MATH 680 : Introduction to Computational Algebraic Geometry

Credits: 3

Course Description: This course provides a strong foundation for the study of computational algebraic geometry and its applications, both within and outside mathematics. It has two foci. The first is the algebra-geometry dictionary, going back to the ideas of Descartes, by which one can translate geometric ideas into algebraic ones, and vice versa. The second is Buchberger's algorithm, which extends the familiar Gauss-Jordan elimination procedure to systems of polynomial equation. By means of this algorithm one can compute almost everything worth knowing about affine algebraic varieties. Computer algebra systems will be used for computation and visualization of this algorithm and its ramifications. Applied areas of exploration may include robotics, computer aided design, automatic theorem proving, invariant theory, projective geometry, and computer vision. In addition, highly motivated students will be prepared to participate meaningfully in current research in invariant theory and the geometry of nilpotent orbits.

Pre-Requisites: Permission of Instructor.