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

延续46年的传统，数学系在印第安纳州大学将提供暑期密集的研究经验，为有才华的本科生。工作一对一或小组与教师，八名学生将花八个星期在我们的校园工作的研究问题由教师选择。 通常，这些问题是开放的，可访问的，并且在数学上是重要的。 纯数学的主题包括台球的动力学、逻辑学、复杂动力学、组合拓扑学和曲面的平铺。 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，基因组进化和遗传学。 学生们一起住在宿舍里，共用办公室，沉浸在数学中受益匪浅。 当地教师的频繁演讲使该群体对数学有了更广泛和更深入的理解。学生通过在全州范围内的本科生数学研究会议上做简短的演讲来传播他们的研究结果，给同行，教师和研究生一个小时的正式讲座，并撰写一份正式的独立研究报告，详细介绍他们的研究结果。 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、金融和其他数十个领域，我们收集大量数据的能力正在带来巨大的新分析挑战。 如何训练一个人去解决这些大的、未解决的、复杂的问题？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给一小群有才华的学生发展抽象的解决问题的能力，智力耐力，创造力，毅力，沟通技巧和职业道德的机会。 我们的学生更好地准备迎接他们将面临的未来挑战，并保持我们国家的重要知识基础设施。

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.