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Summer 2004 REU Program |
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"Inverse Problems and Applications" Conducted by David Dobson and Kenneth Golden (with assistance from Grady Wright and Frank Lynch) Participants:
Dates: Tuesday, June 1 - Friday, July 9, 2004 Description: Inverse problems encompass an extremely wide variety of applications and mathematical techniques. Application areas include medical imaging, geophysics, astronomy, nondestructive testing, and microscopy. Relevant mathematical techniques involve differential equations, optimization theory, functional analysis, numerical analysis, and scientific computation. Problems generally involve obtaining information about inaccessible or "hard to see" quantities (such as the detailed subsurface structure of a certain part of the earth) from indirect measurements (such as recordings of reflections of acoustic waves directed into the earth). The field is rich with fascinating open problems with important scientific applications. The goal of this summer REU was to introduce undergraduates to the basic ideas underlying inverse problems and to quickly transition students to begin work on individual research projects in inverse problems. The REU took place during the six-week period of June 1st through July 9th. We began with preliminary lectures outlining mathematical techniques, computational issues, and examples of problems and how they arise in applications. Guest speakers presented examples of particular inverse problems (for example in geophysics, remote sensing, and medical imaging), and described the current state of the art in research in these areas. Students, in consultation with participating faculty and mentors, did background research in areas of interest to them, with the goal of selecting a particular inverse problem for further research. Depending on the student's background and interests, we pursued research on analytical or computational aspects of the problem. At the end of the REU, students presented a summary of their research projects to fellow students and mentors. |
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