In this proposal, we describe a plan to realize at Ohio State the twin goals of the VIGRE program: (a) to broaden the preparation of undergraduates, graduate students, and postdocs in the mathematical sciences; and (b) to initiate, improve, and sustain education activities which stimulate teaching, learning, and research interactions across the boundaries of academic age, professional standing, and mathematical discipline.
We give an overview here of the parts of this plan:
Invitation to Research: In their first year, VIGRE graduate trainees will take a full year course which will consist of many short lecture series, taught by different faculty: in the fall, by senior faculty, but including junior faculty and VIGRE postdocs as the year progresses. The aim of these short courses is to provide first-year graduate students with a glimpse into the various areas of mathematics in a non-technical way and in an informal setting, and to introduce them to the basic ideas, examples, and problems that motivate research in various fields. We expect that this will be a stimulating challenge for the faculty involved. By the end of the year, the students will have seen a sizeable percentage of the Department's faculty, and will have an overview of many parts of mathematics and some feeling for the possible directions of research. One of the tasks of the faculty who contribute to this course will be to give the students references on where to go next to find out more: articles, texts, courses, and Working Groups (see below). We expect most if not all first-year graduate students to take this course, and we expect that it will attract some of our honors undergraduates as well.
Working Group Rotations: In the second year each VIGRE graduate trainee (and any other interested graduate students) will join a Working Group. These Working Groups are small groups of faculty and students engaged in a common research venture. Several faculty organize a Working Group around an interesting problem or subject, and agree to involve undergraduate and graduate students in the investigation of that topic. The format will be very flexible, and will allow for quite varied experiences: some groups may be able to involve the students in current research; others may function more like a learning seminar. At the end of the quarter, each graduate student will write up a project report and give an oral presentation. Each VIGRE graduate trainee will rotate through three different Working Groups, one per quarter, and will thus become acquainted with different areas of mathematics, different research styles, and different faculty and students as the year progresses.
Professional Development: To round out the professional development of the VIGRE trainees we will offer courses in teaching methods and skills (this is already a standard part of our TA training), computer skills, writing mathematics, delivering seminar talks, proposal writing, and putting together an application. We also will run a seminar in industrial mathematics, providing students and postdocs with experience in how and where mathematical expertise is used outside of academia; and we have identified opportunities for summer internships in industry, which graduate students and postdocs may apply for.
Advising and Mentoring: We have in place a committee to advise and mentor our graduate students; each student is given information on the research interests of the faculty and each student's progress is reviewed yearly. We have a few suggestions for improving the current system.
Pipeline Programs: We have in place two excellent programs that contribute to the mathematical training and experience of undergraduates: the Ross Young Scholars Program (which begins with high school students, but involves students and faculty at all levels) and the Honors Program (which is part of our undergraduate mathematics major program). We discuss ways for the students in these programs to participate in research activities (among them the Working Groups described above), and we propose a conference to bring together participants in REU programs around the country. Finally, we propose a support seminar that would allow us to admit students from our applicant pool whose applications show evidence of potential but lack some of the required background for graduate work.
A Teacher Component to the Ross Program: This year, five high school teachers were included in the Ross Program, to introduce them to the ``exploration method'' on which the Ross Program is based. These teachers plan to try this method in their own classes, and to report back to us on their experiences. We plan to expand this new component of the Ross Program to a class of 15 participants.
The personnel to be supported or partially supported by VIGRE funds in the above outline are
The aim of these initiatives is to introduce both our undergraduate students (especially honors students) and our graduate students to the research environment at a much earlier stage, and to acquaint them with a greater number of faculty. We also aim to increase the interactions between undergraduate students, graduate students, postdocs, junior faculty, and senior faculty. Finally, we want to better prepare our graduate students for academic and non-academic employment.
Among the results we expect from these initiatives is an increased effectiveness of our graduate program: we hope to see a lowering of the time required to obtain a PhD, and we also hope to see better employment placement--whether in academia or industry--for our students after graduation. Finally, we hope that our students will simply be better educated when they graduate, with a broader perspective on the extraordinary variety and range of applications of mathematics.
Some of the sections that follow describe new proposals, while
others describe a feature of our Department which is already in
place. To clearly distinguish between the new and the old, we mark the
title of the sections where something new is being proposed with a
superscript 
.