Mathematics for Computer Science

6.042J is MIT's discrete mathematics course for computer science and engineering students, and the fall 2010 edition taught by Tom Leighton and Marten van Dijk is on OpenCourseWare with a full run of video lectures. It emphasises mathematical definitions and proofs alongside methods you can apply. The syllabus lists formal logic and proof methods, induction and well-ordering, sets and relations, elementary graph theory, integer congruences, asymptotic notation and growth of functions, permutations, combinations and counting principles, and discrete probability, with selected extras such as recursive definitions, state machines, recurrences and generating functions. The twenty-four recorded lectures follow that arc: proofs and induction, two lectures of number theory, several on graph theory including colouring, matching, minimum spanning trees and communication networks, relations and scheduling, sums and asymptotics, divide-and-conquer and linear recurrences, counting rules, and a final block on probability, conditional probability, independence, random variables, expectation and large deviations.

The site provides readings, recitation problems, problem sets, and exams with solutions. The only prerequisite named is single variable calculus (18.01). All materials are free under OpenCourseWare's Creative Commons licence, without registration or a certificate. A version of the same course with instant-feedback exercises is mirrored in MIT's Open Learning Library.