This is the first in a two-course sequence intended for students majoring in mathematics, science, or engineering. It emphasizes the understanding of concepts, and using them to solve physical problems. The course covers functions, limits, continuity, the derivative, rules of differentiation, applications of the derivative, Riemann sums, definite integrals, and indefinite integrals.

This course introduces students to ideas and techniques from discrete mathematics that are widely used in Computer Science. Students will learn about the fundamentals of propositional and predicate calculus, set theory, relations, recursive structures and counting. This course will help increase students’ mathematical sophistication and their ability to handle abstract problems.

This course prepares students for professions that use mathematics in daily practice, and for mathematics courses beyond the introductory level where it is essential to communicate effectively in the language of mathematics. It covers various methods of mathematical proof, starting with basic techniques in propositional and predicate calculus and set theory, and then moving to applications in advanced mathematics.

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).

Combinatorial games are two-player games with perfect information and no randomness or element of chance (such as Go, Chess, and Checkers). The course covers basic techniques of game theory, outcome classes, sums of games, the algebra of games, and top-down induction. Analyses will emphasize no-draw games terminating in a finite number of moves such as Nim, Domineering, Hackenbush, Chomp, and Amazons.

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.

This course is a faculty-guided investigation into appropriate topics that are not part of the curriculum.