Discrete Mathematics I

Introduction to mathematical logic: Propositional logic, propositional calculus, formal proofs. Proof Techniques: Contraposition, Αντιθετοαναστροφή, contradictions, mathematical induction. Sets, relations, functions: Set operations and their properties, inclusion-exclusion principle, one-to-one / onto functions. Equivalence relations, order relations, extreme points and bounds. Asymptotic behavior of functions. Countability: Finite / infinite sets, pigeonhole principle, Russell’s paradox, Cantor’s diagonalization method. Counting: Addition/multiplication rule, permutations and orderings, balls-into-bins, choice of unordered collections of with/without repetition. Discrete probability: Discrete sample space, event, conditional probability, Bayes rule, expected value of variable.

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