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Explanatory Notes
Instructions
Web page:
http://math.feld.cvut.cz/bohata/zdmd.html
Anotation:
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.
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.
Content:
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.
Course outlines:
| 1. | | Basic combinatorics, Binomial Theorem. |
| 2. | | Inclusion and Exclusion Principle and applications. |
| 3. | | Basics 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. | | Uncountable 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. |
Exercises outline:
| 1. | | Basic combinatorics, Binomial Theorem. |
| 2. | | Inclusion and Exclusion Principle and applications. |
| 3. | | Basics 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. | | Uncountable 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. |
Literature:
| K. | | H. Rosen: Discrete mathematics and its applications, 7th edition, McGraw-Hill, 2012. |
Requirements:
Grammar school knowledge.
Keywords:
Permutations and combinations, bijection, countable and uncoutable sets, trees and bipatrite graphs, reltions on set, equivalence and ordering, well-formed formula of propositional calculus, logical consequence and resolution method, formula in predicate calculus.
Subject is included into these academic programs:
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Proposal and Realization: I. Halaška (K336), J. Novák (K336) |