Mathematical Sciences: Experimental Mathematics

数学科学：实验数学

• 批准号: 9100940
• 负责人: Paul Goodey
• 金额: $ 15万
• 依托单位: University of Oklahoma Norman Campus
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-03-15 至 1994-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9100940&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Experimental; Mathematics

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.

十名学生将获得本科生研究经验奖的支持。 他们将在三名教职顾问的指导下工作两个月。 在上一个奖项中，为另外五名学生提供了机构支持；预计收到这笔赠款后也会作出类似的安排。 大部分实验工作涉及计算工作，将在数学计算机辅助学习中心进行。 该中心拥有优秀的计算机和软件资源供研究人员使用。 第一年用于例证数学研究实验性质的主要主题将是计算和组合群论。 在这里，计算机不仅用于检查示例和发现模式，还用于解决已减少到有限数量案例的问题。 经过迎新期后，学生将开始研究有关有限群莫比乌斯函数的问题，找出仿射韦尔群元素的 Coxeter 生成器中约化表达式的数量，并沿着更几何的路线，研究小阶有限简单群的 Hurwitz 问题。 最后一个领域涉及确定所有可能的闭合、可定向曲面的属的问题，这些曲面承认群的对称性。