Discrete Mathematics
Code  Completion  Credits  Range  Language 

B4B01DMA  Z,ZK  5  2P+2S  Czech 
 Course guarantor:
 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:

Highschool 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, McGrawHill, 1998.
 Note:
 Further information:
 https://math.fel.cvut.cz/cz/lide/habala/teaching/dma.html
 Timetable 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 Tue Wed Thu Fri  Timetable for summer semester 2024/2025:
 Timetable is not available yet
 The course is a part of the following study plans:

 Open Informatics  Computer Science 2016 (compulsory course in the program)
 Open Informatics  Internet of Things 2016 (compulsory course in the program)
 Open Informatics  Software 2016 (compulsory course in the program)
 Open Informatics  Computer Games and Graphics 2016 (compulsory course in the program)
 Open Informatics (compulsory course in the program)
 Open Informatics (compulsory course in the program)
 Open Informatics  Artificial Intelligence and Computer Science 2018 (compulsory course in the program)
 Open Informatics  Internet of Things 2018 (compulsory course in the program)
 Open Informatics  Software 2018 (compulsory course in the program)
 Open Informatics  Computer Games and Graphics 2018 (compulsory course in the program)