Duke University Program for Vertically Integrated, Interdisciplinary Reseasrch

Duke University, Durham NC

Investigators

Abstract

Abstract Bertozzi The Duke Mathematics Department's VIGRE program was designed with NSF's stated objectives of "increas(ing) interdisciplinary activities involving mathematics" and "encourag(ing) activities aimed at broadening undergraduate and graduate curricula" in mind while maintaining existing disciplinary strengths. Interdisciplinary research is a perfect setting for vertical integration and the Duke Mathematics Department has existing disciplinary strengths in algebraic geometry, analysis, differential equations, differential geometry, numerical analysis, probability, and topology. We will use the team research model to enhance our graduate training program and our undergraduate and postdoctoral programs. Graduate and undergraduate students will confront research problems early in their careers and will have ongoing exposure to them through their respective programs. Advanced graduate students and postdocs will take on new roles as project leaders in vertically integrated research seminar courses and in team research groups. All students and postdocs will develop skills in computation, communication and collaboration as part of their mathematical training, thereby broadening the range of opportunities available to them as mathematical scientists. The goal of the program is to have students and postdocs completing their programs with a broad scientific knowledge and clear understanding of the inner workings of a scientific team, as well as an academic research and teaching portfolio that will enhance their career advancement potential. In the undergraduate program our goal is to increase students' enthusiasm for mathematics and its role in research at all levels of their training at Duke. We will increase the number of first-year and major seminars aimed at exposing students to current topics of research. Current seminar course topics include cryptography, physiology and medicine, geometry, and optimization. New topics include heart dynamics, gravitational lensing, and artificial intelligence. A new Perspectives on Science seminar aimed at first-year women interested in mathematics, statistics and computer science will expose young students to current research of senior scientists, postdocs, and graduate students. The cornerstone of the undergraduate VIGRE program is a new two-year intensive research program, entitled `Practical Research for Undergraduates with VIGRE' (PRUV, pronounced "prove"), for advanced mathematics majors, which integrates course work, summer internships in a vertically integrated environment, and senior theses. These improvements in the undergraduate program are targeted to involve more students in research activities. We expect that one outcome will be more senior honors theses on research problems and more students choosing to apply to graduate school in the mathematical sciences. For the graduate program, the VIGRE grant will be combined with Duke resources to support all first year students without teaching duties. After the first year, the strongest VIGRE-eligible students will receive a one semester-per-year teaching release in order to direct more of their energy towards research. All graduate students in the graduate program will have the opportunity to work in vertically integrated research teams, including postdocs, graduate students PRUV students, and at least one mathematics professor. Those working on interdisciplinary problems will also collaborate with at least one professor from another discipline. Current interdisciplinary activities include deforestation and aerosol dynamics, geometric computing, granular flow, heart dynamics, liquid films, photonic band gaps, physiology and medicine, string theory, and uncertainty in porous flow, with Duke collaborators in the School of the Environment, Computer Science, Physics, Biomedical Engineering, Cell Biology, Civil and Environmental Engineering, and the Institute for Statistics and Decision Sciences. Graduate teacher training currently begins in the first-year with students supervising calculus laboratories. In order to shorten time to degree and increase retention, we will postpone teaching responsibilities and teacher training by one year for all graduate students. This will enable all first year graduate students to focus on fundamental course work required to pass the qualifying exam before the beginning of year two. The current teacher-training program will be expanded to include alternative teaching experiences for students and postdocs including outreach to high school teachers, and mentoring of undergraduate and graduate students. A new computational requirement will be part of their first-year curriculum. The graduate students currently run a weekly seminar with talks aimed at first and second year graduate students given by graduate students and postdocs. PRUV undergraduates will be encouraged to attend this seminar. VIGRE postdocs will play a leadership role in the overall program. Each year, for the first three years, two VIGRE postdocs will be hired for three year terms. These positions will parallel existing Duke funded Assistant Research Professors (ARP). VIGRE Postdocs will have the opportunity to play a strong leadership role in the team research groups including mentoring graduate students and undergraduates and developing a well-defined independent research program. They will also have the opportunity to take on a significant supporting role in at least one of the following activities: (1) coordinating research seminars and workshops, (2) co-supervising summer PRUV students and graduate student internships, (3) helping undergraduates and graduate students in a writing workshop. Postdocs and students will collaborate with high school teachers in Project CHISEL `Carolina High School Educational Leadership project'. They will design modules for classroom use that will introduce high school students to the use of mathematics in current research. Funding for this activity was provided by the Division of Mathematical Sciences and the MPS Office for Multidisciplinary Activity.