Category: Applied Mathematics

  • Numerical range and pseudospectra of operators

    I would like to do a reading with some students about the numerical range and pseudospectra of operators. We will start by looking at matrices, and if time we will then see how what we have learned about matrices may apply to infinite-dimensional operators. By the end of this reading students will learn about the…

  • Game Theory and Mathematical Economics

    This mentored reading course is intended to provide an introduction to game theory and mathematical economics. This course would be a good fit for both undergraduate and master’s level students in mathematics/statistics who are interested in learning more about how mathematics and statistics are used in economics and related social sciences.

  • The Unified Transform Method for solving partial differential equations

    Fokas at Cambridge discovered the unified transform method (UTM) for solving initial-boundary value problems. The method is more general than the traditional classical methods of Fourier and Laplace, and not more complicated to use. We will discuss the method, applying it to a variety of problems, including some that cannot be solved using the classical…

  • Diffeomorphism groups

    Large groups like diffeomorphism groups have rich algebraic, dynamical and topological properties. Studying these groups from any of these perspectives for an example could be a project.

  • Convex optimization algorithms

    This can be reading or research project on smooth or nonsmooth convex optimization algorithms in various applications. Both analysis and implementation will be covered.

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