Senior Adam Ardeishar was selected as one of the Regeneron Science Talent Search (STS) finalists for this year on Jan 23. STS, often called “the nation’s oldest and most prestigious math and science competition,” selected 40 finalists for 2019. These finalists were selected out of 300 semi-finalists from a pool of 1,964 high school seniors who entered in the competition. Entrants to the competition performed original research, which was then rigorously judged to select the winners. Over the years, many participants have gone on to win Nobel Prizes and other esteemed awards and recognitions in the fields of math and science.

Ardeishar’s project, titled Extreme Values of a Statistical Distribution Relating to the Coupon Collector Problem, used statistics to solve the classic problem in a novel and analytical way.

“For my project, I just worked on a math problem for a while. The problem is a generalization of something called the coupon collector problem. What I did in my project is I took this problem and related it to a statistics problem, which is equal to the average value of the maximum of several gamma variables, which sounds somewhat complicated, but it’s related to a field of math called extreme value theory which is concerned with deviations from the mean,” Ardeishar said.

The way Ardeishar solved the problem was significant in that it generalized the problem to a wider range of applications and could potentially be of use in many cases in the real world.

“I took this problem and generalized it and then I found an analytical solution or way to solve the problem that gives it more relevance and insight into the how the problem behaves for lots of different cases. For example, this is relevant in stock trading, where you want to guard against several independent risks. However, I won’t be pursuing these applications to this problem,” Ardeishar said.

He came up with the idea for this project through the TJ Math Team and with some help from a mentor, he was able to find a new way to solve the problem. At first, he didn’t even think about submitting his work to the Regeneron STS, but later did so on a whim.

“I’m on the TJ Math Team and we go to a competition at MIT every year and one of the problems on the contest was this problem. My mentor, who’s currently a freshman at Harvard, is taking a class called statistics 210 at Harvard, which is a graduate statistics class, and I read his notes for that class and used those techniques to solve this problem. I wasn’t intending to submit my work to STS, but then I solved enough of the problem that it seemed like a reasonable enough result,” Ardeishar said.

Ardeishar, along with the 40 other finalists, will be invited to Washington D.C. in March to display their work and undergo final judging to determine the top ten winners.