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个夏季周进行前沿水平的研究。 学生参与者将学习建立数学模型，从跨科学的问题。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：城市犯罪背后的数学模式;（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。学生将从数学REU活动通常涉及的领域之外招募，包括社区学院学生和数学教育学生，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，以确保具有广泛不同经验水平的学生能够为每个项目做出重要贡献。将作出额外的推广努力，以丰富整个加州高中和中学课堂的数学建模教学。被REU网站招募的数学教育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。这些教案将与教师分享，以便更广泛地使用。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新出现的接口。具体项目将包括：（1）分析微流体室内孢子的合作和竞争，并使用进化博弈论对这些相互作用进行建模;（2）寻找东洛杉矶帮派暴力的时空模式的比例法则;（3）使用冲击理论分析重力下载有颗粒的流体的流动。REU参与者将学习广泛的建模方法，包括微分方程，随机和基于代理的模型，以及缩放理论。所有项目都要求将建模与真实的数据融合，其中两个项目将由学生自己通过实验收集。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的培训。该计划旨在为学生创造沉浸式的研究体验，从大学生涯的早期学生到考虑研究生院的高级本科生，以及未来的专家教师。该计划的最终目标是根据REU项目创建经过实地测试的学习材料，每年将向数百名中学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.