PdF:MA2BP_CGE Geometry - Seminar - Course Information
MA2BP_CGE Seminar of Geometry
Faculty of EducationAutumn 2024
- Extent and Intensity
- 0/2/0. 2 credit(s). Type of Completion: z (credit).
- Teacher(s)
- Mgr. Leni Lvovská, Ph.D. (seminar tutor)
doc. Mgr. Vojtěch Žádník, Ph.D. (seminar tutor) - Guaranteed by
- doc. Mgr. Vojtěch Žádník, Ph.D.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education - Prerequisites
- Good knowledge of linear algebra.
- Course Enrolment Limitations
- The course is only offered to the students of the study fields the course is directly associated with.
- fields of study / plans the course is directly associated with
- Lower Secondary School Teacher Training in Mathematics (programme PdF, B-SPE)
- Lower Secondary School Teacher Training in Mathematics (programme PdF, B-TV)
- Lower Secondary School Teacher Training in Mathematics (programme PdF, M-ZS5)
- Course objectives
- The aim of the course is to acquaint students with an algebraic (analytic) approach to basic geometric concepts in Euclidean plane and space, with their generalisations to spaces of arbitrary dimension and with applications of such approach in solving problems concerning both relative positions and measurements.
- Syllabus
- Affine spaces and subspaces. Parametric and general expressions of affine subspaces. The notion of parallelism, relative positions. Half-spaces and convex hulls. Euclidean spaces. Inner product and the notion of perpendicularity. Exterior and vector product, Gram's determinant, volumes. Distances and angles between subspaces.
- Isometric, similarity, and generic affine mappings, primarily the transformations of Euclidean plane and space. Definition, properties, and matrix representation. Classification via fixed points and eigenvectors. Decomposition into basic mappings (reflections with respect to hyperplanes, homotheties, basic affinities).
- Literature
- HORÁK, Pavel and Josef JANYŠKA. Analytická geometrie. Brno: Masarykova univerzita v Brně, 1997, 151 s. ISBN 80-210-1623-. info
- SEKANINA, Milan. Geometrie. 1. vyd. Praha: Státní pedagogické nakladatelství, 1988, 307 s. info
- BERGER, Marcel. Geometry. Translated by M. Cole - Silvio Levy. Corr. 2nd print. New York: Springer, 2009, xiii, 427. ISBN 9783540116585. info
- ŠEDIVÝ, Ondrej. Geometria : pre študentov matematiky učitel'ského štúdia na univerzitách a pedagogických fakultách. 1. vyd. Bratislava: Slovenské pedagogické nakladatel'stvo, 1987, 277 s. info
- Teaching methods
- Seminar.
- Assessment methods
- Individual homework, several written tests.
- Language of instruction
- Czech
- Further Comments
- The course is taught annually.
The course is taught: every week.
- Enrolment Statistics (recent)
- Permalink: https://is.muni.cz/course/ped/autumn2024/MA2BP_CGE