MA0013 Geometry 3

Faculty of Education
Autumn 2019
Extent and Intensity
0/2/0. 3 credit(s). Type of Completion: k (colloquium).
Teacher(s)
doc. Mgr. Vojtěch Žádník, Ph.D. (lecturer)
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 also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 1 student(s).
Current registration and enrolment status: enrolled: 0/1, only registered: 0/1, only registered with preference (fields directly associated with the programme): 0/1
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 the projective extension of Euclidean, respectively affine spaces and the corresponding characterizations of projective, affine, similarity and isometric mappings.
Learning outcomes
At the end of the course, students should be able to understand the notion of projective extension of Euclidean, respectively affine spaces, its algebraization and the corresponding characterizations of projective, affine, similarity and isometric mappings.
Syllabus
  • Introduction to projective geometry, projective invariants, projective extension of affine spaces. Homogeneous coordinates and analytic expressions.
  • Fundamental theorem of projective geometry and its consequences. Characterization of affine, similarity and isometric mappings among of all projective ones. Transformations and their fixed elements, overview and characterization of basic transformations.
Literature
  • SEKANINA, Milan. Geometrie. 1. vyd. Praha: Státní pedagogické nakladatelství, 1988, 307 s. 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
  • BERGER, Marcel. Geometry. Translated by M. Cole - Silvio Levy. Corr. 2nd print. New York: Springer, 2009, xiii, 427. ISBN 9783540116585. info
Teaching methods
Lectures.
Assessment methods
Individual homework, one written test. Colloquium.
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 Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Autumn 2019, recent)
  • Permalink: https://is.muni.cz/course/ped/autumn2019/MA0013