CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2020/2021

# Introduction to Discrete Mathematics

Code Completion Credits Range Language
B6B01ZDM Z,ZK 5 2P+2S+2D Czech
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. Basic from graph theory, connected graphs.

4. Eulerian graphs, trees and their properties.

5. Weighted tree, minimal spanning tree.

6. Bipartite graph, matching in bipartite graphs.

7. Binary relation, equivalence.

8. Ordering, minimal and maximal elements.

9. Cardinality of sets, countable set and their properties.

10. Uncoutable sets, Cantor Theorem.

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. Basic from graph theory, connected graphs.

4. Eulerian graphs, trees and their properties.

5. Weighted tree, minimal spanning tree.

6. Bipartite graph, matching in bipartite graphs.

7. Binary relation, equivalence.

8. Ordering, minimal and maximal elements.

9. Cardinality of sets, countable set and their properties.

10. Uncoutable sets, Cantor Theorem.

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:
http://math.feld.cvut.cz/tiser/vyuka.htm http://math.feld.cvut.cz/bohata/zdm.html
Time-table for winter semester 2020/2021:
 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 roomT2:A4-204Tišer J.14:30–16:00(lecture parallel1parallel nr.103)DejviceUčebnaroomT2:A4-204Tišer J.16:15–17:45(lecture parallel1parallel nr.101)DejviceUčebnaroomT2:C4-364Tišer J.18:00–19:30(lecture parallel1parallel nr.102)DejviceCvicebna roomT2:C3-5409:15–10:45(lecture parallel1parallel nr.106)DejviceT2:C3-54roomT2:C3-54Tišer J.16:15–17:45(lecture parallel1parallel nr.104)DejviceT2:C3-54 roomT2:C3-54Tišer J.11:00–12:30(lecture parallel1parallel nr.105)DejviceT2:C3-54roomT2:D3-309Tišer J.14:30–16:00(lecture parallel1)DejviceT2:D3-309
Time-table for summer semester 2020/2021:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-09-30
For updated information see http://bilakniha.cvut.cz/en/predmet3129206.html