Subject description - B4B01DMA

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B4B01DMA Discrete Mathenatics Extent of teaching:2+2
Guarantors:Habala P. Roles:P Language of
teaching:
CS
Teachers:Habala P. Completion:Z,ZK
Responsible Department:13101 Credits:5 Semester:Z

Anotation:

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.

Course outlines:

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.

Exercises outline:

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.

Literature:

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

Requirements:

High-school mathematics and ability to think.

Webpage:

http://math.feld.cvut.cz/habala/teaching/dma.htm

Subject is included into these academic programs:

Program Branch Role Recommended semester
BPOI_BO_2018 Common courses P 1
BPOI4_2018 Computer Games and Graphics P 1
BPOI3_2018 Software P 1
BPOI2_2018 Internet things P 1
BPOI1_2018 Artificial Intelligence and Computer Science P 1
BPOI1_2016 Computer and Information Science P 1
BPOI_BO_2016 Common courses P 1
BPOI4_2016 Computer Games and Graphics P 1
BPOI3_2016 Software P 1
BPOI2_2016 Internet things P 1


Page updated 13.5.2019 17:52:55, semester: Z,L/2020-1, L/2019-20, Z,L/2018-9, Z/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)