Mathematical Sciences: Experimental Mathematics

10名学生将获得本科生研究经验奖的支持。他们将在三个指导老师的指导下工作两个月。在前一个奖项中，为另外五名学生提供了院校支助；预计收到这笔赠款后也会有类似的安排。许多实验工作涉及计算工作，这些工作将在数学计算机辅助学习中心进行。本中心有优秀的计算机和软件资源可供研究人员使用。在第一年使用的主要主题，以举例说明数学研究的实验性质将是计算和组合群论。在这里，计算机不仅被用来检查例子和发现模式，而且还被用来解决已经减少到有限数量的问题。经过一段时间的指导，学生将开始研究有限群的莫比乌斯函数问题，寻找仿射Weyl群元素的Coxeter生成器中的简化表达式的数量，并沿着更几何的路线，研究小阶有限简单群的Hurwitz问题。最后一个领域涉及的问题是确定所有可能的闭的、可定向的表面的属，这些曲面承认群的对称性。

Ten students will receive support from this Research Experiences for Undergraduates award. They will work under the direction of three faculty advisors for a period of two summer months. In the preceding award, institutional support for five additional students was provided; a similar arrangement is anticipated with the receipt of this grant. Much of the experimental work involves computational work which will be carried out in the Mathematics Computer Assisted Learning Center. The center has excellent computer and software resources available to the researchers. The primary theme used during the first year to exemplify the experimental nature of mathematical research will be computational and combinatorial group theory. Here computers have not only been used to check examples and discover patterns but also to settle problems which have been reduced to a finite number of cases. After an orientation period, students will begin work on problems concerning the Mobius function of finite groups, finding the number of reduced expressions in the Coxeter generators for elements of the affine Weyl group and, along a more geometric line, to look at the Hurwitz problem for finite simple groups of small order. This final area concerns the problem of determining all possible genera of closed, orientable surfaces which admit a symmetry by the group.