Discrete Mathematics

Propositional Logic (logical operators, truth table, propositional equivalences, Translation), Predicate logic (predicate, quantification, nested quantifiers, equivalences, translation Inference rules), Introduction to proofs (direct proof, proof by contraposition, proof by contradiction, proof by cases), Set theory (set builder notation, subset, Cartesian product, power set, union, intersection, complements, set identities), Functions (types of functions, inverse, composition, ceil and floor functions), Sequence and Summation (arithmetic progression, geometric progression, special integer sequences, summations), Matrices (Introduction, matrix arithmetic, matrix multiplication, transpose, powers of matrices, zero one matrices), Integers (integers, division, division algorithm, modular arithmetic, primes, GCD, LCM), Mathematical Induction, Relations (definitions, properties, combining relations, representation, equivalence relation)