The Williams College SMALL REU Program

在威廉姆斯学院的小型REU项目中，每年夏天有10周的时间(9周在威廉姆斯住校，1周在家)，25到40名本科生在一名数学或统计学教员的指导下从事研究项目。每年夏天通常有4到7个不同规模的团队。夏季的高潮是报告(在威廉姆斯会议上，通常是在会议上)，大多数小组都会写下他们的工作，然后提交给研究期刊。每周都有教师和学生在数学和相关领域的讲座。学生是充满活力的科学社区的一部分；威廉姆斯大学每年夏天都有100多名学生进行数学和科学方面的原创性研究，还有各种各样的学术和社会活动将所有暑期的学生和教职员工聚集在一起。这项REU的目标是向本科生介绍在数学方面进行原创性研究的兴奋和挑战。课程内容包括：代数几何、贝叶斯统计、组合学、交换代数、计算几何、CR结构、离散几何、动力学和遍历理论、图论、双曲流形、纽结理论、数学生物学、数学物理、测度论、极小曲面、数论、概率论、随机矩阵理论、表示论、黎曼几何、对称群和热带几何。在这个过程中，学生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无价的。丰富多彩的数学活动提供了丰富的智力环境。我们的国家需要对数学有更广泛的欣赏和理解，不能把任何人排除在外。在过去的五年里，我们增加了来自传统上代表不足的群体参加该项目的学生数量，我们正在继续寻找新的更好的方式来鼓励来自女性、少数族裔、第一代大学生和其他代表不足的群体的申请。学生、教师和更广泛的数学界将从原创研究的介绍和出版中受益。学生将建立一个终生的同伴和导师网络，其中许多人将攻读研究生课程，部分原因是他们在REU的经验。几乎所有的学生都在研究期刊上发表论文，许多学生在国内和国际研究会议上展示他们的研究成果。

In the Williams College SMALL REU program, for ten weeks each summer (nine in residence at Williams and one at home), 25 to 40 undergraduates work on research projects under the direction of a faculty member in mathematics or statistics. There are usually between 4 and 7 groups each summer of various sizes. The summer culminates with presentations (at Williams and often at conferences), and most groups write up their work for submission to a research journal. There are weekly talks by faculty and students, both in mathematics and in related fields. Students are part of a vibrant scientific community; over 100 students do original research in mathematics and the sciences at Williams each summer, and there are a variety of academic and social activities bringing all the summer students and faculty together.The goal of this REU is to introduce undergraduates to the excitement and challenge of doing original research in mathematics. Topics will be drawn from algebraic geometry, Bayesian statistics, combinatorics, commutative algebra, computational geometry, CR structures, discrete geometry, dynamics and ergodic theory, graph theory, hyperbolic manifolds, knot theory, mathematical biology, mathematical physics, measure theory, minimal surfaces, number theory, probability, random matrix theory, representation theory, Riemannian geometry, symmetry groups, and tropical geometry. 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 students from traditionally under-represented groups 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. 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 mentors, and many of them will pursue graduate studies, partially because of their REU experience. Almost all students publish papers in research journals and many present their results at national and international research conferences.