Optimization concerns the minimization or maximization of an objective function. It often relies on the computation of the gradient of this function. MAA 209 covers several aspects of the classical methods that are used in such problems. For instance, the gradient methods (or steepest descent), the non-linear conjugate gradient methods will be seen. A particularly important topic concerns the Newton-Raphson method which extends the mono-dimensional Newton method to higher dimension. Comp. Mathematics B follows Comp. Mathematics A (MAA 208), since linear algebra methods are heavily used. Applications to the computation of the eigenelements of a matrix or to the resolution of non-linear systems of equations are also studied. As before, the course heavily uses practical sessions which are taken under consideration for the grading.