ANN ARBOR—A team of University of Michigan undergraduates has placed fourth among 346 competing teams from the United States and Canada in the most prestigious undergraduate mathematics competition in North America—the William Lowell Putnam Mathematical Competition.

Students on the U-M team were Dapeng Zhu, a U-M senior from Troy, Mich., who will begin graduate study in computer science next year; Rishi Raj, a U-M junior from Ranchi, India; and Chetan Balwe, a sophomore from Pune, India. The scores obtained by Dapeng Zhu and Rishi Raj placed them among the top 25 competitors, out of a total of more than 2,900 students.

Rishi Raj won silver medals at the International Mathematical Olympiad in 1997, 1998 and 1999. Chetan Balwe won a gold medal at the International Mathematical Olympiad in 1998 and a silver medal in 1997.

The Putnam competition took place on Dec. 4, 1999, and results were communicated this week. The University of Waterloo finished in first place, followed by Harvard University in second and Duke University in third.

The examination consists of two three-hour sessions. In each session, students must solve six problems. Students are not allowed to communicate among themselves, and are supposed to write essay solutions to the problems. All the necessary work to justify an answer and all the necessary steps of the proof must be shown clearly to obtain full credit. Partial credit is given if the contestant has shown significant progress toward the solution.

The problems are intended to test ingenuity, as well as technical competence. Here is an example: Show that a cube can be dissected into n cubes for any number n greater than or equal to 55.

The W.L. Putnam Mathematical Competition began in 1938, because William Lowell Putnam believed in the value of organized team competition in college studies. Putnam, a member of the Harvard class of 1882, wrote an article in the December 1921 issue of the Harvard Graduates’ Magazine describing the merits of an intellectual intercollegiate competition.

Putnam’s dream came true after his death. In 1927, his widow, Elizabeth Lowell Putnam created a trust fund known as the William Lowell Putnam Intercollegiate Memorial Fund. The first competition supported by this fund was in English. A few years later, a competition in mathematics was organized between Harvard and West Point.

After Mrs. Putnam’s death in 1935, the examination was administered by the Mathematical Association of America.

William Lowell Putnam Mathematical CompetitionMathematical Association of America