Mathematical Sciences: Inverse Problems

本科生研究体验奖继续支持华盛顿大学一项非常成功的数学活动。在接下来的三年中，每年将有十名学生获得资助。他们将与两名经验丰富的教师导师一起研究一系列广泛的问题，这些问题通常被归类为逆问题。这些问题既涉及离散环境，也涉及连续环境，并决定倾向于物理应用。在洞察这些问题的过程中，计算机实验将发挥重要作用。学生将研究与网络中导体数值的计算有关的问题，以及大地电磁理论和引力理论中的反问题的离散版本。最基本的问题是通过测量表面的电势和电流来确定整个导体内部的电导率。在试图通过测量表面引力势来确定引力质量的形状时，也出现了类似的问题。学生们将以小组形式工作，并在项目结束时提交关于他们研究的论文。这个网站以前的学生的记录是非常成功的。许多人正在优秀的美国院校攻读研究生理科学位。预计这一趋势将持续下去。

This Research Experiences for Undergraduates award continues support for a highly successful mathematical activity at the University of Washington. Ten students will receive support in each of the next three years. They will work with two experienced faculty advisors on a broad range of questions generally classified as inverse problems. The problems involve both discrete and continuous environments with a decided slant toward physical applications. In gaining insight to the problems, computer experimentation will play a major role. Students will investigate problems associated with the computation of values of conductors in a network, on discrete versions of inverse problems in magneto-telluric theory and in gravitational theory. The fundamental issue is that of determining the conductivity throughout the interior of a conducting body from measurements of potential and currents on the surface. Similar questions arise in attempts to determine the shape of a gravitational mass from measurements of gravitational potential on the surface. Students will work in small teams and will submit papers on their research at the end of the program. The record of former students at this site is one of significant success. A number are pursuing graduate science degrees at outstanding U.S. institutions. It is expected that this trend will continue.