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Abstract:
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The author has written a new course that serves both the statistics and mathematics programs at Kenyon College. This course explores the theory, applications, and interesting consequences when probability is introduced upon various mathematical objects. Some of the core topics are random graphs, random walks, and random permutations, as well as randomness applied to polynomials, functions, integer partitions, groups, and codes. The focus of the course is solving challenging problems and working on small projects. In addition to studying the random structures themselves, a concurrent focus of the course is the development of mathematical tools to analyze them, such as combinatorics, indicator variables, generating functions, laws of large numbers, asymptotic theory, elementary linear algebra, and computer simulation. The prerequisite for the course is only second-semester calculus.
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