Gurantor department | Department of Mathematics | Credits | 4 |

Subject guarantor | RNDr. Jana Volná, Ph.D. | Subject version guarantor | RNDr. Jana Volná, Ph.D. |

Study level | undergraduate or graduate | Requirement | Optional |

Year | 1 | Semester | winter |

Study language | Czech | ||

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

Intended for the faculties | FEI | Intended for study types | Follow-up Master |

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

Login | Name | Tuitor | Teacher giving lectures |

VOL18 | RNDr. Jana Volná, Ph.D. |

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

Form of study | Way of compl. | Extent |

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

Combined | Credit and Examination | 16+0 |

In this course the students can acquaint with properties of affine and euclidean spaces, with affine, isometric and similar tranformations in this spaces.

Lectures

Individual consultations

Tutorials

Other activities

Vector spaces. Orientation, spaces with scalar multiplication. Vector multiplication, orthogonal transformations. Affine spaces. Affine coordinates, relations between linear subspaces. Linear systems of hyperplanes.
Affine transformations, classification of affine transformations in spaces of dimension 2 and 3. Euclidean spaces. Cartesian coordinates, Euclidean metrics, orthogonality. Isometric transformations. Classification of isometries in spaces of dimension 1 and 2. Similarities.

Holme, A.: Geometry. Springer – Verlag, Berlin, Heidelberg, New York, 2002,
ISBN 3-540-41949-7.

Jennings, G.A.: Modern Geometry with Applications, Springer-Verlag, New York,
1994, ISBN 0-387-94222-X.

Conditions for credits of the seminar in Geometry
Necessary conditions:
1. At least 70% presence in seminar.
2. Due to presence and activity on seminar students can obtain up to 9 points.
Supplementary condition:
3. Three tests, each 0 – 7 points.
It is necessary to obtain at least 10 points from possible 30 points.
Conditions for exam in Geometry
1. At least 10 points in seminar.
2. The exam consists of written (0 - 40 points) and oral (0 – 30 points) examination. The minimum of written part is 15 points, in oral part is 10 points.
3. The result consists of sum of the points from seminar and from exam.
4. Evaluation is based on VSB-TUO statue.
Set of questions:
1. Definition of affine space, affine coordinates, arithmetic affine space, linear independent points, transformation of affine coordinates.
2. Subspaces of affine space, analytical expressions of subspaces, symbolic equations, parametric and general equations of affine subspaces.
3. Mutual position of subspaces, collinearity of linear systems of hyperplanes.
4. Affine transformations of affine space, determinateness of analytical expression, module, invariant points, composition of transformations.
5. Classification of transformation classes.
6. Classification for line and plane.
7. Definition of Euclidean space, Cartesian coordinates, distance of points, transformation of coordinates.
8. Orthogonality and distances in Euclidean spaces.
9. Angles in Euclidean spaces for lines, for line and hyperplane and for subspace and hyperplane.
10. Isometries in Euclidean space, analytical expression, group of isometries.
11. Symmetries, classifications of symmetries, particularly in the plane.
12. Similarity in Euclidean space.

Extra requirements are not.

Subject has no prerequisities.

Subject has no co-requisities.

1. Affine spaces, affine coordinates.
2. Subspaces of the affine space, analytical formulation of the subspaces.
3. Mutual position of the subspaces.
4. Collinearity, linear systems of hyperplanes.
5. Affine transformations, affine transformation of the affine space.
6. Classification of the affine transformations.
7. Classification of the affine transformations for the line and the plane.
8. Vector spaces with scalar multiplication, Euclidean space.
9. Cartesian coordinates, orthogonality.
10. Distances, perturbations.
11. Isometries.
12. Classification of isometries in spaces of dimension 1 and 2.
13. Similarities.
14. Reserve.

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 | 10 |

Examination | Examination | 70 (70) | 25 |

Written examination | Written examination | 40 | 15 |

Oral examination | Oral examination | 30 | 10 |

Show history

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

2019/2020 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Optional | study plan | |||

2019/2020 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Optional | study plan | |||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | Choice-compulsory type B | study plan | ||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | Choice-compulsory type B | study plan |

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