REU Site: Rose-Hulman Undergraduate Research Experience in Mathematics

在过去的21年里，罗斯-霍尔曼的夏季数学REU项目已经为150多名本科生提供了服务。这个REU向学生介绍了群论、“集”、双曲几何、数论、逆问题和几何分析等问题，并在这些领域做出了贡献。该项目已经从一名教员发展到一名充满热情的导师，他们每年轮流进出该项目。其结果是，大学生要研究的问题范围更广。REU也得到了数学系作为一个整体和罗斯-霍尔曼社区的大力支持。虽然我们研究的数学主题是多种多样的，但我们已经开发了一种连贯的研究方法：我们首先利用计算工具来帮助学生理解手头的问题，通过制定具体的案例和例子。然后，他们可以开始进行一般的推测，设计算法，并进行大规模的计算和/或统计调查（视情况而定），最终进行严格的分析和证明。我们提出的问题可以被具有相当普通数学背景的学生攻克。然而，这些问题是从活跃的数学领域中提取出来的，并且可以根据学生的能力和动力迅速引导到当前研究的前沿。我们的REU培养学生成为“完整的”数学家，能够独立思考，提出和证明猜想，并交流他们的结果。在这个过程中，我们希望为他们未来的职业决策提供一个基础。因此，在选拔过程中，我们特别感兴趣的学生，除了有充分的准备，对涉及研究的职业表现出兴趣，但可能没有机会在本科研究的机会。

Rose-Hulman's summer REU program in mathematics has served over 150 undergraduates in the past 21 years. This REU has introduced students to problems in group theory, "cwatsets", hyperbolic geometry, number theory, inverse problems, and geometric analysis, and made contributions to each of these areas. The program has evolved from a single faculty member to one involving enthusiastic mentors who rotate in and out of the program year-to-year. The result is a wider range of problems for undergraduates to investigate. The REU has also gained strong support from the mathematics department as a whole and the Rose-Hulman community.Though the mathematical topics we investigate are diverse, we have developed a coherent approach to the research: we initially make use of computational tools to help students understand the problems at hand, by working out specific cases and examples. They can then begin making general conjectures, designing algorithms, and follow up with large scale computational and/or statistical investigations (as appropriate) and eventually rigorous analysis and proofs. The problems we pose can be attacked by students with a fairly modest mathematical background. However, the problems are drawn from active areas of mathematics, and can quickly lead to the frontiers of current research, depending on the student's abilities and drive. Our REU develops the students as "complete" mathematicians, capable of independent thinking, making and proving conjectures, and communicating their results. In the process, we hope to give them a basis for future career decisions. Thus, in the selection process we are especially interested in students who, beyond having adequate preparation, express interest in a career involving research, but who may not otherwise have a chance at an undergraduate research opportunity.