MIT Reports to the President 1995-96




During the academic year 1995-96, there were 216 undergraduates majoring in mathematics, 166 in
Course XVIII, Mathematics, and 30 in Course XVIII-C, Mathematics/Computer Science. Bachelor of Science degrees, including double majors, were awarded to 76 students, 60 in Course XVIII and 16 in Course XVIII-C.

There were a total of 103 graduate students in mathematics, all in the Ph.D. program. This year 24 students received the doctoral degree and one received the master's degree.


There were 52 faculty members in the Mathematics Department. The following were on whole or partial leave:

Professor Sy Friedman (spring term)

Professor Kenneth Hoffman (year)

Professor Michael Hopkins (spring term)

Professor Ehud Hrushovski (year)

Professor Robert MacPherson (year)

Professor Willem Malkus (spring term)

Professor James Munkres (spring term)

Professor Gian-Carlo Rota (spring term)

Professor Gilbert Strang (fall term)

Associate Professor Ezra Getzler (spring term)

Associate Professor Alexander Goncharov (spring term)

Assistant Professor Mauricio Karchmer (spring term)

There was one Visiting Professor and two Visiting Assistant Professors in mathematics this year:

Professor Tomasz Mrowka from the California Institute of Technology (fall term)

Dr. Steven Lee from Oak Ridge National Laboratory (spring term)

Dr. Kate Okikiolu from Princeton University (spring term)



Professor Kenneth Hoffman retired from MIT after a long career as a mathematician and administrator. He joined the MIT faculty in 1959, was Department Head from 1971-79, and in 1989 became the Executive Director of the Mathematical Sciences Education Board.

Professor Willem Malkus retired from MIT after a distinguished career as Professor of Applied Mathematics in the area of fluid dynamics. He joined the Department's faculty in 1969.

Assistant Professors Mauricio Karchmer and Mark Matthews resigned from MIT.


Professor Tomasz Mrowka will join the Department as Professor of Mathematics from the California Institute of Technology. He is a leading figure in gauge theory and differential geometry.

Dr. Daniel Spielman has accepted an Assistant Professorship appointment specialized in theoretical computer science.

Dr. Maurice van Putten has accepted an Assistant Professorship appointment specialized in relativity, fluid mechanics and numerical methods.


Assistant Professors Sergey Fomin, Michel Goemans and James Propp were each promoted to Associate Professor of Applied Mathematics from Assistant Professorship appointments.

Dr. Karen Smith was promoted to Assistant Professor of Mathematics following a C.L.E. Moore Instructorship appointment. Her specialty is commutative algebra.


Professor Sigurdur Helgason received an Honorary Doctorate degree from the University of Uppsala, Sweden.

Professor Gian-Carlo Rota was selected as recipient of the 1996-97 James R. Killian Jr. Faculty Achievement Award. He also received the Doctor Honoris Causa from the University of Bologna, Italy.

Professor Gang Tian was selected as the inaugural holder of the Simons Professorship of Mathematics for a five

year period. The Simons Professorship was established through the support of Marilyn and James H. Simons.

Professor David Vogan was elected as a member of the American Academy of Arts and Sciences.

Assistant Professor Michel Goemans received a National Science Foundation (NSF) Career Award for a four year period from the NSF Division of Computer & Computation Research. He was also awarded the Optimization Prize of the Society for Industrial & Applied Mathematics for the most outstanding paper on a topic in optimization between 1991 and 1994.

Assistant Professors Michael Brenner and Daniel Spielman were awarded Alfred P. Sloan Research Fellowships.

Graduate student Andras Vasy received an Alfred P. Sloan Doctoral Dissertation Fellowship.

The MIT Mathematics Team placed third in the Putnam Intercollegiate Mathematics competition.

Junior David Jao was awarded the Barry M. Goldwater National Scholarship in recognition of his excellent academic achievements.

Seniors Thomas Weston and Ruth Britto-Pacumio were awarded the Jon A. Bucsela Prize in Mathematics in recognition of distinguished scholastic achievement. Among those seniors awarded degrees in mathematics, ten were elected to the national honor society Phi Beta Kappa.


Professor Hung Cheng follows Professor Richard Stanley as Chairman of the Applied Mathematics Committee. Professor Richard Melrose replaces Professor David Vogan as Chairman of the Graduate Committee, and David Vogan follows Professor Michael Artin as Chairman of the Undergraduate Committee. Professor James Munkres continues as Chairman of the Committee of Advisors and Professor Daniel Stroock as Chairman of the Pure Mathematics Committee.


Among the educational initiatives of the department, here are the ones that involve the undergraduate core.

For several years, the department has offered three two-term calculus sequences: 18.01 & 18.02 Calculus, 18.011 & 18.021 Calculus with Applications, and 18.014 & 18.024 Calculus with Theory. Several of these subjects are offered both in the fall and in the spring terms.

At this time, most of the freshmen coming to MIT have taken calculus in high school. About one-half of the freshman class places out of 18.01 (single-variable calculus) and takes 18.02 (multivariable calculus) in the fall term. Many of the others, though perhaps not prepared for 18.02, have had some calculus. This has put a strain on the traditional 18.01 subject. In response to this, two substantial changes are underway. First, Professor David Jerison is in the process of revising the 18.01 curriculum, designing it for students who have had little or no high school calculus. Second, we began last fall to offer a new intermediate calculus sequence: 18.01A and 18.02A. This sequence, which has been well received, is designed for the middle group of students, those who have had some high school calculus but are not yet ready for multivariable calculus. It covers the 18.01 calculus in the first half of the fall term, and then begins with the 18.02 material.

A third innovation in the service courses was made last spring in 18.03 Differential Equations. For many years, we have run that subject with three hours of lecture and one hour of recitation each week. There is general agreement that two hours of recitation would be preferable; and as an experiment, we did have two recitations last spring. This was quite successful, but since 18.03 has a large enrollment each term it is not clear that we have the staff to do this regularly.

Our efforts to improve the quality of teaching seem to be very successful. Our practice teaching program, begun two years ago, is now standard for our graduate students. In this program, Teaching Assistants are put into a classroom situation before they are assigned a recitation of their own. The department's teaching workshops, very ably organized by Professor James Propp and Dr. Lori Breslow, are now required of all new Teaching Assistants. These initiatives supplement the mathematics department's successful videotaping program, which was organized many years ago by Professor Arthur Mattuck and by the Institute-wide teaching programs. We are fortunate that Professor Haynes Miller has agreed to supervise these programs beginning next fall.

David J. Benney

MIT Reports to the President 1995-96