Introduction to Discrete Mathematics
Code | Completion | Credits | Range | Language |
---|---|---|---|---|
B6B01ZDM | Z,ZK | 5 | 2P+2S+2D | Czech |
- Garant předmětu:
- Jaroslav Tišer
- Lecturer:
- Jaroslav Tišer
- Tutor:
- Jaroslav Tišer
- Supervisor:
- Department of Mathematics
- Synopsis:
-
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.
- Requirements:
-
Grammar school knowledge.
- Syllabus of lectures:
-
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.
- Syllabus of tutorials:
-
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.
- Study Objective:
-
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.
- Study materials:
-
K.H. Rosen: Discrete mathematics and its applications, 7th edition, McGraw-Hill, 2012.
- Note:
- Further information:
- https://math.fel.cvut.cz/en/people/tiser/vyuka.html
- Time-table for winter semester 2024/2025:
-
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
Mon Tue Wed Thu Fri - Time-table for summer semester 2024/2025:
- Time-table is not available yet
- The course is a part of the following study plans:
-
- Software Engineering and Technology (compulsory course in the program)
- Software Engineering and Technology (compulsory course in the program)
- Software Engineering and Technology (compulsory course in the program)
- Software Engineering and Technology (compulsory course in the program)
- Software Engineering and Technology (compulsory course in the program)
- Software Engineering and Technology (compulsory course in the program)