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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024
UPOZORNĚNÍ: Jsou dostupné studijní plány pro následující akademický rok.

Introduction to Discrete Mathematics

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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 2023/2024:
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
Cvičebna
roomT2: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
Cvičebna
roomT2: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:C3-54
roomT2:C3-54
Tišer J.
11:00–12:30
(lecture parallel1
parallel nr.102)

Dejvice
T2:C3-54
roomT2: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:C3-54
roomT2: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
Tišer J.
09:15–10:45
(lecture parallel1
parallel nr.110)

Dejvice
Cvičebna
roomT2:C4-155
Tišer J.
09:15–10:45
(lecture parallel1
parallel nr.111)

Dejvice
Cvičebna
Thu
Fri
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-05-25
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet3129206.html