REU Site: Mathematical Modeling at UCLA

该奖项为一个为期三年的REU网站提供资金，以支持12名本科生每年8个暑假周进行前沿水平的研究。学生将学习如何为各个科学领域的问题建立数学模型。研究项目将集中在三个领域：(1)生物学：真菌孢子如何合作创建网络；(2)社会科学：城市犯罪的数学模式；(3)物理学：预测工业或地球物理泥浆开始流动时发生的灾难。将从数学REU活动通常触及的领域之外招收学生，包括社区大学生和数学教育专业的学生，并将利用现有的大学框架来吸引代表性不足的群体。研究活动经过精心设计，以确保具有不同经验水平的学生能够为每个项目做出重要贡献。将做出更多的外展努力，以丰富加州高中和中学课堂上的数学建模教学。被招募到REU网站的数学教育专业的学生将根据他们的研究经验创建新的教案和教材，并在真实的课堂上进行测试。这些教案随后将与教师分享，以供更广泛的使用。建模主题涉及不同的应用领域，包括数学和真菌生物学之间以及数学和犯罪学之间的新出现的接口。具体项目将包括：(1)分析微流体室内的孢子合作与竞争，并使用进化博弈论对这些相互作用进行建模；(2)在东洛杉矶帮派暴力的空间和时间模式中寻找尺度规律；(3)使用激波理论分析重力下携带颗粒的流体的流动。REU学员将学习广泛的建模方法，包括微分方程式、随机和基于代理的模型以及比例理论。所有项目都要求模型与真实数据融合，其中两个项目将由学生自己通过实验收集数据。参与者将接受模型拟合、图像分析、缩放、数据分析和误差估计方面的培训。该项目旨在为学生创造身临其境的研究体验，范围从大学生涯早期的学生到考虑攻读研究生的高级本科生，以及未来的专家教师。该计划的最终目标是在REU项目的基础上创建经过实地测试的学习材料，每年将向数百名初中和高中教师教授这些材料。

This award provides funding for a three-year REU site to support twelve undergraduate students for eight summer weeks each year to perform frontier level research. Student participants will learn to build mathematical models for problems from across the sciences. Research projects will focus on three areas: (1) Biology: how fungal spores cooperate to create networks; (2) Social sciences: mathematical patterns underlying urban crime; and (3) Physics: predicting the catastrophes that occur when industrial or geophysical slurries start to flow. Students will be recruited from outside the spheres normally reached by mathematics REU activities, including community college students and mathematics education students, and an existing university framework will be utilized to attract under-represented groups. Research activities are carefully designed to ensure that students with widely differing levels of experience are empowered to contribute vitally to each project. Additional outreach efforts will be made to enrich teaching of mathematical modeling in high school and middle school classrooms across California. Mathematics education students recruited to the REU site will create new lesson plans and teaching materials based on their research experiences and test them in real classrooms. These lesson plans will then be shared with teachers for wider use. The modeling topics involve different application areas, including newly emerging interfaces between mathematics and fungal biology and between mathematics and criminology. Specific projects will include: (1) Analyzing spore cooperation and competition within microfluidic chambers, and modeling these interactions using evolutionary game theory; (2) Looking for scaling laws in the spatial and temporal patterns of gang violence in East Los Angeles; (3) Analyzing the flow of particle-laden fluid under gravity using the theory of shocks. REU participants will study a broad spectrum of modeling methods including differential equations, stochastic and agent based models, and scaling theory. All projects require that modeling be fused with real data, which in two of the projects will be collected by students themselves through experiments. Participants will receive training in model fitting, image analysis, scaling, data analysis, and error estimation. The program is designed to create immersive research experiences for students ranging from students early in their college careers to advanced undergraduates contemplating graduate school, as well as future expert teachers. A final goal of the program is the creation of field-tested learning materials based on the REU projects that will be taught to hundreds of middle school and high school teachers annually.