Discrete Mathematics
by Dominik Scheder · Shanghai Jiao Tong University
Dominik Scheder's proof-based course on sets, functions and relations, enumerative combinatorics, graph theory, and network flows and matchings, each concept paired with a fully proved non-trivial result. Learners read formal statements and write rigorous proofs of their own.
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Standard undergraduate discrete mathematics textbook covering logic, proof, sets, functions, algorithms, number theory, counting, relations, graphs and trees, with thousands of exercises. Its relations chapter develops equivalence relations, partial orders, closures and matrix representations to a level suited to computer science study.
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The Art of Problem Solving wiki's entry point for discrete mathematics, defining the field and branching into combinatorics, graph theory, set theory, number theory, and abstract algebra. Written for competition students, with links into AoPS problem archives.
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Learn the fundamentals of discrete mathematics! Explore logic, sets, functions, and more with this open-source introductory website.
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Discrete mathematics for computer science: logic and proof methods, induction, sets and relations, graph theory and coloring, number theory and congruences, asymptotic notation, counting, recurrences and discrete probability. This gallery holds 25 lecture videos; the course also offers problem sets and exams with solutions.
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A free, open-licensed undergraduate textbook covering counting and combinatorics, sequences and recurrence relations, symbolic logic, proof techniques including induction, and graph theory, with many worked exercises. Readers build the discrete foundations needed for computer science and upper-level mathematics.
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Designing machine learning algorithms with provable guarantees: nonnegative matrix factorization, topic models, tensor decomposition, sparse recovery, dictionary learning and learning mixture models. Moitra's detailed lecture notes, which read as a complete monograph, and problem sets teach rigorous analysis of learning algorithms.