Mount Holyoke Undergraduate Mathematics Summer Research Institute

芒特霍利奥克学院提议继续为本科生运营一个数学和统计学暑期研究站点。在接下来的五年里，我们计划每年夏天从美国不同的学院和大学中挑选10名学生从事数学或统计研究。这些学生将以五人为一组，在一名教师的指导下进行不同的项目。这些项目将植根于数学或统计研究的主流领域，并经常涉及计算机实验和计算。我们想要强烈传达给学生的信息之一是，例子的力量可以阐明，并可能超越纯理论策略中当前的僵局。这两个小组每天会单独会面几次，但也会有充足的（结构化和非结构化）机会让不同小组的学生交换意见。学生将组织和参与自己的演讲系列，在项目的研究研讨会上每周发表演讲/报告，并鼓励学生参加和参与地方和国家会议。我们打算尽我们所能，模拟研究机构的生活。2009年夏天，Jessica Sidman的小组将研究计算代数几何和交换代数的问题，而Giuliana Davidoff的小组将研究数论。我们的研究项目是实质性的和主流的。我们提供的高强度接触，以及小型工作小组的亲密关系，以具体而非肤浅的方式促进和支持非常深刻和抽象概念的学习。通过REU，学生们对数学和统计学的热情得到了加强；他们学习如何有效地交流数学或统计思想；他们对自己接受新概念的能力有信心，并通过例子和问题的实验，建立对新概念的直觉。对于那些追求这条道路的学生来说，这段经历也是通往研究生院的一座桥梁。通常，项目前几周所涵盖的基础材料与学生在研究生院第一年所遇到的课程相吻合。最后，鼓励每个学生在课程结束前准备一份他或她的作品的预印本。这些预印本可以在项目网站上找到。从暑期项目中获得荣誉论文和期刊出版物并不罕见。密集的研究经验为学生提供了一个机会，让他们亲眼看到作为一名研究人员的生活可以带来什么。因此，它可以帮助他们回答（或重申他们的立场）关于他们在数学或统计学领域的职业潜力的问题。此外，我们力求在那些可能不考虑参加REU的学生中提高我们项目的知名度。特别是，我们计划从传统的黑人学院和大学大量招生。通过这种方式，我们希望为这些学科的多样化和随后的改进做出贡献。

Mount Holyoke College proposes to continue operating a mathematics and statistics summer research site for undergraduates. Each summer, for the next five years, we envisage selecting ten students from a diverse array of U.S. colleges and universities to engage in mathematical or statistical research. These students shall work in groups of five, each group carrying out a different project under the supervision of a faculty member. The projects will be rooted in mainstream areas of mathematical or statistical research and will often involve computer experimentation and computation. One of the messages we intend to communicate strongly to the students is the power of examples to illuminate, and possibly transcend, current impasses in purely theoretical strategies. The two groups will meet separately several times a day but there will also be ample (structured and unstructured) opportunities for students in the different groups to exchange ideas. Students will organize and participate in their own speaker series, give weekly talks/reports in the program's research seminar, and will be encouraged to attend and participate in local and national meetings. We intend to simulate, as best we can, what life at a research institute feels like. For summer of 2009, Jessica Sidman's group will investigate questions in computational algebraic geometry and commutative algebra while Giuliana Davidoff's group will be involved with a number theory investigation.Our research projects are substantial and mainstream. The intense exposure that we provide, along with the intimacy of small working groups, facilitate and support learning of very deep and abstract concepts in a concrete and non-superficial way. Through the REU the students are strengthened in their enthusiasm for mathematics and statistics; they learn how to effectively communicate mathematical or statistical ideas; they develop confidence in their ability to take a new concept and, through experimentation with examples and questioning, build intuition for it. This experience also serves as a bridge to graduate school for those students who pursue that path. Often the foundational material that is covered in the first couple of weeks of the program coincides with courses that students encounter during their first year of graduate school. Finally, each student will be encouraged to prepare a preprint of his or her work by the end of the program. These preprints are made available on the program's website. It is not uncommon for honors theses as well as journal publications to result from the summer projects. The intense research experience provides an opportunity for students to see for themselves what life as a researcher can entail. Thus it may help them answer (or reaffirm their position on) questions about their potential for a career in mathematic or statistics. Additionally, we seek to increase our program's visibility among students who may otherwise not consider attending an REU. In particular, we intend to recruit heavily from historically black colleges and universities. In this way, we hope to contribute to the diversification and subsequent improvement of these disciplines.