REU Site: Rose-Hulman Undergraduate Research Experience in Mathematics

REU 网站：Rose-Hulman 数学本科生研究经验

• 批准号: 1003924
• 负责人: Joshua Holden
• 金额: $ 30.96万
• 依托单位: Rose-Hulman Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-04-15 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1003924&HistoricalAwards=false
• 关键词: REU; Site; Rose; Hulman; Undergraduate

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.

Rose-Hulman 的 REU 数学暑期课程在过去 21 年中已为 150 多名本科生提供服务。 该 REU 向学生介绍了群论、“cwatsets”、双曲几何、数论、反问题和几何分析中的问题，并为这些领域做出了贡献。 该项目已从单一教员发展成为由热心导师组成的项目，他们每年轮流进出该项目。 结果是本科生需要研究的问题范围更广。 REU 还获得了整个数学系和 Rose-Hulman 社区的大力支持。尽管我们研究的数学主题多种多样，但我们开发了一种连贯的研究方法：我们首先利用计算工具，通过制定具体案例和示例来帮助学生理解手头的问题。然后，他们可以开始做出一般性猜想，设计算法，并进行大规模计算和/或统计调查（视情况而定），并最终进行严格的分析和证明。我们提出的问题可以由具有相当普通数学背景的学生来解决。然而，这些问题来自数学的活跃领域，并且可以很快引导到当前研究的前沿，这取决于学生的能力和动力。我们的 REU 将学生培养成“完整的”数学家，能够独立思考、做出和证明猜想、并交流他们的结果。在此过程中，我们希望为他们未来的职业决策提供基础。因此，在选拔过程中，我们特别关注那些除了有充分准备之外还对涉及研究的职业表现出兴趣的学生，但他们可能没有机会获得本科研究机会。