Scientists and engineers often use mathematical models to understand physical phenomena. Most often, the process of model building is learned through experience. In this course, the theory and practice of building mathematical models is explored. We learn from the experiences gained from previous work. Based on journal club style discussions of the research literature, examples from hearing science, speech production, orthopedic bioengineering, plant morphogenisis, and physics are drawn. General, meta-theoretical issues that go beyond the particular subject matter are explored. Examples include: What is a model? What constitutes a good model? What is the process of building a model? What are the different approaches to modeling? Dualisms in modeling will include: General Principles vs. Detailed Models, Analytic vs. Computational models, Forward vs. Inverse approaches, Manual vs. Automated Methods, and the Interplay Between Theory and Experiments. We will also cover special modeling topics like "Dimensional analysis and Scaling" and "Deterministic Randomness and the Limits to Prediction."
