I. Statements, and logical connectives; truth tables.

II. Predicates logic and Quantifiers

III. Proof techniques, the nature of mathematical theorems and proofs; direct proof, proof by contraposition, by contradiction; use of counterexamples; the principle of mathematica induction

I. The notation of set theory - Subsets and the power set; binary and unary operations on a set; set operations of union, intersection, complementation.difference, and Cartesian product

II. Demonstration of the denumerability of some sets and the use of Cantor diagonalization method to prove the uncountability; partition of a set

I. Binary relations as ordered pairs and verbal description; the reflexive, symmetric, transitive and antisymmetric properties of binary relations: the definition and terminology about partial orderings;graphs of partially ordered finite sets; the definition of eauivalence relation and equivalence class

II. Functions: definition and examples; properties of functions one-t-one, onto, biiective: function composition, inverse function

I. Counting; fundamental counting principles, including the multiplication and addition principles

II. Sampling and selecting

III. Permutations and combinations; formulas for counting the number of permutations and combinations of k-obiects from n distinct objects

I. Graph terminology; undirected graphs, simple, complete, path, cycle, adjacency matrix connectivity: Euler's path and Hamiltonian circuit;graph representation, trees

II. Digraphs and connectivity problems - Reachability matrix analysis; Warshall's algorithm

I. Discussion and Definition; sinilarities between propositional logic and set theory; mathematical structures as models or abstractions incorporating common properties found in different contexts

II. Logic circuits; basic logic elements of AND gate, OR gate and inverter; representation of a Boolean expression as a combinational network and vice versa; procedure to find a canonical sum-of-product Boolean expressions using Karnaugh map or Boolean algebra properties

I. Definition of binary operation and structure;discussion of the associative, commutative, identity and inverse properties; definition of semigroup monoid, and a substructure

II. Group structure; elementary group theorems, uniqueness of identity and inverse; cancellatior laws; definition and properties of a subgroup;application to error correcting codes

I. Definition of FSM; state tables and state graphs

II. FSM as transducers and recognizers

III. Discussion of limitations of FSMs; introduction to formal languages