Mathematical Programming

Optimization is the mathematical backbone of operations research, and this course gives you the theory behind why algorithms find optimal solutions rather than just how to run them. You'll work through optimality conditions (Fermat, Lagrange, KKT), prove things about convex sets and duality, and model problems ranging from network flows to integer programs, mostly through problem sets that ask you to derive and justify rather than just compute. Coming after the undergraduate OR sequence, it bridges into research-level work in convex and conic optimization, and it's the foundation you'll lean on for stochastic programming, machine learning theory, and almost any quantitative thesis in IE.