Počet kreditů 5 Vyučováno v Winter Rozsah výuky 2P+2S+2D Garant předmětu Přednášející Cvičící

No advanced knowleges of mathematics are required at the beginning of this course. Using illustrative examples we build sufficient understanding of combinatorics, set and graph theory. Then we proceed to

formal construction of propositional calculus.

Grammar school knowledge.

The aim of this subject is to develop logical reasoning and to analyze logical structure of propositions.

The basics form combinatorics, graph and set theories are included as well.

1.Basic combinatorics, Binomial Theorem.

2. Inclusion and Exclusion Pronciple and applications.

3. Basic from graph theory, connected graphs.

4. Eulerian graphs, trees and their properties.

5. Weighted tree, minimal spanning tree.

6. Bipartite graph, matching in bipartite graphs.

7. Binary relation, equivalence.

8. Ordering, minimal and maximal elements.

9. Cardinality of sets, countable set and their properties.

10. Uncoutable sets, Cantor Theorem.

11. Well-formed formula in propositional calculus.

12. Logical consequence, boolean functions.

13. Disjunctive and conjunctive normal forms, satisfiable sets, resolution method.

14. Well-formed formula in predicate calculus.

1.Basic combinatorics, Binomial Theorem.

2. Inclusion and Exclusion Pronciple and applications.

3. Basic from graph theory, connected graphs.

4. Eulerian graphs, trees and their properties.

5. Weighted tree, minimal spanning tree.

6. Bipartite graph, matching in bipartite graphs.

7. Binary relation, equivalence.

8. Ordering, minimal and maximal elements.

9. Cardinality of sets, countable set and their properties.

10. Uncoutable sets, Cantor Theorem.

11. Well-formed formula in propositional calculus.

12. Logical consequence, boolean functions.

13. Disjunctive and conjunctive normal forms, satisfiable sets, resolution method.

14. Well-formed formula in predicate calculus.

K.H. Rosen: Discrete mathematics and its applications, 7th edition, McGraw-Hill, 2012.

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