# Popis předmětu - AE0B01LGR

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AE0B01LGR Logic and Graph Theory
Role:P, V Rozsah výuky:3+2
Katedra:13101 Jazyk výuky:EN
Garanti:  Zakončení:Z,ZK
Přednášející:  Kreditů:6
Cvičící:  Semestr:L

Anotace:

The course covers basics of logic and theory of graphs. Propositional logic contains: truth validation, semantical consequence and tautological equivalence of formulas, CNF and DNF, complete systems of logical connectives, and resolution method in propositional logic. In predicate logic the stress is put on formalization of sentences as formulas of predicate logic, and resolution method in predicate logic. Next topic is an introduction to the theory of graphs and its applications. It covers connectivity, strong connectivity, trees and spanning trees, Euler?s graphs, Hamilton?s graphs, independent sets, and colourings.

Výsledek studentské ankety předmětu je zde: AE0B01LGR

Osnovy přednášek:

 1 Formulas of propositional logic, truth validation, tautology, contradiction, satisfiable formulas. 2 Semantical consequence and tautological equivalence in propositional logic. 3 CNF and DNF, Boolean calculus. 4 Resolution method in propositional logic. 5 Predicate logic, syntactically correct formulas 6 Interpretation, sematical consequence and tautological equivalence. 7 Resilution method in predicate logic. 8 Directed and undirected graphs. 9 Connectivity, trees, spanning trees. 10 Strong connectivity, acyclic graphs. 11 Euler?s graphs and their application. 12 Hamilton?s graphs and their application. 13 Independent sets, cliques in graphs. 14 Colourings.

Osnovy cvičení:

 1 Formulas of propositional logic, truth validation, tautology, contradiction, satisfiable formulas. 2 Semantical consequence and tautological equivalence in propositional logic. 3 CNF and DNF, Boolean calculus. 4 Resolution method in propositional logic. 5 Predicate logic, syntactically correct formulas 6 Interpretation, sematical consequence and tautological equivalence. 7 Resilution method in predicate logic. 8 Directed and undirected graphs. 9 Connectivity, trees, spanning trees. 10 Strong connectivity, acyclic graphs. 11 Euler?s graphs and their application. 12 Hamilton?s graphs and their application. 13 Independent sets, cliques in graphs. 14 Colourings.

Literatura:

 [1] M. Demlová: Mathematical Logic. ČVUT Praha, 1999. [2] R. Diestel: Graph Theory, Springer-Verlag, 1997