| Course title | Geometry for Informatics |
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| Course code | KMI/GEOMI |
| Organizational form of instruction | Lecture + Exercise |
| Level of course | Bachelor |
| Year of study | not specified |
| Semester | Summer |
| Number of ECTS credits | 4 |
| Language of instruction | Czech |
| Status of course | unspecified |
| 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 course is intended mainly for students of Computer Science. It is a complementary course to Laboratory in Geometry where more practical applications of the theory are presented and excercised on computers. 1. Affine spaces and subspaces. Definition and basic properties of affine spaces; affine combinations, affine hulls, vector combinations and hulls; affine subspaces and their properties. 2. Coordinates in affine spaces. Affine bases, affine coordinates; point bases and point coordinates; transformation matrices; equations of affine subspaces. 3. Affine mappings. Definition and basic properties of affine mapping, affine transformations, basic examples of affine mappings and transformations; matrix of an affine mapping in w.r.t. affine and point bases. 4. More on affine spaces and subspaces. Orientation of spaces and subspaces; convex combinations, convex hulls, convex sets; mutual position of affine subspaces. 5. Euclidean spaces. Vector spaces with scalar product; Euclidean spaces and subspaces, orthogonal and orthonormal bases and coordinates; general equations of affine subspaces; distance. 6. Projective spaces. Projective spaces and subspaces, projective extension of affine spaces; homogenous coordinates; projective mappings and transformations and their matrices. 7. Introduction to differential geometry of curves. The notion of a curve in Euclidean space, continuity, derivative; tangent, normal, binormal; length of a curve, parametrization by length.
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| Learning activities and teaching methods |
| Lecture, Demonstration |
| Learning outcomes |
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The students become familiar with basic concepts of geometry for informatics.
1. Knowledge Recall and deepen you knowledge of analytical geometry. |
| Prerequisites |
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unspecified
KAG/MA1AA ----- or ----- KMI/ALG1 |
| Assessment methods and criteria |
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Oral exam, Written exam
Active participation in class. Completion of assigned homeworks. Passing the oral (or written) exam. |
| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester |
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