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Lecturer(s)
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Zalabová Lenka, doc. Mgr. Ph.D.
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Course content
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Content of lectures: The goal of the course is the studying of analytic theory of conic sections and quadrics. Firstly we explain complex and projective extension of affine space, which are natural constructions useful for the theory. The main object then is to formulate the definition of conic sections and quadrics, and study projective, affine and metric properties. On examples we demonstrate, how is the theory related with the usual facts that students know from high school and other courses. We present projective, affine and metric classifications of conic sections and quadrics, together with method for recognising of the type of conic section or quadric. Summary: 1. The complex extension of vector and affine spaces. 2. Projective spaces, arithmetical and geometric basis. 3. Restriction of projective space to affine space, projective extension of an affine space, homogeneous and non-homogeneous coordinates. 4. Conic sections of projective plane - definition, regular and singular conic sections, pole and polar line, tangent line, the projective classification. 5. Affine properties of conic sections - centres, diameters, asymptotic lines, the affine classification. 6. Metric properties of conic section - principal numbers and directions, axes, vertices, metric classifications. 7. Conic sections as sets of points with suitable properties - connections with high school concepts.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book), Individual preparation for exam
- Preparation for classes
- 56 hours per semester
- Preparation for exam
- 56 hours per semester
- Class attendance
- 56 hours per semester
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Learning outcomes
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The goal of the course is the geometry of conic sections (projective, affine, Euclidean).
Student will acquire knowledge od analytic theory of conic sections.
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Prerequisites
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The konwlege of linear algebra and geometry on the level of courses UMB584 Geometry I a UMB585 Linear algebra II.
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Assessment methods and criteria
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Combined exam, Seminar work
Active participation in the tutorials and understanding of the presented theory, passing both theoretical and practical parts of the exam (50%).
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Recommended literature
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Budínský, B., Analytická a diferenciální geometrie, Praha, SNTL, 1983, 296 stran.
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Janyška , J., Sekaninová, A, Analytická teorie kuželoseček a kvadrik, Brno, Masarykova univerzita, 1996, 178 stran.
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Pech, P., Kuželosečky, Č. Budějovice, Jihočeská univerzita, 2004, 150 stran.
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Pech, P., Kuželosečky, Č. Budějovice, Pedagogická fakulta, Jihočeská univerzita, 1998, 90 stran.
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Sekanina, M. a kol., Geometrie II, Praha, SPN, 1988, 307 stran.
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