In this self-directed course, each student (or group of students) will study a mathematical model that revolutionized biology. After selecting a topic, students will read the primary literature of the chosen model focusing not only on the mathematical and biological aspects of the model, but also on the historical context and long-term impact of the work. The students will then select and read current articles that reference the original models. In some cases, the students may want to expand or modify the model and explore the implications. The students will be responsible for sharing their research with the class and preparing a final paper that compiles all of their research from the semester. Areas of mathematics that are new to the students will be discussed and short problem sets may be assigned. Potential topics include, but are not limited to, models of allometry, natural selection, CAT imaging, predator prey interactions, action potentials, phylogenetic trees, genetic coding, mutating viruses, enzyme kinetics, genetic mapping, hydrogeology, and neural networks. Due to the diversity of topics, students will be able to select models that are appropriate to their level of biological and mathematical expertise.