Can an arc of a parabola inside a circle of radius one have a length greater than four?

Paul Wong
Harm Derksen, mathematics professor and local supervisor for the Putnam Mathematical Competition, explains a proof during a Problem Solving Seminar yesterday.

Stumped already?

This is just a sampling of what some of the University’s most motivated math students will endure during the 63rd William Lowell Putnam Mathematical Competition tomorrow.

Scored out of a maximum of 120 points, the average score for the Putnam exam is zero.

“Most people only score a one or zero on the test. It’s almost impossible to get a maximum score. They have to be super smart to achieve that,” said Harm Derksen, assistant professor of mathematics and Putnam local supervisor.

A six-hour long mathematical marathon, the Putnam competition is a nationwide undergraduate competition sponsored by the Mathematical Association of America. The event consists of an examination on topics common to the undergraduate mathematics curriculum with an emphasis on ingenuity rather than knowledge. This year, roughly 47 University students will participate.

“I like competing against others to see how good I am at it,” said Engineering freshman Dennis Lu, a Putnam contestant.

The examination consists of two three-hour long sessions where contestants are given six problems to solve in each session.

Lu said the extensive testing period is a likely turn-off to those who do not have a strong math skills or an interest in the subject.

“If anything, it’s not enough time,” he said.

Although the statistics are disheartening, Lu said he is approaching the exam with a positive attitude.

“It’s got me kind of worried, but I’m still confident that I can do well.”

Each mathematical proof is graded on a scale of zero to 10 points. For each problem, contestants must provide all work in the form of an essay to justify their answer and obtain full credit.

The highest score in the national competition last year was 101. The highest score from the University of Michigan last year was 50.

Derksen said that it is extremely rare for a student to complete all 12 questions of the exam. “Typically, most students will only work on a few problems, spending much more than 30 minutes on each problem they work on,” he said. “The average person will spend much more time and will probably not even be able to find a proof.”

In preparation for the exam, the Department of Mathematics offers a weekly Problem-Solving Seminar.

The MAA awards prizes as much as $25,000 to the winning schools’ departments of mathematics for high performance in the Putnam competition. In addition, smaller prizes are awarded to individual members of those teams.

William Putnam, a leading advocate for intellectual intercollegiate competition in mathematics studies, inspired the event that started in 1938. The competition was originally designed to encourage a healthful rivalry between university students of mathematics in the United States and Canada.

Results for this year’s exam will be available in early April.

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