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This course will prepare students to apply quantitative techniques to the analysis of experimental data and the modeling of biological systems. To emphasize both practical and theoretical skills, the material will be presented whenever possible in a hands-on workshop style, and the completion of several projects by the students will be required. Topics include: practical aspects of data formatting and management; communication of quantitative concepts (verbal, graphical and mathematical); a review of statistics, with emphasis on the selection of appropriate statistical tests; the use of modern software packages; the interpretation of results; the formulation, evaluation and analysis of mathematical models of biological function, with an emphasis on linear and non-linear regression, determination of model parameters; and the critical comparison of alternative models with regard to over-parameterization. The formal components will introduce (and demystify) ordinary and partial differential equations and basic principles of non-linear dynamics, in order to enable quantitative modeling in biological arenas such as neural function, enzyme kinetics, cardiac dynamics and signaling pathways. Additional special topics will also be presented (e.g., control theory, machine learning, information theory, and image analysis) and their application will be illustrated with ongoing research in the laboratories of participating faculty.
