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

延续近50年的传统，印第安纳大学数学系将为有才华的本科生提供密集的暑期研究经历。我们项目的一个重点是我们国际公认的教师的高水平参与。这些教师帮助学生发展到能够成功解决数学中具有挑战性的开放性问题的程度。通过提供一个平衡和结构化的环境，以及在我们的研究会议上口头展示和书面报告结果的里程碑，IU REU为学生在他们的项目中取得成功奠定了基础。通过培养一个紧张和协作的工作环境，最重要的是通过与导师的定期工作会议，进一步鼓励参与者的成功。除了抽象的解决问题的能力和智力耐力的参与者获得，他们的专业发展通过LaTeX研讨会，参观和演示图书馆和印第安纳大学的广泛的计算资源，提供给参与者，由教师定期研究报告，和类似的机会进一步加强。我们的项目继续强调招募有才华的女性、少数族裔和第一代大学生，他们的成功是我们用来评估和不断提高我们模式有效性的指标的关键组成部分。印第安纳大学REU项目提供了一个身临其境的环境，具有强大的导师导向的研究方法。八名学生将与教师一对一或小组合作，花八周时间在我们的校园里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，并且具有数学意义。纯数学的主题是从广泛的数学中选择的，包括：几何群论，组合拓扑和结论，逻辑，复杂和符号动力学，表面的平铺，范畴论的各个方面等等。应用数学的主题来自计算机科学领域，如递归理论或同伦型理论，以及数学生物学和化学领域，从聚合物组织和细胞功能到系统发育。学生们住在一个宿舍里，共享共同的办公空间，他们从集体沉浸在数学中以及自然产生的自发合作中受益。当地教师的定期报告使小组对数学整体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。其中一些报告有望发展成为同行评议的研究论文。最终，我们的课程显著帮助学员成为当今高技术劳动力的领导者，无论是在学术界还是工业界。

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.