Math153- Discrete Mathematics

Basic concepts of elementary logic: statements and statement forms, connectives, logical equivalence, truth tables; converse, inverse and contrapositive of a conditional statement. Tautologies and contradictions. Universal and existential statements. Boolean algebras: general definitions, Boolean functions, complete sum of products form, complete product of sums form. Karnaugh maps, minimal sum of products forms and minimal product of sums form. Gates and design of logic circuits. Graph theory: basic definitions and examples, paths, cycles, connected graphs, subgraphs. Regular, complete and bipartite graphs. Isomorphism of simple graphs. Trees, spanning trees. Counting Systems: Permutations and Combinations, Binomial Theorem. Sets Theorem