# Applied Mathematics

Applied Mathematics instruction at Brown University began in 1941 to fill a need for applied mathematicians in industry, which had been brought to attention a year earlier in a report prepared by Thornton T. Fry of Bell Telephone Laboratories for the National Resources Planning Board. A Program of Advanced Instruction and Research in Mechanics, a twelve-week course in the summer of 1941, was organized by Dean Roland G. D. Richardson with the support of the U.S. Office of Education and the Carnegie Foundation. Sixty advanced mathematics students attended courses on differential equations given by Jacob D. Tamarkin, Willy Feller, and Stefan Bergman, on fluid dynamics by Richard von Mises and K. O. Friedrichs, and on elasticity by I. S. Sokolnikoff. There were also lectures by a number of other participants, including Norbert Wiener and Brown physics professor R. Bruce Lindsay. An evaluating committee was appointed to appraise the purposes and results of the experiment and advise President Wriston regarding the continuation of the program. This committee, consisting of Professor Marston Morse, then President of the American Mathematical Society, Professor Theodore von Karman of the California Institute of Technology, Dean George B. Pegram of Columbia University, Dr. Warren Weaver of the Rockefeller Foundation, and Dr. Mervin J. Kelley of the Bell Telephone Laboratories, encouraged the continuation of the experiment. In the fall of 1941 William Prager and John L. Synge joined the faculty of the program which had an enrollment of thirty. The next summer program, which featured courses of the theory of flight by S. Bergman, advanced dynamics by L. Brillouin, geometrical foundations of mechanics by Prager, plasticity by Prager, and electromagnetic waves by S. A. Schelkunoff, was attended by 110 students, 45 of whom were postdoctoral fellows supported by the Rockefeller Foundation. The Program awarded the first Brown Ph.D. degree in applied mathematics to Joaquin B. Diaz in 1945.

Formally established as the Graduate Division of Applied Mathematics in May 1946 and staffed by faculty of the Departments of Engineering, Mathematics, and Physics, the program began to offer graduate courses the next semester. In 1949 the first professor appointed to the Graduate Division of Applied Mathematics was E. H. Lee, who became chairman in 1954. Also in 1954 the name of the department was changed to Division of Applied Mathematics when an undergraduate curriculum leading to the Bachelor of Science degree in applied mathematics was instituted. The undergraduate program was intended to meet the needs of industry for personnel able to translate scientific problems into mathematical form for the recently developed electronic computing devices. The first Bachelor of Science in Applied Mathematics degrees were awarded in 1956.

In 1948 Professor Rohn Truell organized the Metals Research Laboratory, a semi-autonomous research group concerned primarily with the study of ultrasonic wave propagation in solids. From its earliest days the division has been recognized internationally as a center for the study of solid mechanics, ranging from the ground-breaking work on the mathematical theory of plasticity under the direction of Professor Prager to the emphasis on viscoelasticity theory under Professor E. H. Lee in the 1950s, followed by Professor R. S. Rivlin’s work on nonlinear and hereditary response, and Truell’s on transport properties and crystalline defects. In 1957 and 1958 Ulf Grenander was professor of probability and statistics. He returned to Brown in 1966 from the Directorship of the Institute of Insurance Mathematics and Mathematical Statistics in Stockholm. Professor Philip Davis, formerly director of the Numerical Analysis section of the National Bureau of Standards, joined the department in 1963.

The Brown Center for Dynamical Systems was established in 1964 by Solomon Lefschetz and Professor J. P. LaSalle for research and advanced study. Lefschetz, former chairman of Princeton’s mathematics department, came out of retirement at the age of 73, prompted by the Russian success with Sputnik, to organize the group of men who worked at the Martin Company’s Research Institute for Advanced Study in Baltimore, and then came to Brown. In 1965 the Center organized an international symposium, held in Puerto Rico and co-sponsored by the U.S. Air Force’s Office of Scientific Research, which was attended by one hundred of the world’s leading mathematicians. The Center was dedicated to Lefschetz in August, 1974. Members of the Center include faculty in the Divisions of Applied Mathematics, Engineering, and Biology and Medicine, and the Department of Mathematics.

In 1986, with the sponsorship of the Federal University Research Initiative Program, the division acquired three new centers: the Laboratory for Fluid Mechanics, Turbulence, and Computation (in cooperation with the Division of Engineering); the Center for Control Sciences; and the Center for Intelligent Control Systems (in cooperation with Harvard and M.I.T.). Two major periodicals edited in the division since their foundation are the *Quarterly of Applied Mathematics,* founded by Professor Prager in 1942, and the *Journal of Differential Equations,* founded in 1965.

The division has been housed since March 1953 in the elegant Henry Pearce House at 182 George Street, designed by Angell and Swift and built in 1898. Its carriage house at 21 Manning Street was used as a physics laboratory and known as Barus Lab or “the Castle.” The Applied Mathematics Division had earlier occupied the Cabinet on Waterman Street, the Powel and Richmond House at Brown and Benevolent Streets (which was razed for the building of the Wriston Quadrangle), the house at 70 Waterman Street, and Richardson Hall. When the Center for Information Technology building was opened in 1988, the division acquired the use of the former Computing Laboratory at 180 George Street. Division chairmen have been Erastus H. Lee, Ronald S. Rivlin, Rohn Truell, Joseph P. LaSalle, Jack K. Hale, Walter F. Freiberger, Wendell H. Fleming, Donald E. McClure, and Harold Kushner.