This course gives an introduction to discrete optimization problems.A discrete optimization problem is the task to optimize a linear function over the integer points in a polyhedron. This topic is very rich in terms of the underlying theoretical tools that one can use to understand and solve such problems.

Introduction to linear algebra: vectors and matrices, solving systems of linear equations, vector spaces and subspaces, orthogonality and least squares, determinants, eigenvalues and eigenvectors, singular value decomposition and linear transformations. Applications in and links to computer science will be presented in parallel.