"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science
| Selected topics of logical mathematics |
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| Teaching Staff in Charge |
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| Aims |
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Determination of the connection between the speculative and the applied aspect of mathematical logic, due to computer science. |
| Content |
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1. The algebra of propositions. Propositions. Propositional formulae. Logical implication and logical equivalence as relations. Lyndenbaum-Tarski algebra. Boole rings and algebras.
2. n-ary bivalent functions. Normal perfect forms. Synthesis problems. Applications. 3. Deductive theories. Interpretation and model. Non-contradiction and consistency. Completeness and categoricity. 4. Predicate logics. |
| References |
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1. N. BOTH: Algebra logicii cu aplicatii, Ed. Dacia, Cluj-Napoca 1984.
2. N. BOTH: Capitole speciale de logica matematica, Lito, Univ Babes Bolyai Cluj-Napoca 1994. 3. P. NOVICOV: Elemente de logica matematica, Ed. Tehn., 1966. 4. Y.I. MANIN: A Course in Mathematical Logic, Springer-Verlag, 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, Springer-Verlag, Berlin, 1998. |
| Assessment |
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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). |