Počet kreditů | 5 |

Vyučováno v | Winter |

Rozsah výuky | 2P+2S |

Garant předmětu | |

Přednášející | |

Cvičící |

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, induction, cardinality of sets, 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.

High-school mathematics and ability to think.

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.

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.

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