REU Site: Research Experiences for Undergraduates in Mathematics in Indiana University

延续了46年的传统，印第安纳大学数学系将为有才华的本科生提供暑期密集研究体验。八名学生将与教师一对一或小组合作，在我们的校园里花八周的时间研究由教师选择的研究问题。通常，这些问题是开放的、可访问的，并且具有数学意义。纯数学的主题包括台球动力学、逻辑学、复杂动力学、组合拓扑和曲面的平铺。应用数学的主题强调数学和生物学之间日益增长的关系，包括群体遗传学和分子进化、聚合物组织和细胞功能、表型进化、基因组进化和系统发育。学生们住在一个宿舍里，共享办公空间，沉浸在数学中，受益匪浅。当地教师的频繁演讲使学生对数学有了更广泛和更深入的了解。学生们通过在全州范围内的本科数学研究会议上做简短的报告，向同学、教师和研究生做长达一小时的正式讲座，并撰写一份正式的独立研究报告，详细介绍他们的发现，来传播他们的发现。技术创新的快速发展不仅创造了新的就业机会，也带来了新的问题。其中许多问题需要定量分析。在生物学、成像、电信、医学、金融和其他几十个领域，我们收集大量数据的能力带来了巨大的新的分析挑战。如何训练一个人去解决这些大型的、未解决的、复杂的问题呢？在他们职业生涯的早期，让他们接触数学研究的刺激和挑战。我们的暑期研究经验将为一小群有才华的学生提供发展抽象问题解决能力、智力耐力、创造力、毅力、沟通技巧和职业道德的机会。我们的学生为迎接未来的挑战做好了更好的准备，并维护了我们国家重要的智力基础设施。

Continuing a forty-six year old tradition, the Department of Mathematics at Indiana University will offer summer intensive research experiences for talented undergraduates. Working one-on-one or in small groups with faculty, eight students will spend eight weeks on our campus working on research problems selected by faculty members. Typically, these problems are open, accessible, and mathematically significant. Topics in pure mathematics include the dynamics of billiards, logic, complex dynamics, combinatorial topology, and tilings of surfaces. Topics in applied mathematics emphasize the growing relationship between mathematics and biology and include population genetics and molecular evolution, polymer organization and cell function, evolution of phenotypes, genome evolution, and phylogenetics. Housed together in a dormitory and sharing common office space, students benefit from being immersed in mathematics. Frequent presentations by local faculty give the cohort a broader and deeper understanding of mathematics. Students disseminate their findings by giving brief presentations at a statewide undergraduate mathematics research conference, giving an hour-long formal lecture to peers, faculty, and graduate students, and writing a formal self-contained research report detailing their findings. The fast pace of technological innovation is creating not only new types of jobs, but also new types of problems. Many of these problems require quantitative analysis. In biology, imaging, telecommunications, medicine, finance, and dozens of other fields, our ability to collect large amounts of data is leading to enormous new analytical challenges. How does one train an individual to work on these large, unsolved, complex problems? By exposing them, early in their career, to the thrill and challenge of mathematical research. Our summer research experience will give a small group of talented students the opportunity to develop abstract problem-solving skills, intellectual stamina, creativity, perseverance, communication skills, and work ethic. Our students emerge better prepared to meet the future challenges they will face and to maintain the important intellectual infrastructure of our nation.