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This course presents a survey of computational algorithms for students who are interested in solving problems from a variety of scientific disciplines. Mathematical modeling is often used to describe a phenomenon of interest, but the model is typically too complex to construct an analytical solution. Numerical algorithms are therefore needed to find a solution that best describes the phenomenon of interest. The survey of numerical methods will be motivated by models that describe events in physics, biology, medicine and will focus on data driven applications. The students will learn appropriate numerical algorithms, as well as how to critically analyze the quality of their results. Specifically, students will mathematically analyze the accuracy, efficiency and convergence properties of their techniques. results. Although programming will not be formally taught as part of the course, students will write numerical code in languages such as MATLAB to compute their solutions. Resources will be provided to help students learn to write MATLAB code.

Course Objectives: Students will master a suite of computational tools for approximating solutions to complex mathematical models. Students will understand how implement algorithms to generate these solutions and evaluate their quality and accuracy. This is not a survey course, although students will program methods to gain understanding of how methods work, in particular to compare advantages and disadvantages of various algorithms.