Research Training Group in Applied Differential Equations and Scientific Computing (EMSW21-RTG)

加州大学洛杉矶分校为促进年轻研究人员的职业发展提供了独特的环境。应用数学的最新研究，包括图像处理、材料科学和流体力学，在充满活力的研究生和博士后群体的充分参与下得到了发展。我们建议在这一计划的基础上，为本科生和研究生早期阶段的年轻学生提供特殊的培训和指导经验。该计划将在五年内支持多达60名来自加州大学洛杉矶分校和哈维穆德学院的REU学生。提出的研究项目包括犯罪数据的时空模式分析、泥浆流动的实验和分析、图像处理和机器人车辆的协同控制。另外还有15名博士生，在他们职业生涯的早期阶段，将发展应用数学的研究生涯。这些学生将有机会与其他系的教师以及工业和国家实验室一起参加暑期实习项目。学生将接受额外的计算和数学分析技能培训，这是成功进入顶级博士项目所必需的。调查人员提出了一项研究培训计划，以加强进入研究、学习、应用和计算微分方程式的美国公民和永久居民的劳动力。这个项目是为处于研究生涯早期的本科生和研究生设计的。他们将在一对一和小型研究小组中与教师导师一起在沉浸式研究环境中解决尖端研究问题。该计划将在五年内支持多达60名来自加州大学洛杉矶分校和哈维穆德学院的REU学生。这些学生将有机会成为大型研究型大学研究团队的一员。拟议的研究项目包括洛杉矶犯罪建模、泥石流实验室和数学研究、医学成像以及自动驾驶车辆的协调和跟踪。此外，多达15名处于职业生涯早期的博士生将参加这个项目，其中包括与其他系的教师以及工业和国家实验室的暑期研究生实习项目。该计划的所有学生都将有机会参加新的课程活动，旨在发展取得计算和应用数学顶级博士课程成功所必需的数学和计算背景。

UCLA has a unique environment for advancing the careers of young researchers. State of the art research in applied mathematics, including image processing, materials science, and fluid dynamics is developed with full participation of a vibrant group of graduate students and postdocs. We propose to build on this program to provide an exceptional training and mentoring experience for younger students at the undergraduate and early graduate level. This program will support, over five years, up to 60 REU students from both UCLA and Harvey Mudd College. Proposed research projects include spatio-temporal pattern analysis in crime data, experimental and analysis of slurry flows, imaging processing, and cooperative control of robotic vehicles. An additional group of 15 PhD students, in the early stages of their career, will develop a research career in applied mathematics. These students will have the opportunity to participate in summer internship projects with faculty from other departments and with industry and national laboratories. Students will receive additional training in computation as well as mathematical analysis skills necessary to succeed in a top PhD program.The investigators propose a research training program to enhance the workforce of US citizens and permanent residents entering research study applied and computational differential equations. This program is designed for undergraduate students and graduate students in the early part of a research career. They will work both one-on-one and in small research groups with faculty mentors on cutting edge research problems in an immersive research environment. This program will support, over five years, up to 60 REU studentsfrom both UCLA and Harvey Mudd College. These students will have the opportunity to be part of a research team in a large research university. Proposed research projects include modeling of crime in Los Angeles, laboratory and mathematical studies of mud slides, medical imaging, and coordination and tracking of autonomous vehicles. In addition, up to 15 PhD students, in the early part of their careers, will participate in this program, which includes summer graduate internship projects with faculty from other departments and with industry and national laboratories. All students in the program will have the opportunity to participate in new curricular activities aimed at developing the mathematical and computational background necessary to succeed in a top PhD program in computational and applied mathematics.