MA0009 Geometry 2

Faculty of Education
Autumn 2024
Extent and Intensity
2/2/0. 5 credit(s). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
doc. Mgr. Vojtěch Žádník, Ph.D. (lecturer)
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
Timetable
Tue 12:00–13:50 učebna 30
  • Timetable of Seminar Groups:
MA0009/01: Thu 8:00–9:50 učebna 37, V. Žádník
MA0009/02: Thu 10:00–11:50 učebna 37, V. Žádník
MA0009/03: Tue 17:00–18:50 učebna 37, V. Žádník
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.
Learning outcomes
At the end of the course, students should be able to understand the concept of algebraization of geometric objects and relations in plane and space, to generalise to spaces of arbitrary dimension and to apply such approach in solving standard problems.
Syllabus
  • Affine invariants, general vector and affine spaces, subspaces and their analytic expressions. Parallelism and relative positions of subspaces. Ordering on lines, half-spaces and convex hulls.
  • Basic metric notions, inner product, general Euclidean spaces. Perpendicularity and orthogonal projection. Distances and angles between subspaces. Areas of parallelograms, volumes of parallelepipeds, exterior and vector product.
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, 1986, 197 s. URL info
  • BERGER, Marcel. Geometry. Translated by M. Cole - Silvio Levy. Corr. 2nd print. New York: Springer, 2009, xiii, 427. ISBN 9783540116585. info
Teaching methods
Lectures and seminar.
Assessment methods
Individual homework, two written tests in seminars. The exam has both written and oral part.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2018, Autumn 2019, autumn 2020, Autumn 2021, Autumn 2022, Autumn 2023.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/ped/autumn2024/MA0009