Selected topics of logical mathematics 
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Teaching Staff in Charge 

Aims 
Determination of the connection between the speculative and the applied aspect of mathematical logic, due to computer science. 
Content 
1. The algebra of propositions. Propositions. Propositional formulae. Logical implication and logical equivalence as relations. LyndenbaumTarski algebra. Boole rings and algebras.
2. nary bivalent functions. Normal perfect forms. Synthesis problems. Applications. 3. Deductive theories. Interpretation and model. Noncontradiction and consistency. Completeness and categoricity. 4. Predicate logics. 
References 
1. N. BOTH: Algebra logicii cu aplicatii, Ed. Dacia, ClujNapoca 1984.
2. N. BOTH: Capitole speciale de logica matematica, Lito, Univ Babes Bolyai ClujNapoca 1994. 3. P. NOVICOV: Elemente de logica matematica, Ed. Tehn., 1966. 4. Y.I. MANIN: A Course in Mathematical Logic, SpringerVerlag, New York 1977 5. S.G. KRANTZ: Logic and Proof Techniques for Computer Science, Birkhauser Boston 2002. 6. R. LIDL, G. PILZ: Applied Abstract Algebra, SpringerVerlag, Berlin, 1998. 
Assessment 
Two reports throughout the semester (each representing 20% of the final mark) and oral exam at the end of the semester (representing 60% of the final mark). 