# Discrete Mathematics (MATH163)

Sets and set operations. Relations and functions: binary relation, equivalence relation, partial order, types of functions, composition of functions, inverse function. Integers and their properties: integers, primes, divisibility, fundamental theorem of arithmetic. Logic and proofs: propositions, theorem, tautology and contradiction, direct proof, proof by contradiction, proof by contraposition, proof by induction. Recursion: recursively defined sequences, homogeneous and inhomogeneus recursive relations, characteristic polynomial, solving recurrence relations. Principles of counting: the addition and multiplication rules, the principle of inclusion-exclusion, the pigeonhole principle. Introduction to Combinatorics: permutations and combinations, repetitions, derangements, the binomial theorem. Boolean algebra: basic Boolean functions, digital logic gates, minterm and maxterm expansions, the basic theorems of Boolean algebra, simplifying Boolean function with Karnaugh maps.