CTU FEE Moodle
Introduction to Discrete Mathematics
B232 - Summer 23/24
Introduction to Discrete Mathematics - B6B01ZDM
| Credits | 5 |
| Semesters | Winter |
| Completion | Assessment + Examination |
| Language of teaching | Czech |
| Extent of teaching | 2P+2S+2D |
Annotation
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.
formal construction of propositional calculus.
Study targets
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.
The basics form combinatorics, graph and set theories are included as well.
Course outlines
1.Basic combinatorics, Binomial Theorem.
2. Inclusion and Exclusion Pronciple and applications.
3. Cardinality of sets, countable set and their properties.
4. Uncoutable sets, Cantor Theorem.
5. Binary relation, equivalence.
6. Ordering, minimal and maximal elements.
7. Basic from graph theory, connected graphs.
8. Eulerian graphs, trees and their properties.
9. Weighted tree, minimal spanning tree.
10. Bipartite graph, matching in bipartite graphs.
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.
2. Inclusion and Exclusion Pronciple and applications.
3. Cardinality of sets, countable set and their properties.
4. Uncoutable sets, Cantor Theorem.
5. Binary relation, equivalence.
6. Ordering, minimal and maximal elements.
7. Basic from graph theory, connected graphs.
8. Eulerian graphs, trees and their properties.
9. Weighted tree, minimal spanning tree.
10. Bipartite graph, matching in bipartite graphs.
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.
Exercises outlines
1.Basic combinatorics, Binomial Theorem.
2. Inclusion and Exclusion Pronciple and applications.
3. Cardinality of sets, countable set and their properties.
4. Uncoutable sets, Cantor Theorem.
5. Binary relation, equivalence.
6. Ordering, minimal and maximal elements.
7. Basic from graph theory, connected graphs.
8. Eulerian graphs, trees and their properties.
9. Weighted tree, minimal spanning tree.
10. Bipartite graph, matching in bipartite graphs.
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.
2. Inclusion and Exclusion Pronciple and applications.
3. Cardinality of sets, countable set and their properties.
4. Uncoutable sets, Cantor Theorem.
5. Binary relation, equivalence.
6. Ordering, minimal and maximal elements.
7. Basic from graph theory, connected graphs.
8. Eulerian graphs, trees and their properties.
9. Weighted tree, minimal spanning tree.
10. Bipartite graph, matching in bipartite graphs.
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.
Literature
K.H. Rosen: Discrete mathematics and its applications, 7th edition, McGraw-Hill, 2012.
Requirements
Grammar school knowledge.