Introduction to Discrete Mathematics
Code  Completion  Credits  Range  Language 

B6B01ZDM  Z,ZK  5  2P+2S+2D  Czech 
 The course cannot be taken simultaneously with:
 Discrete Mathenatics (B4B01DMA)
 Lecturer:
 Jaroslav Tišer (guarantor)
 Tutor:
 Jaroslav Tišer (guarantor), Matěj Novotný
 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. Wellformed formula in propositional calculus.
12. Logical consequence, boolean functions.
13. Disjunctive and conjunctive normal forms, satisfiable sets, resolution method.
14. Wellformed 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. Wellformed formula in propositional calculus.
12. Logical consequence, boolean functions.
13. Disjunctive and conjunctive normal forms, satisfiable sets, resolution method.
14. Wellformed 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, McGrawHill, 2012.
 Note:
 Further information:
 https://math.fel.cvut.cz/en/people/tiser/vyuka.html
 Timetable for winter semester 2021/2022:

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  Timetable for summer semester 2021/2022:
 Timetable 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)