| Course title | Geometry I. |
|---|---|
| Course code | UMB/584 |
| Organizational form of instruction | Lecture + Lesson |
| Level of course | Bachelor |
| Year of study | not specified |
| Frequency of the course | In each academic year, in the summer semester. |
| Semester | Summer |
| Number of ECTS credits | 6 |
| Language of instruction | Czech |
| Status of course | Compulsory |
| Form of instruction | Face-to-face |
| Work placements | This is not an internship |
| Recommended optional programme components | None |
| Lecturer(s) |
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| Course content |
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The content of the course is the coordinated geometry, mainly the studying of linear objects in affine and Euclidean spaces. The main goal of the course is to explain the theory, which generalizes the knowledge of students on geometry in plane and space from high schools. In the course, we focus on solution intersection and distance problems. Summary: 1. Affine spaces. 2. Affine frames and coordinates. 3. Affine subspaces and their description. 4. Intersection problems for affine subspaces. 5. Sheaves of hyperplanes. 6. Distinguished subsets; half-spaces, angles, convex sets, simplices. 7. Euklidean spaces. 8. Orthonormal frames and coordinates. 9. Perpendicular subspaces, normal line of hyperplane. 10. Cross product, Gramm determinant, volume of parallelepiped. 11. Distance and angle between subspaces. 12. Affine mappings and affine transformations. Content of practicals: Solving of concrete problems demonstrating the theory.
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| Learning activities and teaching methods |
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book), Individual preparation for exam
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| Learning outcomes |
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The goal of the course is the coordinated geometry of linear objects (affine, Euclidean).
Student will acquire knowledge of affine geometry. |
| Prerequisites |
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The knowledge of linear algebra on the level of the courses UMB551 Linear algebra a UMB585 Linear algebra II.
UMB/CV551 ----- or ----- UMB/551 and UMB/CV585 ----- or ----- UMB/585 |
| Assessment methods and criteria |
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Combined exam, Self-reflection
Active participation in the tutorials and understanding of the theory, learning the system geogebra, and passing both written and oral parts of the exam (50%). |
| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester | |
|---|---|---|---|---|
| Faculty: Faculty of Science | Study plan (Version): Mathematics for future teachers (1) | Category: Mathematics courses | 2 | Recommended year of study:2, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Mathematics for future teachers (1) | Category: Mathematics courses | 2 | Recommended year of study:2, Recommended semester: Summer |