This one-day event will introduce current UCLA students and community college students in math, engineering, computer science and physics to two topics in applied math. UCLA Professors of Mathematics Joseph Teran and Luminita Vese will present their research and engage the students in an activity to demonstrate the power of mathematics to solve real-world problems. The event may also include a tour of a research facility and a demonstration of computer software.
The goals of the program include: 1) to stimulate interest in applied math; 2) to encourage students to choose math as a major; and 3) to recruit students who intend to transfer to UCLA for the CSUMS program, which includes a series of courses and applied math research during their junior and senior years.
The program will begin at 9:30 am and end around 3:00 pm. Each lesson will be two hours:
The presentation will illuminate several problems arising in the area of image processing and some of their solutions using applied mathematics models. Thus students will have the opportunity to learn about image denoising (removing random noise from images), image deblurring (making images sharper), image segmentation (detecting and delineating objects and their boundaries in images). The students will also be exposed to applications arising in medical imaging.
The presentation will be followed by a short Q & A session. Then students may break into smaller groups, and each group will meet with one researcher from the mathematics department imaging group to discuss in details a specific application related with the presentation, or about the CSUMS program.
At the end of this part, students and their teachers will have the opportunity to participate in a presentation in the UCLA School of Medicine, Laboratory of Neuro-science and Imaging (LONI). Here students will learn about the human brain, about neurons, about functions of the brain and about imaging techniques to study its growth, functions and disease. This will be done by a state-of-the art computer graphics presentation and animations.
As computers get faster and more sophisticated, simulating natural phenomena with computers is becoming a common tool for creating virtual worlds in movie special effects, video games and even in medicine. For example, nearly all companies involved in effects for movies and video games have a team dedicated to simulating water, fire, smoke, and explosions. The bar has been raised so high for realism in these industries that simulating the physics of such phenomena is necessary to produce effects at the state of the art.
The governing equations for such phenomena mostly come from classical physics — most often in the form of a system of partial differential equations. The development of algorithms for solving such equations with the computer is one of the cornerstones of applied mathematics. In this seminar, I will give an overview of how a major in mathematics can be used for these exciting new frontiers of application.