Modeling biological systems with differential and difference equations. Examples from: ecology (population growth, disease dynamics); biochemistry and cell biology; and neurobiology (Hodgkin-Huxley and neural networks). Methods include linear stability analyses, phase-plane analyses, and perturbation theory.
In AMATH 422/522, you will learn about models that arise in the life sciences and how they're analyzed using modern mathematical and computational techniques. We will cover statistical models, discrete- and continuous-time dynamical models, and stochastic models. Applications will sample a wide range of scales, from biomolecules to population dynamics, with an emphasis on common mathematical concepts and computational techniques. Throughout, our themes will include interpretation of existing data and predictions for new experiments. MATLAB and Python (see more below) will be used for numerical computations, visualization, and data analysis -- and mathematical tools taught in parallel with their computational implementation. No prior programming experience is assumed. This course is designed for students in a wide variety of departments and with backgrounds across the sciences. A working knowledge of calculus is assumed, together with a desire to learn more about the underlying science, mathematics, or both.
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