This proposal seeks to build meaningful interconnections among the various educational and research components of the mathematics enterprise at Stony Brook. The Departments of Mathematics and of Applied Mathematics and Statistics have developed strongly but in largely divergent directions. This joint proposal enhances the instruction and research training in both departments through (i) cooperation in areas where the strengths of one department can benefit the other, and (ii) new initiatives that will benefit both departments. Its emphasis on building vertical research teams ties in with the university mandate to develop opportunities for undergraduates to participate in research. Its emphasis on developing pedagogy ties in with the university mandate to revitalize undergraduate education.

The proposal has the following general components:

1. Broadening the Research Training of Undergraduates, Graduate Students and Postdocs;
2. Developing Vertically Integrated Research Teams;
3. Strengthening the Educational Experiences of Undergraduates, Graduate Students and Postdocs;
4. Promoting Greater Interactions Among Students, Postdocs and Faculty in The Two Departments

Undergraduates
Up to 20 juniors and seniors each year may accepted to participate in mathematics research teams or individually planned research projects during a semester of the academic year or during the summer. In Applied Mathematics and Statistics, the general areas of research are:

1. Computational Applied Mathematics–preferred background: AMS 326 and 361;
2. Statistics–preferred background: AMS 310 and either AMS 294 or AMS 315; and
3. Computational Geometry–preferred background: AMS 301 and AMS 345.

VIGRE undergraduate participants will be mentored by a faculty member or VIGRE Postdoctoral Fellow. They will typically participate in a vertically integrated research team consisting of faculty, postdocs, graduate students, undergraduates, and visiting scholars. Participants will expected to produce a written final report of their work and to contribute, as appropriate, to any papers prepared by their research team for publication.

Stipends of $1000 during the academic year and $2000 during the summer are available for U.S. citizens and permanent residents. Academic credit (AMS 487) is available for all VIGRE undergraduate participants.

Graduate Students
There will be eight VIGRE Doctoral Fellowships for 5 years at a minimum of $17,000 a year (plus $3,000 a year in tax-free educational expenses) beginning in fall 2000 and fall 2001, four in Applied Mathematics and Statistics and four in Mathematics. VIGRE Fellows will have a special program integrating interdisciplinary research and enriched training in collegiate mathematics education. Interested applicants should contact Prof. Kim, AMS graduate program director (631-632-8360; wjkim@notes.sunysb.edu).

Postdocs
There will be five VIGRE Postdoctoral Fellows each year, with VIGRE postdocs typically staying for three years. Postdoctoral Fellows will have a teaching load of one course per semester. They will have interdisciplinary research experiences and special instructional training, similar to the VIGRE Doctoral Fellows. Interested applicants should contact Prof. Tucker, VIGRE project co-director (631-632-8365; atucker@notes.sunysb.edu).