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Master elementary discrete mathematics essential for computer science through this comprehensive course covering logical notation, sets, relations, graph theory, state machines, induction, proof techniques, recurrences, asymptotic analysis, number theory, cryptography, combinatorics, and probability theory. Explore fundamental mathematical tools and proof methods including contradiction, strong induction, and casework while developing skills in algorithm analysis and discrete probability. Learn to work with predicates, sets, and various proof techniques before progressing to state machines and invariants. Study summation techniques, asymptotic notation, and recurrence relations to analyze algorithmic complexity. Delve into number theory concepts including divisibility, modular arithmetic, and cryptographic applications. Examine graph theory topics such as coloring, matching, connectivity, trees, directed graphs, and DAGs. Build counting skills through permutations, combinations, and advanced counting techniques. Conclude with probability theory covering conditional probability, independence, random variables, expectation, variance, and large deviation bounds including Chebyshev and Chernoff bounds.
