Mathematical Sciences: The Probability Theory of Patters andRuns

为期八周的本科生研究经验项目 将得到这个奖项的支持。 六名本科生将在 概率论中的问题 主题不同，但 相互关联，具有很强的理论成分， 重大应用。 该项目将持续八周。 大型计算机将可用于大规模 计算以及几个微型计算机的本地访问 和文字处理。 符号操作程序，例如MAPLE 和MACSYMA将可用于测试设备。 每个学生项目将从两个基本的调查领域。 首先，运行和模式的精确分布理论， 二是著名的Poisson-Gaussian Chen-Stein方法 近似 统计结果的应用或 密码学将受到鼓励。 预计学生 将被赋予两个一般性的问题领域。 他们将按照 更有希望通过这个项目。 选择学生的一个标准是他们的意愿， 希望花大量的时间后，正式 项目完成后，将取得的成果写下来， 在专业会议上介绍他们， 文件在议程上。

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.