Randolph-Macon College mathematics majors Martha Hartt ’20 and Maria Cummings ’20 won awards for presentations they gave on their original mathematics research at MathFest, which took place in Cincinnati, Ohio July 31 – August 3, 2019. MathFest is the annual summer meeting of the Mathematical Association of America (MAA).

Hartt and Cummings presented their work in special sessions for members of Pi Mu Epsilon, the national mathematics honor society. The awards for Excellence in Student Exposition or Research are funded by the American Mathematical Society, the American Statistical Association, and the Budapest Semesters in Mathematics.

Martha Hartt ’20
Hartt presented “A Proof of Bertrand’s Postulate,” which was based on research she did in conjunction with the Schapiro Undergraduate Research Fellowship (SURF) program in summer 2018. She worked under the guidance of Mathematics Professor Adrian Rice.

Hartt’s research focused on the distribution of prime numbers. “I came up with an improved proof of a famous result in number theory called Bertrand’s Postulate,” she explains, “which claims that for every positive whole number n, there is always at least one prime number between n and 2n.” Bertrand’s Postulate was originally proposed in 1845.

“MathFest was an opportunity to attend some fun math lectures, meet other undergraduate math majors and explore Cincinnati,” says Hartt. “I had a lot of fun, and the fact that I won an award made it even better.” She credits Rice for keeping her on track during the research process. “Professor Rice was super helpful. He directed me to the relevant articles that I needed to be reading and helped me structure my proof.”

This was the second time that Hartt’s work has received accolades. In spring 2019, she won the award for Best Student Paper for “A Proof of Bertrand’s Postulate” at the meeting of the Maryland-DC-Virginia Section of the MAA.

Maria Cummings ’20
Cummings, who presented  “Investigations into the Discrete Arithmetic-Geometric Mean,” also began her research during SURF 2018, working with Mathematics Professor Chiru Bhattacharya and continuing this work during SURF 2019.

“Drawing on concepts from number theory and abstract algebra, we applied Carl Gauss’ Continuous Arithmetic-Geometric Mean (AGM) to discrete sets of integers,” explains Cummings, who plans to pursue a Ph.D. in pure mathematics. “What has been exciting is how many areas of mathematics we have found in what we thought would be only a discrete and number theory problem. We were able to apply principles from graph theory, linear algebra, abstract algebra, geometry, dynamical systems, and algebraic topology as well.”

Attending MathFest, says Cummings, was “an opportunity to meet others who are passionate about mathematics, learn from them and their accomplishments, and share my own discoveries. So many professors have helped me along the way, and I cannot thank them enough for fostering my passion in mathematics. Professor Bhattacharya was a tremendous source of support: always willing to help me when I was stuck on a proof, explore related topics and encourage me.”