The general goals of the National Science Foundation VIGRE Program are to unify research and education in mathematics for postdoctoral and Ph.D. students and to introduce talented undergraduates to potential careers in science and mathematics.  At NYU, the award will foster the integration of postdoctoral and Ph.D. programs in mathematics at the Courant Institute, together with research experiences for undergraduates in mathematics.  The objectives of the program include the creation of undergraduate research experiences and formalization of internship opportunities for undergraduate and graduate students in industry, government (and university) science laboratories, to support graduate students and postdocs in mathematics at the Courant Institute, and to accomplish these objectives by unifying undergraduate and graduate students, with postdocs and members of the faculty, in their study and research.

All individuals supported by VIGRE funds must be US citizens, nationals, or permanent residents.

VIGRE at COURANT

VIGRE aims to prepare undergraduate students, graduate students, and postdoctoral fellows for the broad range of opportunities available to individuals with training in the mathematical sciences.  Given the mode of operation at Courant, i.e., the existence of many working groups, vertical integration occurred - before the VIGRE initiative - very naturally on the level of faculty, postdocs and advanced graduate students (year 3 and higher).  Therefore, it was natural to build our VIGRE project on these proven structures and to extend these to the advanced undergraduate and beginning graduate level.  Based on the Courant Institute's long tradition with a very pragmatic view of education and research, the VIGRE program has been designed to combine individually tailored activities so as to generate interactions between the different educational and research levels of undergraduates, beginning and advanced graduate students, postdoctoral fellows, and faculty.

We understand VIGRE as an important element of our overall program.  It encouraged and continues to encourage changes and further developments in our structure benefiting not only those who have been supported by it directly, but also strengthening and streamlining the entire research and educational mode at Courant to our mutual benefit.  We have implemented changes in our program (such as vertical integration, mentoring, presentations, internship opportunities, etc.) so as to benefit all students and postdocs; whether supported by VIGRE or not.  The progress of our program is being monitored by an internal review committee consisting of:

H. Hofer, Committee Chair
F. Bogomolov, Director of Graduate Studies
C. Newman, Director of the Courant Institute
J. Shatah, Chair of the Department of Mathematics
E. Tabak, Director of Undergraduate Studies
L.-S. Young, Chair of Visiting Member (Postdocs) Committee

In our VIGRE program, a variety of specific measures for broadening graduate and undergraduate mathematics education at the Courant Institute were proposed and have been implemented.  At the core is the establishment of undergraduate research experiences.  The Undergraduate Lounge, a special study/meeting room for undergraduate majors was created and has been a success.  The Undergraduate Math Colloquium features presentations on career opportunities in the mathematical sciences as well as mathematical talks accessible to undergraduates.

As an additional activity, besides carrying out research within a research group, we are implementing the idea of an "undergraduate mathematics lab".   It involves undergrads doing research projects on problems in "pure" math which have an experimental component to discover and numerically check fundamental conjectures.  There are many such problems in number theory, probability and dynamical systems.  The undergraduate student works on a problem under the supervision of a faculty member.  As part of the project, the student writes a report with his/her findings.

This undergraduate mathematics lab was given for the first time in Fall 2002 and called the "Honors Laboratory in Mathematics"; it was supervised by Peter Sarnak, who earlier designed a similar course as part of the Princeton VIGRE program, and assisted by Steve Miller of Princeton.

This spring, the course is being offered for the second time as “Senior Honors II, Mathematical Wave Dynamics,” taught by Oliver Bühler and Alex Barnett.  This course brings together a professor (Bühler) with expertise in geophysical fluid dynamics and a postdoc (Barnett) with expertise in quantum wave mechanics to create a unique project-based interaction with advanced undergraduates on the topic of waves.  This constitutes an ‘undergraduate mathematics lab’ where novel research can occur under faculty supervision.  As with its predecessor, students will present their work orally and in written reports at the end of the semester.

An internship advising network has been created in order to help students (graduate students and Honors undergraduates) find internships and cross-disciplinary opportunities.  There are many more activities and implementations creating a stimulating environment of learning, teaching and research.

We invite interested institutions to contact us to learn about our activities and experiences.  Please contact: Prof. Helmut Hofer (hofer [at] cims.nyu.edu).

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This material is based upon work supported by the National Science Foundation under Grant No. 9983190.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.