This REU site award supports six undergraduate research students who will work under the supervision of research faculty on mathematical problems in five areas. They include harmonic analysis and the phi-transform, complex analysis and differential equations, population genetics, image processing and combinatorial number theory. Seven faculty will be involved at various stages of the program. Regularly scheduled meetings together with informal discussions are used to develop interactions among the students and faculty. Although not required, students will be encouraged to prepare their results for presentation and publication. As Washington University is one of the preeminent research institutions in the country, the students have an exceptional opportunity to meet many of the visitors who pass through the campus during the summer.