Program Description (2007-2009): Two teams of four students each will work collaboratively with this summer's program faculty, Professor Kurt Bryan, Professor David Finn, or Professor Joshua Holden.     Professor Bryan's team will investigate determining the nature and location of cracks or defects in materials using nondestructive testing through solving inverse problems.    Professor Finn's team will explore "the shape of a cookie", a problem involving geometric analysis (differential geometry and partial differential equations) that concerns the shape assumed by a sesile drop (the "cookie dough") on a flat surface (the "cookie sheet"). Professor Holden's team will conduct research on the "discrete logarithm problem," and closely related to cryptographic applications. The teams will make use of computers and software such as Matlab and Maple. Brief mathematical descriptions of the two research areas are given below: Computational Number Theory, Geometric Analysis, Inverse Problems

In addition to the technical program, participants will engage in a companion program to develop their oral and written mathematical communication skills, as well as collaborative and other professional skills. This will be accomplished through required oral presentations, written technical reports, and a close, positive working environment among the participants and the program faculty. The bulk of the work will take place in the "Theorodrome", the computer laboratory/workplace devoted to the REU, and in adjoining classrooms. A list of technical reports and refereed papers prepared by participants since 1990 is available: RHIT REU Publications

Program Philosophy: The Rose-Hulman REU  will be entering its twenty-first year of operation. It has been very successful because of its approach to undergraduate research: participant ownership of the research work. A great deal of time is spent thinking up open-ended but "do-able" research problems which participants can immediately tackle upon arrival and make significant progress on in eight weeks. The initial work is experimentation and discovery through computer-based calculation and analysis of special cases. In this way participants build intuition, then make more general conjectures and decide how to proceed with deeper analysis and proofs. Participants are strongly encouraged to work in teams. The program faculty work closely with the participants on a daily basis, serving as colleagues, mentors and guides to mathematical research. Our goal is that participants have a strong sense of ownership and personal pride in their work, and a good foretaste of what professional mathematical research is about. This pride of ownership is reinforced by the on-campus and off-campus presentations, the technical report, and the follow-up program in which participants improve and polish their work for the technical report series and possible publication in a journal.

Accommodations: Participants will live in one of the on-campus residence halls, all of which are air-conditioned, with easy access to dining and recreational facilities. The housing is provided free, and affordable on-campus dining is available (with a partial meal allowance provided).  Here is a campus map and tour. Work will be carried out in the Theorodrome, the Mathematics Department's computer lab/classroom, (and adjoining classroom) providing access to software like Matlab, Magma, Maple, TeX, as well as email and Internet services. Terre Haute is a mid-sized, mid-west city, 70 miles west of Indianapolis, with all the usual amenities and nearby recreational facilities. One of the REU traditions has been a canoe trip through nearby Turkey Run State Park.