Courses

(i) Logic. The language of propositional logic, alphabet and syntax. Types and tree diagrams. Truth evaluation and semantics of logical conjunctions. Truth tables. Normal forms. Logical inference. The basic equivalences. The expressiveness of propositional logic. Propositional calculus and formal proof. The syntax of primary formulas and their use in the expression of various mathematical propositions. (ii) Combinatorics. Measurement of discrete structures. The additive and multiplicative rules. Permutations, arrangements, combinations without and with repetition. Examples. Models of beads in boxes. The inclusion-exclusion principle. Generating functions and recursive relations. (iii) Introduction to Graph Theory. Definitions and types of graphs. Connectivity in simple graphs. Subgraphs. Euler cycle. Euler's theorem. Hamilton cycle. Graph matrices. Isomorphic and homomorphic graphs. Planar graphs. Kuratowski's theorem. Graph coloring. Trees. Binary trees. Directed graphs.