MATH 310: Mathematical modeling for life (scientists)

Life is sustained by constant change: molecules react, genes are expressed, populations evolve. These dynamic regimes are best represented by mathematical models that explicitly describe these processes.

This seven-week course introduces mathematical modeling of biological systems with an emphasis on dynamic models. To that end, an introduction and refresher of calculus – the mathematics of change – is done in the context of classic models like enzyme (Michaelis–Menten) kinetics, Predator-Prey (Lotka-Volterra) equations, and epidemic (Ross-McDonald) models. Modern applications of dynamic models and their combination with data through state-of-the-art statistical inference are then presented with an overview of the challenges and perspectives in a broad context of real-world research.

Prerequisites Previous knowledge (preferably a full-semester course) of calculus is strongly recommended, but not required – solid understanding of functions of the form \(y=f(x)\) and their 2D graphing is required.

Learning Objectives:

• Describe natural processes as explicit mathematical functions
• Formulate models in the absence of complete mathematical knowledge by implicitly describing known interactions
• Modify the output of model solution or simulation by changing variables (parameters)
• Acknowledge and recognize inference as the inverse of computing/simulating function output