Mathematical Sciences: The Probability Theory of Patters andRuns

一个为期八周的本科生研究经历项目将获得该奖项的支持。六名本科生将研究概率论中的问题。这些主题是不同的，但相互关联的，具有很强的理论成分和重要的应用。该项目将持续八周。一台大型计算机将用于大规模计算，还有几台微型计算机用于本地访问和文字处理。像MAPLE和MACSYMA这样的符号操作程序将可用于测试猜想。每个学生的专题将源自两个基本的探究领域。首先是运行和模式的精确分布理论，其次是著名的泊松和高斯近似陈斯坦方法。将鼓励将结果应用于统计学或密码学。预计学生将被分配到两个一般性问题领域。他们将在整个项目中追随那些更有前途的人。学生选择的一个标准将是他们是否愿意和渴望在项目正式完成后花费大量的时间来撰写所获得的结果，并在专业会议上展示这些结果，学生的研究论文将被列入议程。

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.