Logic and Graph Theory
Kód | Zakončení | Kredity | Rozsah | Jazyk výuky |
---|---|---|---|---|
AE0B01LGR | Z,ZK | 6 | 3+2s | česky |
- Přednášející:
- Marie Demlová, Pavel Pták, Jiří Velebil
- Cvičící:
- Marie Demlová, Pavel Pták, Jiří Velebil
- Předmět zajišťuje:
- katedra matematiky
- 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.
- Požadavky:
-
Discrete Mathematics, Linear Algebra
- Osnova 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.
- Osnova 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.
- Cíle studia:
- Studijní materiály:
-
[1] M. Demlová: Mathematical Logic. ČVUT Praha, 1999.
[2] R. Diestel: Graph Theory, Springer-Verlag, 1997
- Poznámka:
-
Rozsah výuky v kombinované formě studia: 21p+6s
- Rozvrh na zimní semestr 2011/2012:
- Rozvrh není připraven
- Rozvrh na letní semestr 2011/2012:
-
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
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