Introduction to logic and proofs: Direct proofs; proof by contradiction; mathematical induction. Fundamental structures: Functions (surjections, injections, inverses, composition); relations (reflexivity, symmetry, transitivity, equivalence relations); sets (Venn diagrams, complements, Cartesian products, power sets); pigeonhole principle; cardinality and countability. Boolean algebra: Boolean values; standard operations on Boolean values; de Morgan’s laws. Propositional logic: Logical connectives; truth tables; normal forms (conjunctive and disjunctive); validity. Digital logic: Logic gates, flip-flops, counters; circuit minimization. Elementary number theory: Factorability; properties of primes; greatest common divisors and least common multiples; Euclid’s algorithm; modular arithmetic; the Chinese Remainder Theorem. Basics of counting: Counting arguments; pigeonhole principle; permutations and combinations; binomial coefficients
- editing-lecturer: Jeremiah Onunga