It is proposed to provide ten undergraduate mathematics majors, recruited nationwide, with a research topic and a research environment which is as close to that of a working mathematician as possible, given the sudent's background. Each student will work with a single faculty member. Sample topics are: Continuous Logic, The implicit Programming Problem, Bruhat Ordering On the Symmetric Group, The Alternating Group, and Applications to Certain Puzzles, Representations of Symmetric Bilinear Forms, Spaces of Triangulations, Random Walks and Electrical Networks in the Plane, Affine Diffeomorphisms of Surfaces, Wavelets and/or Hidden Markov Models, The Dynamics of Piecewise-Linear Maps, Peano Functions and Descriptive Set Theory, The Mathematics of Finance, Algebraic Codes, and Bifurcation of Planar Conservative Systems. The students will meet privately with their faculty advisors two to three times a week. Throughout the eight weeks the students will give frequent progress reports to the group. One of the most important aspects of the program is the interaction among the students themselves. For some this will be their first opportunity to get to know other students of comparable mathematical interest and ability. We will encourage this interaction in a number of ways: The students will be living together in a single dormitory and eating in the same cafeteria. There will be a room in Rawles Hall (the Mathematics Department) in which students can gather to work. During the last week the students will give lectures on the work they have done. They will also prepare written reports on their work. These will be collected into a single bound volume.
