The Rutgers University Mathematics Department, in its project "Extending and Renewing the Education of Mathematicians," will change the way that postdoctoral fellows and graduate students interact with faculty, undergraduates, and each other. It will also increase opportunities for undergraduates, graduate students and post-docs to participate in applications of mathematics in other disciplines and in industrial practice. The improved, vertically integrated program will bring new research areas to the curriculum, prepare beginning mathematicians for the variety of career paths available to them, and increase the access of students to mathematical research at the highest level. Five research groups - discrete mathematics, number theory, control theory, non-linear partial differential equations, and mathematical physics - will participate in the program.
Postdoctoral fellows will be chosen to work with these groups, and their research and pedagogical opportunities will be designed to promote interaction across all levels of mathematical experience within the University. Faculty mentors from these groups will supervise the research development of the post-docs. The post-docs will be provided a mentored progression through a variety of types of teaching at the university level, such as instruction in large multi-section courses, small upper level undergraduate and graduate courses, courses with non-traditional pedagogy including small group work, and courses involving appropriate use of technology. They will engage actively in the construction of course modules for undergraduate courses and seminars for undergraduates and graduate students, while being involved with undergraduates in REUs and with graduate students in guided study and minitutorials. The faculty mentors will also see that the post-docs have opportunities to interact across disciplinary boundaries. Opportunities for internships in industry and government will be provided where appropriate.
Graduate students chosen as VIGRE Trainees will participate in a program designed to provide broadened curricula and early exposure to and active involvement in research in the five core areas. Mentored "rotations" - guided study and research participation with faculty members - will supplement the first two years of graduate course work. Examples of the tasks of the trainees in the rotations could include reading a technical paper or part of a book, scientific programming in support of the research efforts of a faculty member, or preparation of a small-scale seminar talk. The trainees will interact with faculty, VIGRE post-docs, and undergraduates in seminars in the five research areas, and will be exposed to the cross-disciplinary and non-academic uses of mathematics in an Outside Speakers Seminar. Opportunities for internships in industry and government will be provided for the trainees where appropriate. The trainees will have a structured and mentored progression through a variety of types of teaching, such as grading, recitation instruction, independent courses, course development, use of technology, workshops, supervision of independent study, and will participate in an ongoing seminar on Issues in Mathematics Education at the Post-Secondary Level.
Additional professional development support will be provided to VIGRE trainees and post-docs in such areas as professional communications (writing papers and giving presentations), understanding and using funding opportunities (reading requests for proposals, writing responses), refereeing and reviewing, getting invited to meetings and making good use of them.
Undergraduates will participate in the project through direct research opportunities; seminar activities; mentoring relationships with faculty, post-docs, and graduate student trainees; and curriculum revision. Advanced undergraduates will be encouraged to engage in REU activities during the academic year, and a summer REU, in which faculty from the five core areas will participate, will be supported by VIGRE. "Junior seminars" in these areas will be developed to present work at a level that advanced undergraduates and graduate students can understand; VIGRE post-docs will help to organize the seminars and talks will include those by VIGRE trainees. In addition to the REU's, which will provide faculty, post-doc and graduate trainee mentoring to undergraduates, upper level undergraduates will have the opportunity to work with first-year students and sophomores and through participation in workshop sections and involvement with the Gelfand Outreach Program in Mathematics. Course modules and revised courses will be designed as part of a curriculum review; such redesign will involve undergraduates (as a part of an REU activity) and graduate students. For example, the undergraduate number theory course can be reconsidered to provide more emphasis on applications (encryption, coding theory, etc.); a new year-long upper level undergraduate course devoted to mathematical modeling will be developed; control theory modules can be designed to provide students with the opportunity to actually see ordinary differential equations and computer controls combined to predict and modify some simple-appearing physical situations. Undergraduate and graduate courses involving elements of the five core areas have grown in number as faculty add new and updated courses; the VIGRE project offers the opportunity to conduct careful analysis of the content, level, and prerequisites for these courses, with the goal of designing coherent packages of such courses.
Funding for this award is provided by the Division of Mathematical Sciences and the MPS Directorate's Office of Multidisiplinary Activities.
