Take a moment to read through this mathematics problem. It is one of 12 that undergraduate students from Canada and the U.S. tackled in the notoriously difficult William Lowell Putnam Mathematical Competition in December. And the most common score for competitors is zero.
But this year, the five-member University of Saskatchewan team, recruited and coached by Professor James Brooke in the Department of Mathematics and Statistics, pulled off a very respectable 41st-place finish out of 402 teams comprised of 4,277 individual competitors from 578 institutions. “This year,” said Brooke, “we had an abundance of riches.”
The gruelling Putnam competition, which requires students to work all 12 problems on a single day, took place in December but the results were just released in mid-April. It is an event that Brooke said “leaves the students drained by 5 pm” despite weeks of practice and problem review. And this year’s result is the best team ranking for the U of S since 2000, and its third best since 1996.
The abundance of riches continued with the recent release of results from the Mathematical Contest in Modeling (MCM) 2013. In that team competition, students are given real-world problems that, over the course of 96 hours, must be formulated into mathematical terms, solved and then returned to the original context. This year, three of the four three-member U of S teams were awarded the meritorious designation. Brooke said achieving meritorious is significant because it goes to only 15 per cent of the competing 5,635 teams from around the world and placed the U of S well ahead of all other Canadian competitors.
Brooke, who shared MCM coaching and advising duties with his colleague Professor Alexey Shevyakov, said competitors chose one of two possible problems. The first, called The Ultimate Brownie Pan, required students to develop a model to show heat distribution across the outer edges of different shaped pans to avoid what Brooke termed “the build up of over-hard crunchy bits along the edges and in the corners.” The second problem – Water, Water Everywhere – required a mathematical model for determining an effective, feasible and cost-efficient water strategy to meet projected water needs in one of five countries.
The problems were released around the world late on Thursday, Jan. 31 and the students were required to submit their solution the following Monday, explained Brooke. They can consult any print or online resources they choose but cannot speak to anyone. For Brooke and Shevyakov, it is 96 hours of fretting and worrying, “and frankly, these kids spend as much time on this as they would in an entire three-credit course.”
This year’s results build on the university’s already impressive record in mathematics competitions. The Putnam contest in particular “really calls upon what I would term an unusual interest and talent,” said Brooke. Some students compete in both the Putnam and MCM but because the MCM problems are not phrased mathematically, “it appeals to a different type of thinking.”
Whatever the competition, Brooke admits it is “a young person’s game. It takes a fresh mind” but he also sees many advantages to competing, not the least of which is a maturation process for students. “They certainly understand themselves better in terms of their own limitations, and they understand what real competition is about. It’s often a wake-up call; they may be on top of the local heap but they discover that it’s a big world out there.
“We want our students to not be sheltered,” he continued. “If they’re not aware of where they stand in the field of mathematics, when they graduate they won’t be competitive. Competitions are an external measure of their future potential.”