Imagine a cold, wintery Saturday morning. Imagine waking up early and trudging through the snow to the basement of the Jadwin physics building to take a three-hour mathematics exam. Now imagine, after lunch, going back to take another three-hour mathematics exam.
Now imagine you are doing this voluntarily.
That is exactly what about 30 students did Dec. 4 when they participated in the William Lowell Putnam Mathematics Competition — the nation's best-known mathematics contest for undergraduates. The contest draws more than 2,000 participants nationwide, all of whom each year gather simultaneously at their respective schools on the first Saturday in December to take the exam.
This year's contest consisted of "self-contained questions involving elementary concepts from group therogy, set theory, graph theory, lattice theory, number theory and cardinal arithmetic," acccording to the competition Website.
For many of the students, competing in math tournaments was nothing new — many had participated in math competitions, such as the International Olympiad, while in high school.
"The competition is fun and challenging," Stefan Hornet '03 said. "I have had a passion [for math] ever since seventh grade and I've kept it." As a result of his high marks in the competition — he finished in the top 25 nationwide — Hornet, along with Radu Mihaescu '03, took home $250 in prize money.
Michael Korn '00, a math major, agreed. "Math competitions are interesting because there is a lot of problem solving and not just application of theoroms. When you get the problem in the competition, you have to think of new ways to attack the problem, and new techniques."
Classroom work, in contrast, Hornet said, is "not as challenging because we just apply set formulas from textbooks."
Mihaescu agreed, noting that the level of difficulty is considerably higher in the math competitions than in regular classwork.
To prepare for the competition, Ari Turner '00, a physics major, said many people practice on past exams. The 12 problems that make up the competition are so difficult that "if you can get two or three correct, you're already high up there in the lead," he said.
However, Turner still derives great joy from working on math problems. "I like the way it is is creative and there are always new ideas of thinking about things," he said. "Also, there are neat patterns."
Turner's favorite problem on the exam was one that involved a "double infinite series." To get the answer, "you have to do a trick in which you switch a couple of the terms. If someone gives you a clue, or tells you what to look for it's not so hard, but if you don't know where to look, it's sometimes impossible," he said.
Math professor Hale Trotter, who organized Princeton's team, said, "People who participate in the competition find it fun to do. Usually the questions are rewarding to do because they are so original and full of ingenuity."
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