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 students from 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.
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. This project built on the existing program to provide an exceptional training and mentoring experience for younger students at the undergraduate and early graduate level. The project supported, over six years, approximately 100 undergraduate students from UCLA and Harvey Mudd College. Undergraduate research projects involved a diverse set of scientific problems with external collaborators from different disciplines. Some examples include spatio-temporal pattern analysis in crime data, experimental and analysis of slurry flows, imaging processing, cooperative control of robotic vehicles, cloud modeling, and bone growth modeling. An additional group of 31 PhD students, in the early stages of their career, were supported to help them develop a research career in applied mathematics. These students participated in summer internship projects with faculty from other departments and with industry and national laboratories and took core courses for the PhD program. Students received additional training in computation as well as mathematical analysis skills necessary to succeed in a top PhD program. This research training program enhanced the workforce of US citizens and permanent residents entering research study applied and computational differential equation. The students worked both one-on-one and in small research groups with faculty mentors on cutting edge research problems in an immersive research environment. These students had the opportunity to be part of a research team in a large research university. The students were trained in scientific research and in the oral and written presentation of their results. PhD students supported in the early years of this program have completed their dissertations and gone on to postdoctoral positions at top research universities (including the National Science Foundation Postdoctoral Fellowship and the Fulbright Fellowship for overseas study). Some are now in industry working for leading companies in computer graphics and movie special effects, internet social analytics, the defense industry, and the National Laboratories. First year PhD students supported in the later years of this program are now working on their dissertations and include a recent NSF graduate fellow and an NDSEG fellow. Their research projects including graph-based clustering of high dimensional data, modeling of optimal placement of policing for crime hotspots, and computational algorithms for fluid mechanics and solid mechanics.
