Combinatorial Theory: Introduction to Graph Theory, Extremal and Enumerative Combinatorics
An MIT OpenCourseWare graduate course covering the core methods of modern enumerative and algebraic combinatorics. Topics include partition identities, bijections built from Young tableaux, spanning trees in graphs, and techniques for randomly generating combinatorial objects. The course also touches on extremal combinatorics and points out connections to algebra, probability, and other areas of mathematics where these tools are used. Materials include lecture notes and problem sets published by MIT, following the structure of an advanced combinatorics seminar. No enrollment fee applies since this is a self-paced OpenCourseWare release; there is no certificate track, only the course materials themselves for self-study. Suited to students who already have a background in discrete mathematics and want a rigorous treatment of enumeration and graph-theoretic combinatorics rather than a first introduction to the subject.