ABSTRACT Penn State's Mathematics Department aims to become a leading training center for the next generation of mathematical scientists. The Department's rise to research prominence in recent years has placed it in a position from which a comparatively modest investment will lead to exceptional returns in training effectiveness. The Department has planned an integrated program of training initiatives at all levels, from K-12 through postdoctoral. It builds upon the Department's current strengths: its research excellence in several areas; its MASS program, which was founded in 1996 to provide an intensive learning environment for talented undergraduates from around the country; and its unique fluid mechanics laboratory. The Department will expand its recently instituted Chowla postdoctoral program from one to three three-year appointments per year. These positions will include a limited, carefully designed, supervised teaching component. Many postdoctoral fellows will be associated with departmental centers of excellence; some will be selected for interdisciplinary research; and some will be closely involved with our fluids laboratory. The Department will increase the attractiveness of its doctoral program to the country's best students by creating three annual fellowships, called VIGRE Traineeships, with special terms of appointment. Features will include periods of concentration on learning and thesis research, along with a program of closely supervised teaching at various levels. The target time-to-degree for VIGRE Trainees will be five years. Formal graduate training will be extended to the summer months by programs of intensive summer courses and industrial internships. The Department will solidify its innovative MASS program, expanding its visibility and securing its funding. It will also institute a program of six-week summer research experiences for undergraduates (REU's). MASS students and instructo rs are expected to be involved prominently in the REU program. In addition a vigorous program is planned to develop mathematical thinking and enthusiasm for mathematics among area high school students. The Department is responsible for the mathematical education of future scientists and engineers within the largest undergraduate student body in Pennsylvania, and must at the same time promote mathematical literacy across the full breadth of Penn State's student population. To make certain it meets these challenges as effectively as possible, the Department will undertake a thorough review of its entire undergraduate curriculum. A task force will lead a broad effort to generate, discuss, select, and implement the most effective curricular reforms, emphasizing the relation of mathematics to other scientific disciplines and industrial applications. The Department will strengthen the educational and research missions of its Pritchard Fluids Mechanics Laboratory by according it a high priority in the selection of some graduate and postdoctoral fellowships, and by building experimental apparatus which can be used for undergraduate research projects, faculty demonstrations, and K-12 outreach activities. The vertical integration of students, postdoctoral fellows and faculty, both in research and training, is already central to the Department's activities: intensive and extensive interactions among all three groups are day to day realities. Future initiatives will further strengthen vertical integration in a number of very definite ways. For instance, graduate students funded through VIGRE fellowships and participating in the MASS program as assistants will benefit from a double mentoring relationship: they will work closely with an accomplished researcher and teacher while themselves being mentors for talented and committed undergraduates. Postdoctoral fellows affiliated with the fluids laboratory will assist faculty and, in turn, assist graduate and undergraduate students in carrying out the research and training activities of the laboratory. The teaching program planned for all postdoctoral fellows will bring them into contact with other faculty as mentors and with both graduate and undergraduate students in the classroom. It presents opportunities to develop innovative teaching and learning strategies, while still providing a structured environment with defined goals. This project is being supported by the Division of Mathematical Sciences and the Office of Multidisciplinary Activities within the Directorate of Mathematical and Physical Sciences, and the Division of Elementary, Secondary, and Informal Education within the Director of Education and Human Resources.
