Subject description - B4B01DMA
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Explanatory Notes
Instructions
| B4B01DMA | Discrete Mathematics | ||
|---|---|---|---|
| Roles: | P | Extent of teaching: | 2P+2S |
| Department: | 13101 | Language of teaching: | CS |
| Guarantors: | Habala P. | Completion: | Z,ZK |
| Lecturers: | Habala P. | Credits: | 5 |
| Tutors: | Habala P. | Semester: | Z |
Web page:
https://math.fel.cvut.cz/cz/lide/habala/teaching/dma.htmlAnotation:
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.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. Subject is included into these academic programs:| Program | Branch | Role | Recommended semester |
| 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 of Things | P | 1 |
| BPOI_BO_2018 | Common courses | P | 1 |
| BPOI4_2018 | Computer Games and Graphics | P | 1 |
| BPOI3_2018 | Software | P | 1 |
| BPOI2_2018 | Internet of Things | P | 1 |
| BPOI1_2018 | Artificial Intelligence and Computer Science | P | 1 |
| Page updated 14.10.2024 17:51:34, semester: Z/2025-6, Z,L/2024-5, L/2023-4, Send comments about the content to the Administrators of the Academic Programs | Proposal and Realization: I. Halaška (K336), J. Novák (K336) |