CofC professors are not just teachers but also practitioners of their fields. Our students learn history from historians, psychology from psychologists, math from mathematicians, and so on. Not only does this guarantee that the instructors are experts with practical knowledge of their discipline, it also means that undergraduates here have a rare opportunity to work on real research with their professors. Here are just two of the research projects being conducted in the math department this summer:
In a project with medical applications, undergraduate Michael Lanier is working with Professor Mukesh Kumar to mathematically analyze wireless capsule endoscopy (WCE) images to identify cancerous polyps automatically. Utilizing deep learning and neural networks,
the team hopes to help doctors combat the third most common cancer in the US through early detection. Lanier and Kumar explain their research this way: “In this project, we will develop an
automated system for polyp detection in WCE images based on deep learning which is an improvement to the neural networks that contain more computational layers that allow for higher levels of abstraction and prediction in the data.”
Undergraduates Monique Sparkman and John Cobb along with graduate student Albert Serna and Professor Alex Kasman are studying the particle-like waves called “solitons”,
but instead of the usual real-valued functions, the solitons they are studying are described by quaternions, abstract numbers that do not satisfy the familiar commutative property. Since waves and non-commutativity are both fundamental to quantum physics, studying this combination could someday have practical value, but for now this team is happy to simply have made some surprising discoveries about how these two ideas fit together mathematically.