Mathematical Sciences: The Probability Theory of Patters andRuns

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An eight-week project of Research Experiences for Undergraduates will be supported by this award. Six undergraduates will work on problems in probability theory. The topics are distinct but interrelated having a strong theoretical component with significant applications. The project will run for eight weeks. A mainframe computer will be available for large scale computations as well as several microcomputers for local access and word processing. Symbol-manipulative programs such a MAPLE and MACSYMA will be available for testing conjectures. Each student project will derive from two basic areas of inquiry. First, the exact distribution theory of runs and patterns and second, the celebrated Chen-Stein method of Poisson and Gaussian approximation. Applications of results to statistics or cryptography will be encouraged. It is expected that students will be given two general problem areas. They will follow the more promising through the project. One criterion for student selection will be their willingness and desire to spend a substantial amount of time after the formal completion of the project in writing up results obtained and to present them at professional meetings in which student research papers are on the agenda.