REU Site: Nebraska REU in Applied Math

该基金资助内布拉斯加州应用数学REU，由内布拉斯加州林肯市内布拉斯加州大学数学系管理。pi将在2013年、2014年和2015年夏季提供项目，每个项目将持续八周。大多数项目都是跨学科的，同时也是应用型的，其中许多项目结合了计算机探索，以便深入了解数学问题。重点是数学生物学，该网站将提供草食动物-植物相互作用、河流种群移动和循环神经网络动态方面的项目。也会有微分方程的项目，包括时间尺度上的离散分数微积分，弹性和扩散的非局部模型，以及波动方程的有限元方案。REU的学生分成两组工作，每组五名本科生，以及一到两名教师导师和一名研究生导师。每个小组在一个共同的主题下一起解决一个或多个问题。主要目标是给学生一个完整的研究经验，重点是定义好问题，解决问题，（在一些项目中）给出严格的证明，写数学，并通过演讲和海报展示工作成果。这是通过使用精心设计的结构来实现的，该结构利用了有才华的本科生的优势，同时弥补了他们相对缺乏经验和有限的背景。学生们几乎每个工作日都与导师见面，并花大量额外的时间与研究生导师交流。在这八个星期的过程中，这些项目将逐渐从侧重于准备过渡到完全侧重于研究，再过渡到侧重于准备结果以供传播。研究、教育和社会活动将结合起来，培养一个强调互动和合作的环境。当结果产生时，学生们以专业数学风格的书面报告记录他们的工作。在网站的最后一周，项目团队将大部分精力投入到准备结果的传播上，其中包括向内布拉斯加大学林肯分校数学社区进行的小组演讲，以及准备在次年1月的联合数学会议上展示的海报。REU项目会在一次或多次会议上发表演讲，许多项目还会在本科或专业期刊上发表论文。

This grant funds the Nebraska REU in Applied Mathematics, held at the University of Nebraska in Lincoln, Nebraska, and run by the Department of Mathematics. The PIs will offer projects during the summers of 2013, 2014 and 2015, and each project will last for eight weeks. Most of the projects are interdisciplinary as well as applied, and many incorporate computer exploration in order to gain insight into mathematical problems. There is an emphasis on mathematical biology, and the site will offer projects in herbivore-plant interactions, population movement along a river, and dynamics in recurrent neural networks. There will also be projects in differential equations, including discrete fractional calculus on time scales, nonlocal models for elasticity and diffusion, and finite element schemes for wave equations. REU students work in two teams of five undergraduates each, along with one or two faculty mentors and one graduate student mentor. Each group works together on one or more problems with a common theme. The main goal is to give the students a complete research experience, with attention given to defining good problems, solving problems and (in some projects) giving rigorous proofs, writing mathematics, and presenting work with a talk and a poster. This is achieved by using a structure carefully designed to make use of the strengths of talented undergraduates while compensating for their relative inexperience and limited background. The students meet with their mentors almost every weekday, and spend significant additional time with their graduate student mentors. Over the course of the eight weeks, the projects will gradually transition from a focus on preparation to an exclusive focus on research to a focus on preparing results for dissemination. Research, educational, and social activities will combine to cultivate an environment that emphasizes interaction and collaboration. The students document their work as a written report in professional mathematics style as results are produced. In the final week of the Site, the project teams devote the bulk of their energy to preparation of results for dissemination, which includes a group talk presented to the larger University of Nebraska-Lincoln mathematics community and a poster intended for presentation at the Joint Mathematics Meetings the following January. REU projects result in one or more conference presentations, and many also produce papers published in undergraduate or professional journals.