There is a growing realization that there is a gap between the mathematics taught to undergraduate life science students and the mathematics actually used by biologists and life scientists in their research. This situation has lead professional organizations to call for a reform of the mathematics education of biology and life science students (e.g.,[1–3] ). These calls reflect the increased use of mathematics in the life sciences [4]. In this presentation I will show how the study of modeling and dynamical systems can be used to create a first-year course that introduces mathematical concepts used in life science research in a contextualised way. The course starts by having students learn how to write models describing important biological phenomena such as hormonal levels in the body, predator-prey populations, and populations of susceptible, infected and recovered individuals. Using computer simulations, students learn how to determine the long-term behaviors of these systems by analyzing their phase plane trajectories and time series. We next introduce equilibrium points and how to determine their stability. This enables us to study important biological phenomena such as the notion of “biological switch” or how a cell can start or stop the production of a protein. Studying the stability of equilibrium points naturally leads us to the all-important notion of bifurcation, or qualitative change. In particular, students learn about Hopf bifurcations or how a system can start or stop to oscillate. In the second part of the course, we move somewhat away from the mainly geometrical approach and learn how to determine the stability of equilibrium points using the linearization of a model, motivating the study of the necessary notions from linear algebra by studying discrete-time models.