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Fall
Semester Program:
Mathematical Tools for Modeling
During this semester, we focus on six areas of Mathematics which have had a huge impact on applications: Algebra, Linear Algebra, Differential Equations, Differential Geometry, Complex Variables and Probability. The courses combine an overview of the basic aspects of each area with interesting applications based on state-of-the-art software. The ability to use mathematical techniques to model real-life situations gives participants in this semester a definite advantage in a world with problems that become more challenging and complex every day. In this semester, we provide the basic tools to tackle a variety of interesting problems.
1. Master the core results in the mathematical areas covered during the semester—linear algebra, differential equations, differential geometry, complex variables, algebra and probability—needed to develop mathematical models for concrete problems.
2. Gain experience utilizing the main software tools related to these fields and be able to solve relevant modeling problems.
To participate in projects that solve or explore problems with modeling tools and in cocurricular activities that showcase how mathematicians are currently collaborating with industry, government and academia to solve problems.
Prerequisites
Students must have studied at least one linear algebra course and the standard calculus sequence ending with multivariate calculus.
Core competencies expected of applicants:
• In calculus, the applicant should be familiar with the notions of integration, derivatives, series, limits.
• in linear algebra, the student should be familiar with the concepts of vector spaces, bases, dimensions, matrices, linear transformations, determinants, kernels.
• In multivariate calculus, the student should be familiar with the concepts. of derivative of a map from R^d to R^k for d and k up to three, chain rule, Hessian, maxima and minima, gradient, cross and dot products.
• Have completed a course that involved proof writing.
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