MA2BP_CGE Seminar of Geometry

Faculty of Education
Autumn 2024
Extent and Intensity
0/2/0. 2 credit(s). Type of Completion: z (credit).
In-person direct teaching
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
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.
The course is also listed under the following terms Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, autumn 2020, Autumn 2021, Autumn 2022, Autumn 2023.
  • Enrolment Statistics (recent)
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