Discrete Mathematics I
Weekly Hours: 5
ECTS Credits: 6.5
Course Homepage: http://ecourse.uoi.gr/enrol/index.php?id=777
Description: Introduction to mathematical logic: Propositional logic, propositional calculus, formal proofs.
Proof Techniques: Contraposition, 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.