Research projects are not out of the ordinary in undergraduate education. Having that research result in a published article? That is far less common. But, for Christendom graduate Peter Cermak ’21, his mathematics research project, which he began as a freshman at the college, did just that, gaining publication in the Rose-Hulman Institute of Technology’s mathematics journal — a major accomplishment and a testament to the strength of Christendom’s mathematics department.
Cermak, who currently works as an engineer at Clark Construction Group, first began thinking about what would eventually become his research project during high school. Wondering how to determine when the graph of a polynomial has rotational or reflectional symmetry based on the coefficients used to define the polynomial, Cermak brought the question to mathematics and natural science professor Dr. Douglas Dailey upon arriving at Christendom.
“The project started as an inquiry into the relationship between calculus and geometry, inspired by a kind of shortcut solution I had found to a certain type of question that regularly came up in Calculus 1,” explains Cermak. “I had been able to prove geometrically that the solution worked in the general case, and the natural question was, how far could this relationship between these two disciplines be extrapolated in these types of questions. With Dr. Dailey’s encouragement and guidance, I arrived at a conclusion that applies to all polynomials of a real variable: a single equation that is satisfied if and only if the polynomial in question is symmetric. In short, I had used geometry to prove a calculus problem, and then used that solution and some other calculus techniques to then prove the general theorem in geometry.”
Once they solved the problem, Dailey tasked Cermak with writing up his findings in a paper as part of the college’s Advanced Studies Program. The solution was so satisfactory, however, that they also sought to publish it in an academic journal. After two years of waiting, Cermak finally heard back: his article had been accepted and would be published. For Dailey, this is a remarkable accomplishment for an undergraduate.
“While it is not uncommon for undergraduate math majors to participate in research, it is far less common for that research to produce something worthy of publication,” says Dailey. “Even then, it takes a special student to take the time to write his findings carefully and go through the process of publishing the paper. In Peter’s case, this took almost four years from beginning to end. Peter’s accomplishment is all the more remarkable given that he completed this project in the midst of his other academic coursework.”
For Cermak, the accomplishment is a great source of validation and confidence in his decision to study mathematics at Christendom. The college’s smaller mathematics department is exactly what led to the project coming to fruition in the first place, according to Cermak, with the time and attention he was afforded resulting in his work being published.
“[This accomplishment] confirmed that the small size of the program actually was a positive benefit, and not a hindrance, since it provided an environment in which I could grow in this way under the mentorship of the faculty who had time to devote to individual students, and so allowed me to produce an article worth publishing,” says Cermak. “The mathematics program at Christendom trained me to look for connections between concepts by approaching each subject with a theoretical motivation. It was this perspective developed by the theoretical focus of the math program, combined with the experience of the faculty in academic writing that prepared me to write this article.”
While Cermak’s project is the first to reach publication, Dailey hopes it will certainly not be the last based on the scholarship coming out of the college’s mathematics majors. Each year, all of the college’s mathematics majors are required to write a senior thesis which involves research beyond what is typically covered in the mathematics curriculum. For some, this has meant a project focusing on the mathematics behind facial recognition. For others, it has meant research on web search engines and encryption.
The department’s smaller size allows the level of personal attention necessary for these projects to flourish as they do, making studying mathematics at Christendom ideal, according to Cermak.
“To anyone who is wishing to study mathematics in college, but is unsure about coming to Christendom because of the size or theoretical focus of the program, I would immediately refer them to the fact that it was the individualized approach that is almost unique to Christendom that allowed this project of mine to reach fruition, and that it was the theoretical and broad focus of the program that taught me to connect the fundamental concepts across disciplines,” concludes Cermak.
To learn more about the college’s mathematics and natural science department, visit here.
To read Cermak’s article, visit here.