The purpose of this course is to present at a high level of mathematical rigor the background topics that are necessary for a good understanding of the theoretical underpinnings of optimization. Many of these topics are traditionally higher-level linear algebra topics that are not present in undergraduate and most basic graduate linear algebra courses. Traditional supporting material covering real-valued functions in multidimensional space receive a thorough review.  Theoretical material supporting linear programming and nonlinear programming will be presented. MATLAB will be used for examples and projects. Homework will consist primarily of the construction of proofs.