Outline:

1. Univariate and Multivariate Polynomials
2. Geometry, Algebra, and Algorithms
3. Groebner Bases
4. Predictor-Corrector Methods
5. Homotopy Continuation Method

Objective:

This class contains the theoretical and computational aspects of numerical polynomial algebra. We will study the classical and state-of-the-art methods.

Textbook:

1. D. Cox, J. Little, and D. O' Shea, Ideals, Varieties, and Algorithms
2. Hans J. Stetter, Numerical Polynomial Algebra