REU Site: The Williams College SMALL REU program

在威廉姆斯学院SMALL REU项目中，2009-2013年夏季，大约23名本科生将在大约6名教师的带领下，以大约4人一组的方式进行为期9周的原创研究。研究课题包括：粘结、粒子碰撞的拓扑、多变量连分数、局部环的补全、随机矩阵理论、密度流形和等周问题、全局场的类群、遍历理论和各类随机矩阵的特征值分布。这个REU的目标是向本科生介绍做数学原创性研究的兴奋和挑战。在这个过程中，学生们自然会学到很多背景知识，并被鼓励展示和发表他们的作品，这些对研究生院来说都是非常宝贵的。各种各样的数学活动提供了丰富的智力环境。我们的国家需要更广泛地欣赏和理解数学，不能把任何人排除在外。在过去五年中，我们增加了妇女和少数族裔参与该项目的人数，我们将继续寻找新的、更好的方式来鼓励妇女、少数族裔、第一代大学生和其他未被充分代表的群体申请。该提案的PI是一名女性，副PI是西班牙裔。学生，教师和更广泛的数学界将受益于原创性研究的展示和出版。学生将建立一个终身的同龄人网络，他们中的许多人将继续研究生学习，部分原因是他们在REU的经历。

In the Williams College SMALL REU program, for nine weeks each summer, about 23 undergraduates will work in groups of about four on original research with about 6 faculty, for the summers 2009-2013. Topics of research include stick knots, topology of particle collisions, multivariable continued fractions, completions of local rings, random matrix theory, manifolds with density and isoperimetric problems, class groups of global fields, ergodic theory, and eigenvalue distribution of various classes of random matrices.The goal of this REU is to introduce undergraduates to the excitement and challenge of doing original research in mathematics. In the process, students naturally learn lots of background and are encouraged to present as well as publish their work, all invaluable for graduate school. The variety of mathematical activities provides a rich intellectual environment. Our nation needs a wider appreciation and understanding of mathematics, and cannot afford to leave anyone out. We have increased the numbers of women and minorities participating in the program over the last five years, and we are continuing to look for new and better ways to encourage applications from women, minorities, first generation college students, and other underrepresented groups. The PI for this proposal is a woman and the co-PI is Hispanic. Students, faculty and the broader mathematics community will benefit from the presentation and publication of original research. Students will develop a lifetime network of peers and many of them will pursue graduate studies, partially because of their REU experience.