MC senior completes Investigative Study project in mathematics

Marietta College senior Casey Trail of Glenshaw, Pa., recently completed his study on “Investigating Finite Geometries from a Graph Theoretic Point of View,” which was part of an Investigative Study at MC.

Trail, who is majoring in mathematics with a double minor in economics and philosophy, spent the summer working on his project with his mentor, Dr. Mark Miller, assistant professor of math at Marietta.

“This was a great opportunity for me to do independent work and discover something new in mathematics,” said Trail the son of Deborah Trail of Glenshaw and the late Daniel Trail. “Such an opportunity is rare for undergraduates, and I am immensely thankful to the Honors Committee for the chance to spend the summer doing what I love.”

Trail began studying the relationship between graph theory and finite geometry just after the close of classes in May. He and Miller started with reading through the first few chapters of “Algebraic Graph Theory” (Godsil and Royle), a graduate level textbook.

“One of Casey’s main tasks was to take some well known ideas from one area of mathematics (Finite Geometry) and recast them in terms of another area of mathematics (Graphic Theory),” Miller said.

At the end of May, Trail and Miller traveled to the Middle Tennessee State University to attend the Cumberland Conference on Combinatorics, Graph Theory and Computing. There, Miller gave Trail a problem to investigate. Trail spent a week at a summer mathematics program at Brigham Young University in Provo, Utah.

Within a few weeks of his return, Trail was able to prove his theory. Since then Trail and Miller have submitted their results to the “Bulletin of the Institution for Combinatorics and its Applications” for publication. Also in August, Miller presented their results to the “Rocky Mountain Discrete Mathematics Days,” a conference at Colorado College, where he received a good deal of feedback from other mathematicians.

“Casey Trail exhibits all of the characteristics that are necessary for success as a mathematician,” Miller said. “Specifically, Casey has a keen intellect, a tenacious work ethic, and a quick wit. I have no doubt that this Investigative Studies project was just the first in a series of mathematical achievements in store for Casey.”

Trail is also involved in many campus organizations. He is president of the Delta Tau Delta social fraternity, and president of Kappa Mu Epsilon, Marietta’s mathematics honorary. Trail was the recipient of the 2004 Theodore Bennett prize, which is presented annually to one junior majoring in mathematics.