Mathematical Foundations for Bioinformatics

The course provides a review of some of the fundamental mathematical techniques commonly used in bioinformatics and biomedical research. These include: 1) principles of multi-variable calculus, and complex numbers/functions, 2) foundations of linear algebra, such as linear spaces, eigen values and vectors, singular value decomposition, spectral graph theory and Markov chains, 3) differential equations and their usage in biomedical system, which includes topic such as existence and uniqueness of solutions, two dimensional linear systems, bifurcations in one and two dimensional systems and cellular dynamics, and 4) optimization methods, such as free and constrained optimization, Lagrange multipliers, data denoising using optimization and heuristic methods. MATLAB, R and Python will be introduced as tools to simulate/implement the mathematical ideas.