| Course title | Geometry 2 |
|---|---|
| Course code | KAG/MGEO4 |
| 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 | 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 |
|
1. Quadratic and bilinear forms, polar bases, signatures. 2. Diagonalisation of the matrix of a real quadratic form. 3. Conics in the Euclidean plane. Canonical equations. 4. Lines and conics. 5. Metric and affine classification of conics, affine and metric invariants. 6. Quadratic surfaces in a 3-dimmensional Euclidean space (quadrics). Canonical equations. 7. Lines and quadrics. Planes and quadrics. 8. Metric and affine classification of quadrics.
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| Learning activities and teaching methods |
| Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming), Demonstration |
| Learning outcomes |
|
Understand the analytic geometry of conics and quadrics in Euclidean plane resp. 3-dimensional space. To master corresponding tasks.
1. Knowledge Students describe elements of coordinated geometry of quadrics in euclidean plane and 3-dimensional space and define relations between quadrics and other geometrical configurations. |
| Prerequisites |
|
unspecified
KAG/ALG1 and KAG/GEO1 ----- or ----- KAG/MGEO3 |
| Assessment methods and criteria |
|
Oral exam, Written exam, Student performance
Credit: the student has to participate actively in seminars and pass a written test. Exam: the student has to understand the subject and be able to prove the principal results. The student has to be able to solve problems. |
| 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 Education (2023) | Category: Mathematics courses | 2 | Recommended year of study:2, Recommended semester: Summer |