# Subject description - A8B01DMG

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ISBN-10: 0387745270

A8B01DMG | Discrete Math.& Graphs | Extent of teaching: | 3P+1S | ||
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Guarantors: | Demlová M. | Roles: | P | Language of teaching: | CS |

Teachers: | Demlová M. | Completion: | Z,ZK | ||

Responsible Department: | 13101 | Credits: | 5 | Semester: | Z |

**Anotation:**

**Study targets:**

**Content:**

1. | Sets. Cardinality of sets. | |

2. | Binary relalations, equivalence relation, partial order. | |

3. | Integers, Eclid's algorithm and Bezout's theorem | |

4. | Relation modulo n, rezidual classes and operations with them | |

5. | Binary operations, semigroups, groups. | |

6. | Sets with two binary operations, Boolean algebras. | |

7. | Rings of rezidual classes, finite fieldst of rezidual classes over a prime, polynomials |

8. | Galois fields GF(2^k). | |

9. | Homomorfisms of algebraic structures. | |

10. | Undirected graphs, directed graphs, trees and spanning trees. | |

11. | Strongly connected and acyclic graphs, topological sort | |

12. | Combinatorics. | |

13. | Asymptotic growth of functions. |

**Course outlines:**

1. | Sets. Cardinality of sets. | |

2. | Binary relalations, equivalence relation, partial order. | |

3. | Integers, Eclid's algorithm and Bezout's theorem | |

4. | Relation modulo n, rezidual classes and operations with them | |

5. | Binary operations, semigroups, groups. | |

6. | Sets with two binary operations, Boolean algebras. | |

7. | Rings of rezidual classes, finite fieldst of rezidual classes over a prime, polynomials |

8. | Galois fields GF(2^k). | |

9. | Homomorfisms of algebraic structures. | |

10. | Undirected graphs, directed graphs, trees and spanning trees. | |

11. | Strongly connected and acyclic graphs, topological sort | |

12. | Combinatorics. | |

13. | Asymptotic growth of functions. |

**Exercises outline:**

1. | Sets. Cardinality of sets. | |

2. | Binary relalations, equivalence relation, partial order. | |

3. | Integers, Eclid's algorithm and Bezout's theorem | |

4. | Relation modulo n, rezidual classes and operations with them | |

5. | Binary operations, semigroups, groups. | |

6. | Sets with two binary operations, Boolean algebras. | |

7. | Rings of rezidual classes, finite fieldst of rezidual classes over a prime, polynomials |

8. | Galois fields GF(2^k). | |

9. | Homomorfisms of algebraic structures. | |

10. | Undirected graphs, directed graphs, trees and spanning trees. | |

11. | Strongly connected and acyclic graphs, topological sort | |

12. | Combinatorics. | |

13. | Asymptotic growth of functions. |

**Literature:**

1. | Lindsay N. Childs: A Concrete Introduction to Higher Algebra, Springer; 3rd edition (November 26, 2008), |

2. | Jiří Demel: Grafy a jejich aplikace, Academia; 2002, ISBN 80-200-0990-6 | |

3. | Richard Johnsonbaugh: Discrete Mathematics, Prentice Hall, 4th edition (1997), ISBN 0-13-518242-5 |

**Requirements:**

**Webpage:**

**Keywords:**

**Subject is included into these academic programs:**

Program | Branch | Role | Recommended semester |

BPOES | Common courses | P | 1 |

Page updated 17.1.2020 17:52:14, semester: Z,L/2020-1, L/2018-9, Z,L/2019-20, Send comments about the content to the Administrators of the Academic Programs | Proposal and Realization: I. Halaška (K336), J. Novák (K336) |