Using a form of experimental mathematics called random walking, the two worked with rational and irrational numbers to discover and create patterns using computers and numerical analysis.
Both students are math majors, but neither had a background in programming before working with Assistant Professor of Mathematics Enrique Treviño for the three-week research experience. So, they spent the first couple of days getting the basics down.
Then, Treviño introduced them to various challenges related to experimental mathematics and had them select one to pursue in more depth as a team. They chose random walking.
Rawlings and Kupiec spent the next two and a half weeks learning the base 4 number system and assigning numbers with a direction—up, down, left, right—that the computer should move every time that number appears in the base 4 expansion of the rational number. In the end, they were using multi-digit numbers to create letters and form words, such as their first names, “Marina” and “Kevin.” They demonstrated this process for other Richter students during their symposium poster presentation.
Both students say they applied for the Richter Scholar Program to experience what it’s like to work closely with a professor and to validate their decision to study in math, an “employable major,” said Rawlings, a Johnsburg, Illinois native who also is minoring in economics.
“I don’t want to find out junior year that I don’t want to be a math major,” she said. “This allowed me to test the waters.”
Kupiec, who is from Chicago, is minoring in music and exploring a second major. At the moment, he is considering a career in math, perhaps as a statistician. He appreciates the flexibility of the three-week Richter program, which allowed him to gain experience but also left room for him to travel with his band and work during the summer.