| Course Unit Code | 230-0541/01 |
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| Number of ECTS Credits Allocated | 4 ECTS credits |
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| Type of Course Unit * | Choice-compulsory type B |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | |
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| Semester when the Course Unit is delivered | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| VOL18 | RNDr. Jana Volná, Ph.D. |
| Summary |
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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.
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| Learning Outcomes of the Course Unit |
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| In this course the students can acquaint with properties of affine and euclidean spaces, with affine, isometric and similar tranformations in this spaces. |
| Course Contents |
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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.
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| Recommended or Required Reading |
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| Required Reading: |
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Holme, A.: Geometry. Springer – Verlag, Berlin, Heidelberg, New York, 2002,
ISBN 3-540-41949-7.
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Burian, K.: Kapitoly z geometrie I. Učební texty Ostravské univerzity,Ostrava,
1996, ISBN 80-7042-732-9.
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| Recommended Reading: |
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Jennings, G.A.: Modern Geometry with Applications, Springer-Verlag, New York,
1994, ISBN 0-387-94222-X.
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Budinský, B.: Analytická a diferenciální geometrie. SNTL Praha, 1983,
ISBN 04-005-83.
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| Planned learning activities and teaching methods |
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| Lectures, Individual consultations, Tutorials, Other activities |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| 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 |