Gurantor department | Department of Applied Mathematics | Credits | 6 |

Subject guarantor | RNDr. Pavel Jahoda, Ph.D. | Subject version guarantor | doc. Mgr. Petr Kovář, Ph.D. |

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 3 | Semester | winter |

Study language | Czech | ||

Year of introduction | 2019/2020 | Year of cancellation | |

Intended for the faculties | FEI | Intended for study types | Bachelor |

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

JAH02 | RNDr. Pavel Jahoda, Ph.D. | ||

KOV16 | doc. Mgr. Petr Kovář, Ph.D. |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+2 |

Part-time | Credit and Examination | 10+10 |

After passing the course the student will be familiar with the definitions of basic concepts selected theory of algebraic structures and relationships between them. He will understand their significance and will be able to take advantage of their knowledge to solve simple algebraic structures theory tasks. He will also understand the importance of these concepts for the solution of the selected application roles, so that he could formulate a practical role in the language of group theory, solve the problem using theory and tools to interpret the outcome in the context of the original task.

Lectures

Tutorials

Selected topics of general algebra constitute content of course Algebra. Possibilities of using this knowledges to solve some practical problems are demonstrated here. Students have the opportunity to obtain basic familiarity with mathematical apparatus, which stands behind the above mentioned applications. So they can understand how these applications work in practice.

J. GALLIAN: Contemporary Abstract Algebra, Cengage Learning; 8 edition (2012), ISBN13 978-1133599708.

J. Gallian, Contemporary Abstract Algebra, Cengage Learning; 8 edition (2012), ISBN13 978-1133599708.
LANG, S.: Undergraduate Algebra, Springer, 1990, ISBN 0-387-97279-X.
GALLIAN, J.: Contemporary Abstract Algebra, Houghton Mifflin, Boston 2002, ISBN 0-618-122141

Midterm test and a final exam.

The student attending the course of Algebra is expected to be of decent behavior, to be attentive at the lectures and exercises and we expect his busy preparation for the exam.

Subject has no prerequisities.

Subject has no co-requisities.

Lectures
1) introduction to the group theory: symmetry and dihedral groups
2) group: definition, basic properties
3) finite groups and subgroups, examples
4) cyclic groups, classification
5) group of permutations, definitions, cycles, properties and use
6) normal subgroups and Lagrange's theorem
7) factor groups
8) homomorphisms of groups, definitions, examples
9) isomorfisms: motivation, properties, Cayley's theorem
10) direct product of groups, definitions, examples, applications
11) rings and fields: definitions, finite and infinite examples, applications
12) fields, algebraic extensions, examples, applications
13) vector spaces: definition and examples, subspaces, linear independence
Cvičení:
1) examples of dihedral groups, geometric meaning, examples
2) examples of groups, verification of the axioms of groups
3) subgroups, examples, design and verification
4) cyclic groups, examples, properties, verification
5) group of permutations, cycles, solving the practical examples
6) factorisation the group by its subgroup
7) examples of factor groups, construction and verification
8) homomorfisms of groups, definitions, examples
9) isomorfisms, examples and counterexamples, verification of axioms
10) direct product of groups, examples
11) homomorfisms og groups
12) rings and fields: examples, verification
13) vector spaces: finite and infinite examples, verification of linear independence

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points |
---|---|---|---|

Credit and Examination | Credit and Examination | 100 (100) | 51 |

Credit | Credit | 30 | 15 |

Examination | Examination | 70 | 35 |

Show history

Academic year | Programme | Field of study | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2020/2021 | (B0541A170008) Computational and Applied Mathematics | AM | P | Czech | Ostrava | 3 | Compulsory | study plan | ||||

2020/2021 | (B0541A170008) Computational and Applied Mathematics | AM | K | Czech | Ostrava | 3 | Compulsory | study plan | ||||

2019/2020 | (B0541A170008) Computational and Applied Mathematics | AM | P | Czech | Ostrava | 3 | Compulsory | study plan | ||||

2019/2020 | (B0541A170008) Computational and Applied Mathematics | AM | K | Czech | Ostrava | 3 | Compulsory | study plan |

Block name | Academic year | Form of study | Study language | Year | W | S | Type of block | Block owner |
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