Quantitative methods and mathematical modeling are playing an increasingly important role across disciplines. As a result, interdisciplinary mathematics courses are increasing in popularity. However, teaching such courses at an advanced level can be challenging. Students often arrive with different mathematical backgrounds, different interests, and divergent reasons for wanting to learn the material. Here we describe a course on stochastic processes in biology, delivered between September and December 2020 to a mixed audience of mathematicians and biologists. In addition to traditional lectures and homeworks, we incorporated a series of weekly computational challenges into the course. These challenges served to familiarize students with the main modeling concepts, and provide them with an introduction on how to implement them in a research-like setting. In order to account for the different academic backgrounds of the students, they worked on the challenges in small groups, and presented their results and code in a dedicated discussion class each week. We discuss our experience designing and implementing an element of problem-based learning in an applied mathematics course through computational challenges. We also discuss feedback from students, and describe the content of the challenges presented in the course. We provide all materials, along with example code for a number of challenges.