EXCEL Scholar: Rob McEwen ’05 Will Present Complex Math Research at National Conference

Marquis Scholar Rob McEwen ’05 (Morgantown, Pa.) will present complex math research involving the sequencing of numbers next month at the national Joint Mathematics Meetings in Phoenix, Ariz., and has submitted a coauthored paper to an academic journal.

The research concerned the use of surprisingly short periods of the Fibonacci sequence, a recursive sequence derived from a rabbit population model by medieval mathematician Leonardo Pisano. The chain of numbers is constructed by summing the first two terms to calculate the next one. This process is then repeated to create the sequence.

A double major in mathematics and computer science, McEwen worked alongside Cliff Reiter, professor of mathematics, this summer with four other college students from across the United States in the National Science Foundation’s Research Experience for Undergraduates at Lafayette. Funding was supplemented by Lafayette’s distinctive EXCEL Scholars program, in which students assist faculty with research while earning a stipend. Lafayette is a national leader in undergraduate research. Many of the 180 students who participate in EXCEL each year go on to publish papers in scholarly journals and/or present their research at conferences.

“Some of the properties [of the Fibonacci sequence] allow for fast computation,” Reiter explains, adding that the objective of the project was to find out if the same properties held true to elliptic curve arithmetic. This arithmetic is commonly used in cryptography and computer security. Elliptic curve arithmetic has been in existence since the 1900s, but has become more prevalent in the last 15 years because of advancements in computer security, he notes.

The students worked together to write computer programs and run computer experiments using the Fibonacci sequence and elliptic curve arithmetic. They also read papers on the two topics and wrote a 20-page paper, submitted to the mathematical journal Fibonacci Quarterly.

While the other students worked on the project for eight weeks and did not get to complete the project, McEwen spent two extra weeks with Reiter to put the finishing touches on the paper.

“Rob certainly played a significant role. It was special that he got to complete the project,” Reiter says. The group is waiting to hear if the paper will be approved for publication.

Elliptic curve arithmetic is not as well understood as the Fibonacci sequence, Reiter says. Although he has previous knowledge about elliptic curve arithmetic, Reiter says most of the information generated through the project was new even to him.

“It’s really nice to be on the same side of the problem as the students. It is such a different dynamic than in the classroom,” he says. “You interact hours at a time instead of moments at a time.”

The students didn’t spend all of their time with Reiter researching, McEwen says, explaining that the professor invited them to his house to hang out and play frisbee.

“It was very cool,” he says. “He wasn’t just interested in the day’s results.”

Programs such as EXCEL and the Research Experience for Undergraduates are important tools for college students, Reiter notes.

“It’s one of Lafayette’s strengths,” he says. “I’m really pleased to see the math department taking advantage of it.”

McEwen agrees and adds that he appreciates being able to learn mathematical skills and techniques while earning money.

In addition to working on a previous EXCEL Scholars project with Gary Gordon, professor of mathematics, McEwen is president of the student chapter of the Pi Mu Epsilon mathematics honor society and The Chorduroys, a male a cappella group. He is also chairperson for the student chapter of the Association for Computing Machinery, a professional group for computer science majors, and plays trumpet in the pep and jazz bands and the brass ensemble.

A graduate of Twin Valley High School, McEwen plans to attend graduate school and hopes to one day receive his doctorate in a mathematical field; however, he is not closing the door to any options. “Things can certainly change,” he says, adding, “Graduate schools look very favorably upon people who do undergraduate studies.”

As a national leader in undergraduate research, Lafayette sends one of the largest contingents to the National Conference on Undergraduate Research each year. Over the past five years, more than 130 Lafayette students have presented results from research conducted with faculty mentors, or under their guidance, at the conference.