The US National Science Foundation's (NSF's) Undergraduate Biology and Mathematics (UBM) program significantly increased undergraduate research in the biomathematical sciences. We discuss three UBM-funded student research projects at Clarkson University that lie at the intersection of not just mathematics and biology, but also other fields. The first project focused on optimizing a network model for how the brain detects and reacts to threats, an important problem in neuroscience. The second project sought to classify species of lizards based on geometric features of their shapes. This is a classic problem in evolutionary biology that became an innovative problem in mathematical imaging science when the students developed methods to analyze on features extracted from image data. The final project was psychology based and aimed at developing statistical methods for analyzing the behavioral and psychosocial effects of caffeine use by college students. This article describes the logistics of our UBM research program, the student projects, and, most importantly, the lessons learned working with students and other researchers from a wide range of backgrounds in the formal setting of an NSF-funded undergraduate research program.