Discrete Mathematics

Contents: Sets, number systems: decimal, binary, octal and hexadecimal numbers; signed numbers, floating point numbers. Relations and functions: injective, surjective and bijective functions; floor and ceiling functions. Algorithms: pseudo codes, searching algorithm, complexity of algorithms, division algorithm: greatest common divisors and least common multiples, the Euclidean algorithm. Boolean algebra: Huntington postulates: Boolean algebraic theorems; Boolean functions Logic logical statements and connectives: truth tables: tautology, absurdity and contingency; logical gates, mathematical reasoning, counting problems. Graphs types of graphs: simple graphs, multigraphs. pseudo graphs, directed graphs, directed multigraphs graph terminology; the handshaking theorem; complete graphs, cycles, wheels, n-cubes, bipartite graphs, isomorphism of graphs; connectivity of graphs: paths; Euclidean and Hamiltonian paths; planar graphs; Euler formula, coloring of graphs and applications. Trees: basic definitions; rooted trees; applications of trees; trees and sorting, spanning trees.