CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2022/2023
UPOZORNĚNÍ: Jsou dostupné studijní plány pro následující akademický rok.

Discrete Mathenatics

Code Completion Credits Range Language
B4B01DMA Z,ZK 5 2P+2S Czech
Garant předmětu:
Petr Habala
Lecturer:
Petr Habala
Tutor:
Petr Habala
Supervisor:
Department of Mathematics
Synopsis:

In this course students meet some important topics from the field of discrete mathematics. Namely, they will explore divisibility and calculations modulo n, diophantine equations, binary relations, mappings, cardinality of sets, induction, and recurrence equations. The second aim of this course is to teach students the language of mathematics, both passively and actively, and introduce them to mathematics as science.

Requirements:

High-school mathematics and ability to think.

Syllabus of lectures:

1. Divisibility, Euclid's algorithm.

2. Calculations modulo n, the set Zn of integers modulo n.

3. Diophantine equations, congruence equations and systems.

4. Binary relations and their basic properties.

5. Special relations: partial ordering and equivalence.

6. Mappings. Cardinality of sets, countable and uncountable sets.

7. Matematical induction and its applications.

8. Sequences and sums, asymptotic gowth.

9. Linear recurrence equations.

10. Computatinal complexity of algorithms, the Master theorem.

11. The inclustion and exclusion principle.

Syllabus of tutorials:

1. Divisibility, Euclid's algorithm.

2. Calculations modulo n, the set Zn of integers modulo n.

3. Diophantine equations, congruence equations and systems.

4. Binary relations and their basic properties.

5. Special relations: partial ordering and equivalence.

6. Mappings. Cardinality of sets, countable and uncountable sets.

7. Matematical induction and its applications.

8. Sequences and sums, asymptotic gowth.

9. Linear recurrence equations.

10. Computatinal complexity of algorithms, the Master theorem.

11. The inclustion and exclusion principle.

Study Objective:
Study materials:

[1] K.H.Rosen: Discrete matematics and its aplications, McGraw-Hill, 1998.

Note:
Further information:
https://math.fel.cvut.cz/cz/lide/habala/teaching/dma.html
Time-table for winter semester 2022/2023:
 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:C3-51Habala P.09:15–10:45(lecture parallel1parallel nr.104)DejviceT2:C3-51roomT2:C3-51Habala P.14:30–16:00(lecture parallel1parallel nr.101)DejviceT2:C3-51roomT2:C3-51Habala P.16:15–17:45(lecture parallel1parallel nr.102)DejviceT2:C3-51 roomT2:C3-51Habala P.09:15–10:45(lecture parallel1parallel nr.107)DejviceT2:C3-51roomT2:C3-51Habala P.11:00–12:30(lecture parallel1parallel nr.103)DejviceT2:C3-51roomT2:C3-51Habala P.14:30–16:00(lecture parallel1parallel nr.105)DejviceT2:C3-51roomT2:C3-51Habala P.16:15–17:45(lecture parallel1parallel nr.108)DejviceT2:C3-51 roomT2:C3-51Habala P.11:00–12:30(lecture parallel1parallel nr.106)DejviceT2:C3-51 roomKN:E-107Habala P.11:00–12:30(lecture parallel1)Karlovo nám.Zengerova posluchárna K1roomHabala P.14:30–16:00(lecture parallel1parallel nr.109)roomKN:E-128Habala P.16:15–17:45(lecture parallel1parallel nr.112)Karlovo nám.Cvičebna K3 roomT2:D3-309Habala P.11:00–12:30(lecture parallel1)DejviceT2:D3-309roomHabala P.14:30–16:00(lecture parallel1parallel nr.110) roomKN:E-128Habala P.12:45–14:15(lecture parallel1parallel nr.111)Karlovo nám.Cvičebna K3
Time-table for summer semester 2022/2023:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2023-03-26
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet4680906.html