# Math students score in Putnam, win and show in Missouri math competition

The Department of Mathematics in Arts & Sciences at Washington University in St. Louis has announced the results of the 72nd William Lowell Putnam Mathematics Competition.

The university fielded 16 students in the competition, which was held on the first Saturday in December 2011. Altogether, 572 colleges and universities in the United States and Canada took part.

Three students must be designated in advance as the school team, and the team score is based on the three individual scores.

This year, the WUSTL team, consisting of senior Alex Anderson and juniors Tom Morrell and Ari Tenzer, placed 28th out of 460 teams.

“My toughest task is picking the students for the team,” says Victor Wickerhauser, PhD, professor of mathematics and this year’s Putnam coach. “It’s not really possible to predict how students will perform,” he says, “but we convince ourselves each year that we can.

Individual performances also are ranked. Anderson earned an honorable mention with a rank of 26 out of 4,440 contestants. Two other students ranked in the top 200 and one more in the top 250.

Anderson will be awarded the Putnam Exam Prize this year. The prize is given to a graduating senior who has done exceptionally well on the Putnam exam during his or her time at WUSTL.

The exam consists of two three-hour sessions during which contestants work individually on 12 problems.

“It’s a very hard test,” says Wickerhauser. “The median score is zero. More than half the people who try it make no progress on any of the 12 problems and get a zero.”

The problems are famous for testing ingenuity and cleverness rather than profound mathematical insight. “Typically,” Wickerhauser says, “they belong to a class of problems that are not solvable, but the one selected for the Putnam has some special properties that make it solvable.

“So those who are good at the Putnam exam are those who are quick to locate the central difficulty of a problem and quick to realize this problem doesn’t have the central difficulty because of some quirk or a particular choice of numbers.”

The exam is based in part on the famous tripos, the competition held at the University of Cambridge in England that also rewards cleverness and thinking on one’s feet, says Wickerhauser. Those who gain ‘first-class’ degrees in this competition are called Wranglers and the highest scorer is the Senior Wrangler.

“The students who take the Putnam really enjoy it,” Wickerhauser says. “For the real Wranglers like Alex, this is a very pleasant activity.”

“My goal was pleasure,” Anderson says. He explains that he was tired of grinding through problem sets in the three physics courses he was taking that term, and was looking forward to “using a limited set of ideas in clever ways rather than learning a breadth of new concepts.”

This doesn’t mean there is never any grousing. Between the morning and the afternoon sessions this year, Wickerhauser took the students to lunch where they pronounced one of the morning’s problems as ‘evil.’

“You were supposed to find all of the numbers for which some property held,” Wickerhauser says, “and there were eight solutions. The first seven you could find by elegant thinking, and to get the eighth you had to work out a whole bunch of cases to convince yourself it was true.”

Elizabeth Lowell Putnam established the William Lowell Putnam Intercollegiate Memorial Fund in memory of her husband, who graduated in mathematics from Harvard. The first competition was held in 1938 and the contest has been sponsored since then by the Mathematical Association of America.

Students prepare for the Putnam during Friday afternoon practice sessions in the fall semester. The practices featured free pizza, paid for by the mathematics department from money won by past Putnam teams. (The top team can win as much as \$25,000.)

An archive of Putnam problems can be found at the Putnam Competition Directory.

Missouri Collegiate Mathematics Competition

WUSTL math students also did well in the 17th annual Missouri Collegiate Mathematics Competition, held April 12 and 13 on the campus of the University of Missouri-St. Louis. Forty-one teams from colleges and universities across Missouri took part.

The two WUSTL teams took first and third place. A team consisting of freshman Alan Talmage and juniors Morrell and Tenzer captured first place. The second team consisting of sophomore Jason Zhang and juniors Matt Halpern and Josh Levin took third place.

“It was a little scary going into the competition as the only freshman,” Talmage says, “but after making it through both sessions, I think that I have gained valuable experience — it was grueling, but it was also fun.”

Wickerhauser notes that several freshmen did well on the Putnam, which means the department should be able to field strong teams in the next three years.

The competition consists of two sessions, in each of which teams work collaboratively on five problems for two-and-a-half hours. It is sponsored by the Missouri section of the Mathematical Association of America and began in 1996. Since then, a WUSTL team has captured first place 11 times.

The faculty sponsors for the competition were Russ Woodroofe, PhD, the Chauvenet Postdoctoral Lecturer in Mathematics, and Edward Wilson, PhD, professor emeritus of mathematics.

To view this year’s problems from the state competition, visit the competition’s site.