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Lecturer(s)
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Pařez Klaus, doc. RNDr. Ph.D.
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Course content
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Affine space, affine coordinate system and its transformations. Subspaces and their descriptions. Mutual position of subspaces, specially for hyperplanes. Ratio of lengths, linear (specially convex) combination of points, subsets of affine subspaces. Euclidean space and its subspaces, Cartesian coordinate system and its transformations (mainly translation and rotation). Cross and scalar triple products, their generalizations and geometric meaning. Orthogonality and distances of subspaces, angles of lines and hyperplanes. Conics in the plane, quadrics in the space ? definitions, properties, applications. This course is lectured in English, its content is equivalent to KMA/G1.
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Learning activities and teaching methods
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Interactive lecture, Lecture supplemented with a discussion, E-learning, Cooperative instruction, Discussion, Task-based study method, Students' self-study, Textual studies, Lecture, Practicum
- Contact hours
- 39 hours per semester
- Preparation for an examination (30-60)
- 60 hours per semester
- Preparation for formative assessments (2-20)
- 15 hours per semester
- Preparation for comprehensive test (10-40)
- 20 hours per semester
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| prerequisite |
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| Knowledge |
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| A good knowledge of linear algebra and vector calculus (KMA/LA or equivalent). Basic knowledge of space analytic geometry at the secondary school level. Skills in computing with vectors, matrices and determinants and in solving systems of linear and quadratic equations. In case of insufficient background knowledge, the teachers will suggest reading material to make up for it. Since this course is taught in English, the active understanding of English language is presumed. |
| Skills |
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| apply the acquired procedures to elementary geometric problems at the secondary school level |
| calculate vectors, matrices and determinants and solve systems of linear and quadratic equations |
| use the calculus apparatus for basic and intermediate problems |
| Competences |
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| bc. study: recognizes the problem, clarifies its essence, breaks it down into parts, |
| N/A |
| learning outcomes |
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| Knowledge |
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| Upon completion of the course a student will be able to: - give the definition of affine space and introduce a suitable coordinate system; - understand affine spaces, write down their descriptions and determine their mutual position; - give the definition of Euclidean space and introduce Cartesian coordinate system as the specialization of affine coordinate system; - determine equations of orthogonal subspaces, compute distances and angles of Euclidean subspaces; - define and classify conics in Euclidean plane. Rewrite their equations on canonical form, identify and use them; - define and classify quadrics in 3-dimensional Euclidean space. Rewrite their equations on canonical form, identify and use them; - independently use the analytic method for solving problems from mathematics a from praxis; - understand and use the English terminology of the theory stated above. |
| teaching methods |
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| Lecture |
| Lecture supplemented with a discussion |
| Interactive lecture |
| Practicum |
| E-learning |
| Task-based study method |
| Textual studies |
| Cooperative instruction |
| Self-study of literature |
| Discussion |
| assessment methods |
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| Combined exam |
| Test |
| Seminar work |
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Recommended literature
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Boček, L., Šedivý J. Grupy geometrických zobrazení. SPN Praha, 1980.
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Boček, Leo. Geometrie. I. Praha : Univerzita Karlova, 1982.
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Budinský, B. Analytická a diferenciální geometrie. 1. vyd. Praha : SNTL, 1983.
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Coxeter, Harold Scott MacDonald. The beauty of geometry : twelve essays. 1st pub. Mineola : Dover Publications, 1999. ISBN 0-486-40919-1.
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Ježek, František; Míková, Marta. Maticová algebra a analytická geometrie. 2., přeprac. vyd. Plzeň : Západočeská univerzita, 2003. ISBN 80-7082-996-6.
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Mahel a kol. Sbírka úloh z lineární algebry a analytické geometrie. ČVUT, 1980.
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Sekanina, M. a kol. Geometrie. 1. díl..
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Sekanina, M. a kol. Geometrie. 2. díl.. 1. vyd. Praha : Státní pedagogické nakladatelství, 1988.
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Sekaninová, A. a Janyška, J. Analytická teorie kuželoseček a kvadrik. Alfa, Bratislava, 1984.
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