Instructor: Maggie Regan
Systems of equations arise in many areas of science and engineering along with a wide variety of numerical solving techniques. When the equations are polynomial, algebraic geometry can be combined with numerical methods based on homotopy continuation to develop rigorous numerical solving algorithms. This course will introduce students to such algorithms, collectively called numerical algebraic geometry, from a computational viewpoint. The material will begin with a solid introduction to numerical analysis for solving linear systems, collectively called numerical linear algebra, move through topics such as polynomial interpolation and ordinary differential equations, and end with a discussion on local solving methods such as Newton's method and global solving methods using homotopy continuation. At the end of the semester, students will complete a project and give a presentation regarding solving nonlinear systems of equations in an application of their choice.
Prerequisites: MATH 216/218/221, or equivalent.
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