In this talk, we will review a number of past and ongoing research projects, primarily involving undergraduates, in applied mathematics. The topics span a variety of domains such as, but not limited to, (1) physics, including investigating how surface roughness perturbs magnetic fields in superconductors and experimental studies of negatively buoyant particles flowing in a viscous suspension under gravity; (2) social sciences, including using machine learning to build predictive models for changes within the homeless population of Los Angeles; and (3) biology/medicine, including studying how COVID-19 affects the disabled community and developing an ab initio model to quantify how oligomers of amyloid beta can lead to Alzheimer's Disease. The projects have been carried out through directed research courses and summer REU programs.