(i) Logic. The language of propositional logic, alphabet and syntax. Types and tree graphs. Truth assignment and the meaning of the logical connectives. Truth tables. Regular forms. Logical implication. Basic equivalences. Applications. The expressibility of propositional logic. The propositional calculus and formal proofs. The syntax of first-order types and their use in expressing mathematical statements.
(ii) Combinatorics. Counting of discrete structures. The addition and multiplication rule. Permutations and combinations without and with repetition. Examples. The balls in urns paradigm. The principle of inclusion-exclusion. Generating functions and recursive relations.
(iii) Introduction to Graph Theory. Definition and graph types. Connectivity in simple graphs. Subgraphs. Multigraphs. 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.