Algebraic Combinatorics
MIT OpenCourseWare's Algebraic Combinatorics covers how algebraic structures illuminate combinatorial problems. Topics include enumeration methods, permutations and partitions, partially ordered sets and lattices, Young tableaux, graph theory, the matrix tree theorem, electrical networks, and convex polytopes. The course follows MIT's mathematics curriculum and includes lecture notes and problem sets that build from basic counting techniques toward the structural theorems connecting algebra and combinatorics. Materials are freely available online under a Creative Commons license, with no enrollment fee or certificate track since MIT OCW does not charge for its published course content. The course suits students who already have a foundation in linear algebra and want to see how tools like generating functions and lattice theory formalize combinatorial reasoning.