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Explanatory Notes
Instructions
Web page:
https://math.fel.cvut.cz/en/people/tiser/vyuka.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 a brief formal construction of predicate calculus.
Study targets:
The aim of this subject is the basics of combinatorics, graph and set theories and to develop logical reasoning in predicate calculus.
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 a brief formal construction of predicate calculus.
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 and their characterizartion. |
| 9. | | Trees, basic properties. |
| 10. | | Weighted tree, minimal spanning tree. |
| 11. | | Bipartite graph, matching in bipartite graphs. |
| 12. | | Well-formed formula in propositional calculus. |
| 13. | | Well-formed formula in predicate calculus. |
| 14. | | Reserve. |
Exercises outline:
| 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 and their characterizartion. |
| 9. | | Trees, basic properties. |
| 10. | | Weighted tree, minimal spanning tree. |
| 11. | | Bipartite graph, matching in bipartite graphs. |
| 12. | | Well-formed formula in propositional calculus. |
| 13. | | Well-formed formula in predicate calculus. |
| 14. | | Reserve. |
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 in propositional calculus, well-formed formula in predicate calculus.
Subject is included into these academic programs:
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Proposal and Realization: I. Halaška (K336), J. Novák (K336) |