Mathematical Biology requires a unique combination of skills that prepares students for jobs in both the private sector and academia. At both graduate and undergraduate levels our students learn to:
- Create mathematical and statistical models of real world phenomena to address questions posed by managers, scientists and engineers.These models run the gamut from simple functions and discrete models to coupled ordinary and partial differential equations.
- Develop and apply appropriate statistical and computational tools to estimate unknown parameters from using observational data.
- Use model competition and goodness-of-fit metrics to determine which models perform best in comparison with data and where models fail.
- Construct numerical simulations to illustrate and test system behaviors.
- Use mathematical tools to understand the dynamics of models and the systems they describe.
- Communicate with interdisciplinary audiences, interchanging ideas with non-mathematical communities and conveying results of model construction, parameter determination, simulation evaluation, and systems analysis.
- Develop their own professional networks, participate in local and national academic events where they show their latest research advances, and learn about the importance of scientific independence and collaboration.
What is Mathematical Biology?
Mathematical Biology (or "BioMath" for short) is that branch of applied mathematics specifically concerned with answering biological questions and exploring biological mechanisms. There are some notable differences from `standard' applied mathematics. In mathematics applied to physics and engineering, mostly the governing equations and mechanisms are well known (e.g. the Navier-Stokes equations in fluid physics, or Maxwell's equations for electromagnetics, Newton's laws and Hamilton's principle in mechanics). Consequently the emphasis in mathematics applied in these fields is analyzing the solution and behavior of known equations in complex circumstances. Experiments tend to be aimed at measuring specific physical quantities, and are therefore very specific and technical. In biology and ecology, by contrast, there are seldom any accepted governing equations. What the governing mechanisms are, and how they may be represented mathematically, is part of the question. Consequently, Bio Mathematicians are often concerned with modeling, and whether or not a given model describes data. Additionally, biological systems thrive on and are dominated by variability. Consequently we end up dealing with some issues which are often regarded as statistical (e.g. how can we determine if one model is better than another, given the inherent uncertainties in the data?).