Research Experiences for Undergraduates in Mathematics

建议为全国范围内招收的10名本科数学专业学生提供一个研究课题和研究环境，考虑到毕业生的背景，尽可能接近工作中的数学家的研究环境。每名学生将与一名教职员工一起工作。例如：连续逻辑，隐式规划问题，对称群上的Bruhat序，交替群，及其在某些难题上的应用，对称双线性形式的表示，三角空间，随机游动和平面上的电网络，曲面的仿射微分，小波和/或隐马尔可夫模型，分段线性映射的动力学，Peano函数和描述集合论，金融数学，代数码，以及平面保守系统的分支。学生们将每周与他们的教师顾问私下会面两到三次。在整个八周的时间里，学生们将经常向小组报告进度。该项目最重要的方面之一是学生之间的互动。对于一些人来说，这将是他们第一次有机会结识其他有类似数学兴趣和能力的学生。我们将通过多种方式鼓励这种互动：学生们将一起住在一个宿舍里，在同一个自助餐厅吃饭。在罗尔斯大厅(数学系)将有一个房间，学生们可以在那里聚集在一起工作。在过去的一周里，学生们将就他们所做的工作进行演讲。他们还将编写关于其工作的书面报告。这些将被收集到一个单独的装订卷中。

It is proposed to provide ten undergraduate mathematics majors, recruited nationwide, with a research topic and a research environment which is as close to that of a working mathematician as possible, given the sudent's background. Each student will work with a single faculty member. Sample topics are: Continuous Logic, The implicit Programming Problem, Bruhat Ordering On the Symmetric Group, The Alternating Group, and Applications to Certain Puzzles, Representations of Symmetric Bilinear Forms, Spaces of Triangulations, Random Walks and Electrical Networks in the Plane, Affine Diffeomorphisms of Surfaces, Wavelets and/or Hidden Markov Models, The Dynamics of Piecewise-Linear Maps, Peano Functions and Descriptive Set Theory, The Mathematics of Finance, Algebraic Codes, and Bifurcation of Planar Conservative Systems. The students will meet privately with their faculty advisors two to three times a week. Throughout the eight weeks the students will give frequent progress reports to the group. One of the most important aspects of the program is the interaction among the students themselves. For some this will be their first opportunity to get to know other students of comparable mathematical interest and ability. We will encourage this interaction in a number of ways: The students will be living together in a single dormitory and eating in the same cafeteria. There will be a room in Rawles Hall (the Mathematics Department) in which students can gather to work. During the last week the students will give lectures on the work they have done. They will also prepare written reports on their work. These will be collected into a single bound volume.