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

印第安纳大学数学系延续了近50年的传统，将为有才华的本科生提供密集的暑期研究体验。我们计划的一个重点是我们国际公认的教职员工的高度参与。这些教师帮助学生发展到能够成功地解决数学中具有挑战性的开放问题的程度。通过提供一个平衡和结构良好的环境，以及在我们的研究会议上进行口头阐述和书面结果报告的里程碑，该大学REU为学生在他们的项目中取得成功奠定了基础。通过培养紧张和协作的工作环境，以及最重要的是通过与导师的定期工作会议，进一步鼓励参与者取得成功。除了参与者获得的抽象问题解决技能和智力耐力外，他们的专业发展还通过乳胶研讨会、图书馆之旅和演示以及印第安纳大学向参与者提供的广泛计算资源、教职员工定期的研究报告和类似的机会得到进一步加强。我们的项目继续强调招聘有才华的女性、少数族裔和第一代大学生，他们的成功是我们用来评估和持续改进我们模式有效性的指标的关键组成部分。印第安纳大学的REU项目提供了一个身临其境的环境，提供了一种以导师为导向的研究方法。八名学生将与教职员工一对一或小组合作，在我们的校园里花八周时间解决精心挑选的研究问题。通常，这些问题是未解决的、可访问的，并且在数学上具有重要意义。纯数学的主题选自广泛的数学，包括：几何群论、组合拓扑和纽结理论、逻辑、复数和符号动力学、曲面的平铺、范畴理论的各个方面等等。应用数学的主题来自计算机科学的领域，如递归理论或同伦类型理论，以及数学、生物学和化学的领域，从聚合物组织和细胞功能到系统发育。学生们一起住在一个宿舍里，共享共同的办公空间，从集体沉浸在数学中以及自然地随之而来的自发合作中受益。当地教师的定期演讲使该小组对整个数学有了更广泛和更深入的理解。学生们通过在全州范围内的本科生数学研究会议上发表简短的演讲，向同行、教师和研究生进行长达一小时的正式讲座，以及撰写一份详细介绍他们的发现的正式研究报告来传播他们的发现。其中一些报告预计将发展成同行评议的研究论文。归根结底，我们的计划将极大地帮助学员为成为当今高科技劳动力的领导者做好准备，无论是学术界还是产业界。

Continuing a tradition dating back nearly fifty years, the Department of Mathematics at Indiana University will offer an intensive summer research experiences for talented undergraduates. A keystone of our program is the high level of participation from our internationally recognized faculty. These faculty help develop students to the point of being able to successfully tackle challenging open problems in mathematics. By providing a well-balanced and structured environment together with milestones for both oral exposition at our research conference and written reports of results, the IU REU lays the groundwork for student success in their projects. Participant success is further encouraged by the fostering of an intense and collaborative work environment, and most importantly through the regular working sessions with mentors. In addition to the abstract problem solving skills and intellectual stamina gained by the participants, their professional development is further enhanced through LaTeX workshops, tours and demonstrations of libraries and Indiana University's extensive computational resources which are made available to participants, regular research presentations by faculty members, and similar opportunities. Our program continues to emphasize the recruiting of talented women, minorities and first generation college students, and their success is a key component of the metrics we use to evaluate and continually improve the effectiveness of our model. The Indiana University REU program provides an immersive environment with a strong mentorship-oriented approach to research. Eight students will work one-on-one or in small groups with faculty members, spending eight weeks on our campus tackling carefully selected research problems. Typically, these problems are unsolved, accessible, and mathematically significant. Topics in pure mathematics are chosen from a broad swath of mathematics including: geometric group theory, combinatorial topology and knot theory, logic, complex and symbolic dynamics, tilings of surfaces, aspects of category theory and several more. Topics in applied mathematics are drawn from areas in computer science such as recursion theory or homotopy type theory and areas of mathematical biology and chemistry from polymer organization and cell function to phylogenetics. Housed together in a dormitory and sharing common office space, students benefit from being immersed in mathematics collectively and from the spontaneous collaboration that naturally follows. Regular presentations by local faculty give the group a broader and deeper understanding of mathematics as a whole. 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. Some of these reports are expected to develop into peer-reviewed research papers. Ultimately, our program significantly helps prepare participants to be the leaders in today's highly technical workforce, whether in academia or industry.