Some Truly Impressive Figures

Monday, May 2, 2011 - 3:24pm

Of the 4,296 college students who took the Putnam math exam last December, 3,285 of them scored a zero out of a possible 120 points. Even if you’re not a math wiz, those numbers are easy to understand: the Putnam test is hard--to the tenth power.

Which makes it all the more impressive that the small band of Mount Holyoke students who took the test scored well enough to place in the top 15 percent of participating schools which included traditional mathematical powerhouses like MIT and Caltech.

“Over the last several years our group has been doing better and better on the Putnam exam,” said mathematics professor and this year's MHC Putnam coach Margaret Robinson. The squad’s training takes place at lunch on Fridays when students in the Problem-Solving Group meet up with Robinson to take on a different slate of math problems.

“It’s wonderful that we’ve been doing better on the exam each year, but the main point of the Problem-Solving Group is to have fun and, at the same time, sharpen our wits,” Robinson said.

The Putnam competition, which began in 1938 to create a “healthy rivalry in mathematical studies in the colleges and universities of the United States and Canada,” is a daylong, annual event in which undergraduates tackle a problem set that tests their “originality as well as technical competence.” Competitors can earn up to ten points for each of the 12 problems. If you’re curious, here’s an example:

Players 1, 2, 3, …, n are seated around a table and each has a single penny. Player 1 passes a penny to Player 2, who then passes two pennies to Player 3. Player 3 then passes one penny to Player 4, who passes two pennies to Player 5, and so on, players alternately passing one penny or two to the next player who still has some pennies. A player who runs out of pennies drops out of the game and leaves the table. Find an infinite set of numbers n for which some player ends up with all n pennies.

Now you know why only one person who took the exam this year finished with a perfect score. Fortunately, participants can be awarded partial credit if they show “significant and substantial progress toward a solution.” The Mount Holyoke team, which included Amalia Culiuc ’11, Shiyun Zou ’14, Celine Mathijsen ’13, Yihan Li ’13, Cory Ventres-Pake ’13, Phoebe Yineng Sun ’14, and Xueying Zhao ’12 did that—and then some—in finishing near the top of the standings.

“Despite being a six-hour-long math exam, it somehow manages to be fun,” said Culiuc (pictured right). “Some of the problems are very beautiful. They do not require advanced mathematics or complicated computations, but they expect creativity and thinking outside the box. Other problems may require more background, but they are definitely not the kind of questions you would see in a homework assignment. It is not how much you know that matters, but how creatively you can use it.

“There is no penalty for not doing well and just answering one question is already a good result,” Culiuc continued. “At the end of the day, if I manage to solve a problem or two, I feel very proud, but if I don't, there is nothing to be embarrassed about. Not to mention there is the Putnam party to look forward to in the evening.”

The Putnam party has become a tradition in the Five College area. Each year, all of the students who take the test from Amherst, Smith, UMass, Hampshire, and Mount Holyoke are invited to celebrate the accomplishment that night. But when the Mount Holyoke team showed up at Amherst for this year’s shindig, they were confronted with another kind of math problem. They were the only women in the room.

“We didn't feel intimidated by it--we actually had a lot of fun,” Culiuc said. “As to why we ended up being the only women in the room, I am not sure, but the gender ratio at that party is not very different from the gender ratio one usually sees in mathematics. Maybe there is still some misconception that mathematics is a men's field, but I do hope we managed to prove that women can do math and we can do it well.”