The method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equation constraints. It involves forming the Lagrangian function and finding the stationary points, which can be identified among the saddle points from the definiteness of the bordered Hessian matrix. This method allows optimization to be solved without explicit parameterization in terms of the constraints and can also take into account inequality constraints.

This course explores the relationship between algebra and computation, focusing on algorithms used for symbolic computation and modern algebra concepts. Subjects covered include proving combinatorial identities, Gröbner bases, symbolic integration, and experimental mathematics. Prerequisites suggest this is a mid-level course.