Senior Seminar Topics
نویسنده
چکیده
2006-2007 Discrete Probability Instructor: Abra Brisbin (CAM) The first few days introduced set theory and combinatorics. After that, they turned to probability distributions, expected value, and independence. In the second half of the course, they worked on conditional probability, Bayes’ Theorem, the Monte Carlo method, and Markov chains. Throughout the course, they tackled questions involving applications of probability in biology, medicine, social policy, and everyday life. Game Theory Instructor: Jason Anema (Math) This course began with a study of matrix games and a proof of the existence of Nash equilibria. Students then studied decision graphs, which included backwards induction, uncertainty and multiple-person decisions, and as an example played “Indian Poker” in class. The next topic was the problem of maximizing utility in auctions with incomplete information. The course concluded with a consideration of voting schemes and coalitions. Revisiting Combinatorics Instructor: Jay Schweig (Math) Combinatorics was taken in new directions for the students, covering graph and tree enumeration, partitions, compositions, and generating functions. Responding to a request from the students, the second part of the session covered the beginnings of formal logic, including a treatment of sentential logic, a discussion of the completeness and incompleteness theorems, and a full proof of the compactness theorem for sentential logic.
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