State Math Contest
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Research Experience for Undergraduates
Qualifying Exam Problem Sessions
Summer 2003 VIGRE Mini-courses
The Mathematics Behind Biological Invasions
June 2 - 13, 2003
With support from a National Science Foundation VIGRE grant, the Mathematics Department at the University of Utah hosted a two week mini-course on the Mathematics of Biological Invasions. Biological invasions are one of the greatest threats to biodiversity and ecosystem function, and are also one of the largest perturbation experiments our species has tried. This mini-course examined the many ways that mathematical models have been used to make sense of this important and interesting problem. This program was designed for students who had studied differential equations at the graduate school level.
Fred Adler, University of Utah
Mark Lewis, University of Alberta
Mike Neubert, Woods Hole Oceanographic Institution
During the first week, Dr. Lewis and Dr. Adler presented lectures on the spread and ecology of invasions. During the second week, Dr. Neubert presented more advanced lectures on invasions and biocomplexity, and other speakers presented the biological background on emerging problems like West Nile Virus. Afternoons during the first week were given over to problem sessions, led by postdoctoral fellow Nancy Sundell-Turner. During the second week, students worked on projects that were presented on the final day.
Additional Mini-Course Information
Photo of Participants
Waves in Inhomogeneous Media
July 28 - August 8, 2003
Principal Speakers: George Papanicolaou (Stanford University) and William Symes (Rice University)
Other Speakers Included: Alexander Balk, Andrej Cherkaev, Elena Cherkaev, David Dobson, Ken Golden, Graeme Milton, and Jerry Schuster
Waves frequently propagate through inhomogeneous media. This manifests itself in phenomena as diverse as the twinkling of stars, the appearance of rainbows, the blueness of distant mountain ranges, the colors of opal and Venetian glasses, the mikiness of colloidal suspensions. Technologically, an understanding of wave propagation in inhomogeneous media is important to tomographical applications where one seeks to say something about underlying inhomogeneities from seismic or electromagnetic measurements. It is also important to the design of photonic and phononic band gap materials (which prevent the propagation of waves over a band of frequencies), of diffraction gratings, and of selective absorbers of solar energy. This mini-course focused on both electromagnetic and elastic wave propagation in linear and non-linear media.
Waves in Chains and Lattices
Waves in Geophysical Media
Waves in Photonic and Phononic Band Gap Structures
Waves in Non-Linear Media
The Theory of Rainbows, Halos, and Glories
In addition to lectures, the mini-course featured discussions and problem sessions. The mini-course concluded with a special session where students, post docs, and other invited researchers had an opportunity to present their work.
Notes and exercises courtesy of Prof. Jerry Schuster:
Notes on seismic migration in HTML or PDF
Diffraction modeling and migration MATLAB code exercise
Past mini-courses: 2005 2004 2003 2002
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