics and business (auctions, bankruptcy, bargaining, pricing, two-sided markets), philosophy (ethics, morality, social norms), and political science (apportionment, elections, military strategy, stability of government, voting).

This course is a faculty-directed project that could be considered original in nature. The level of work is appropriate for students in their final two years of undergraduate study.

Masters-level research by the candidate on an appropriate topic as arranged between the candidate and the research advisor.