9531561 Maki This REU site award will 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 is possible, given the student s background. Each student will work with a single faculty member. Sample topics are: Root Systems and Weyl Groups, Modeling Uncertainty in Economics, Topology of Planar Linkages, Logic with Diagrams, and Speech Recognition by Computers. 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. This interaction will be encouraged 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 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.