MATHEMATICAL AND COMPUTATIONAL LOGICS

1. Propositional Logic: Logical operations, Logical equivalence of formulas, Duality law 2. Decision Problem. Perfect normal forms. 3. Propositional calculus elements: The concept of formula. True formulas 4. Deduction theorem. Rules of propositional calculus. 5. Logically equivalent formulas. Deductibility theorems. Formulas in propositional algebra and propositional calculus. 6. No contradiction and completeness of propositional calculus. Independence of propositional calculus axioms. 7. Predicate calculus: Definitions of predicates and quantifiers. Normal forms. 8. Predicate calculus formulas and axioms. 9. Noncontradiction and narrowly completeness of predicate calculus. Theorems of predicate calculus. 10. Equivalent formulas in predicate calculus. Axioms of predicate calculus. 11. Numeral: positional representation of numbers, algorithms for crossing a number from one base to another, the four operations in various numeral, numeral 2, 8, 16; characteristic elements. 12. Representation of numerical information in memory computer systems: fixed-point representation of numerical information, floating point representation of numerical information, arithmetic operations with floating point numbers, IEEE P754 Standard 13. Boolean functions and their realization: the notion of Boolean function of several variables, Boolean operations AND, OR, NOT 14. The operation of AND gate, OR gate, NOT gate circuits; Implementation of Boolean functions. Boolean functions applications

Acquiring fundamental knowledge concerning the discipline specific concepts: formal systems, judgments and sentences, modal logic elements, probability, predicate logic elements; training in problem solving skills necessary for circuit design and optimization of computer systems based on structural formulas, representing information in memory computer systems.