Introduction to Discrete Mathematics

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	roomT2:C4-155 Tišer J. 14:30–16:00 (lecture parallel1 parallel nr.103) Dejvice CvičebnaroomT2:C4-155 Tišer J. 16:15–17:45 (lecture parallel1 parallel nr.101) Dejvice Cvičebna roomT2:C4-155 Tišer J. 14:30–16:00 (lecture parallel1 parallel nr.108) Dejvice CvičebnaroomT2:C4-155 Tišer J. 16:15–17:45 (lecture parallel1 parallel nr.109) Dejvice Cvičebna
Tue	roomT2:C3-54 09:15–10:45 (lecture parallel1 parallel nr.106) Dejvice T2:C3-54roomT2:C3-54 Tišer J. 11:00–12:30 (lecture parallel1 parallel nr.102) Dejvice T2:C3-54roomT2:C3-54 Tišer J. 16:15–17:45 (lecture parallel1 parallel nr.104) Dejvice T2:C3-54 roomT2:C3-54 Tišer J. 11:00–12:30 (lecture parallel1 parallel nr.105) Dejvice T2:C3-54roomT2:C3-54 Tišer J. 16:15–17:45 (lecture parallel1 parallel nr.107) Dejvice T2:C3-54 roomT2:D3-309 Tišer J. 14:30–16:00 (lecture parallel1) Dejvice T2:D3-309
Wed	roomT2:C4-155 09:15–10:45 (lecture parallel1 parallel nr.110) Dejvice Cvičebna roomT2:C4-155 09:15–10:45 (lecture parallel1 parallel nr.111) Dejvice Cvičebna
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)