The aim of Computational mathematics course is to teach students how to use computational (both numerical and symbolic) methods in applications coming from various branches of mathematics.
The course covers the following subjects:
1. Polynomial algorithms: square-free factorization, polynomial factorization over finite fields, factorization of rational polynomials, monomial orders and Groebner bases;
2. Elimination theory: elimination with Groebner bases, classical elimination with resultants;
3. Inifinite summation and Gosper's algorithm;
4. Numerical integration: Monte-Carlo algorithm.