MA2BP_CGE Seminar of Geometry

Faculty of Education
Autumn 2012
Extent and Intensity
0/2/0. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
Mgr. Leni Lvovská, Ph.D. (seminar tutor)
doc. RNDr. Otta Říha, CSc. (seminar tutor)
doc. Mgr. Vojtěch Žádník, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Jaroslav Beránek, CSc.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
Timetable of Seminar Groups
MA2BP_CGE/01: Mon 11:10–12:50 učebna 37, L. Lvovská
MA2BP_CGE/02: Mon 14:50–16:30 učebna 32, L. Lvovská
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
Course objectives
At the end of the course students should be able to (a) solve standard problems in general Euclidean space including relative positions, distances, and deviations of affine subspaces, (b) characterize and analytically express isometric, similarity, and generic affine transformations, primarily in the Euclidean plane and space.
Syllabus
  • (a) 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, Gramm's determinant, volumes. Distances and deviations of subspaces.
  • (b) 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). Transformations of real plane by means of algebraic operations with complex numbers.
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
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, autumn 2020, Autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2012, recent)
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