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Princeton math whiz creates video based on combinatorial proofs, wins prize from MoMath museum

 

High schooler Amy Wang from Princeton proved that math is more than just numbers when she recently won the runner up Steven H. Strogatz Prize for Math Communication award presented to high school students worldwide by the National Museum of Mathematics (MoMath).

Every year, MoMath, the only math museum in North America, located in New York City, awards the Strogatz Prize to a select group of international high school students for creating projects that uniquely incorporate math in social media, art, literature, videos and performance.

“MoMath is delighted to award the second annual Strogatz Prize to talented high school students who have created exceptional projects that reveal their love of math in so many different ways,” said MoMath’s CEO and Executive Director Cindy Lawrence. “This friendly competition celebrates students of all backgrounds who, through their unique talents, inspire others to appreciate the beauty and wonder of mathematics in the world around us.”

Amy and her teammate, Shreya Mogulothu from Plainsboro, students at West Windsor-Plainsboro High School North, created a video called “Combinatorial Proofs…And Basketball” to explain a combinatorial proof using basketball.

“At first glance, combinatorics looks like a lot of algebra. Its famous identities are written as complicated jumbles of symbols with an equals sign in the middle. It takes away from the beauty of the concept the equation is trying to convey, which is often much simpler than it seems. So, we decided to make a short video on a combinatorial proof.

“We were debating on various identities to prove but decided on this one, 2^n = sum of (n choose k) from k going from 0 to n, because it is a classic example of the idea of counting things in different ways. We enforced this concept by asking the same question to two friends, XXX and XXX (us!), and having them come up with different expressions for the same thing.

“When it comes to the actual counting, this identity is normally proven combinatorially using the power set of some set S with cardinality n. We decided to put it in the context of something many people can relate to: shooting baskets. When you take shots, there are two outcomes for each ball (making the shot or missing it), similar to how when you choose a subset of S, each element has two choices (being in or being out). So, we can omit the set notation and just focus on the real concept.

“This idea immediately leads us to count 2^n possibilities for one side of the identity. For the other side of the identity, we decided not to burden the viewer with the algebraic definition of (n choose k), because that takes away from what we’re really trying to convey, which is just the idea of choosing some balls from the total, and then adding that up for all possible scores you could get,” according to their project.

To view their video, visit https://bit.ly/3cM2hLu

The Steven H. Strogatz Prize for Math Communication is awarded based on content, creativity and communication. This year, MoMath received 63 entries from 15 states and 11 countries, including Brazil, Czech Republic, China, India, Korea, Mexico, Philippines, Saudi Arabia, Spain, Turkey and the United States.

“It’s a thrill to see the creative work of these students,” said Steven Strogatz, American mathematician and Jacob Gould Schurman Professor of Applied Mathematics at Cornell University. “The winners are all so imaginative, and their projects reflect such great effort to communicate clearly and even entertainingly. Bravo to all of them.”

Amy and Shreya will accept their award in a virtual ceremony on June 27.

  • This information was provided by Gary Zarr & Associates on behalf of the National Museum of Mathematics.

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