Combinatorial Optimization
A graduate-level treatment of linear programming and combinatorial optimization from MIT OpenCourseWare. The course covers network flow algorithms, matching theory, matroid optimization, and approximation algorithms for NP-hard combinatorial problems. Materials include lecture notes, problem sets, and reading assignments drawn from the underlying MIT course, giving a rigorous path through the mathematical foundations that connect linear programming duality to discrete optimization. Topics build from classical results, such as max-flow min-cut and bipartite matching, toward more advanced structures like matroids and submodular functions, before turning to the design and analysis of approximation algorithms for problems that resist exact polynomial-time solutions. As with other MIT OCW offerings, the site provides free access to all course materials with no certificate offered, aimed at students who already have a solid grounding in algorithms and linear algebra.