MUC23 Analytical Geometry 2

Faculty of Science
Spring 2026
Extent and Intensity
2/2/0. 4 credit(s). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
prof. RNDr. Josef Janyška, DSc. (lecturer)
RNDr. Jakub Novák (lecturer)
RNDr. Pavel Šišma, Dr. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Janyška, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 16. 2. to Fri 22. 5. Mon 12:00–13:50 M1,01017
  • Timetable of Seminar Groups:
MUC23/01: Mon 16. 2. to Fri 22. 5. Thu 16:00–17:50 M5,01013, P. Šišma
MUC23/02: Mon 16. 2. to Fri 22. 5. Thu 18:00–19:50 M5,01013, P. Šišma
MUC23/03: Mon 16. 2. to Fri 22. 5. Tue 14:00–15:50 M5,01013, J. Novák
Prerequisites
Knowledge of MUC31 Lineární algebra a MUC22 Analytická geometrie 1.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 7 fields of study the course is directly associated with, display
Abstract
The goal of the course is:
- analytical theory of affine mappings of affine spaces, especially in plane and three-dimensional space;
- analytical theory of isometric and similar mappings of Euclidean point spaces, especially in plane and three-dimensional space;
- theory of circle inversion in a plane;
- mastering relevant computing techniques;
- supporting students' spatial imagination.
Learning outcomes
Student will be able to:
- solving problemses with affine mappings;
- solving problems using isometric and similar mappings;
- solving problemss using circle inversion.
Key topics
  • Invariant subspaces of linear transformations of the vector space.
  • Invariant subspaces of orthogonal transformations of a vector space with a scalar product.
  • Afine mappings:
  • - associated linear mappings;
  • - coordinate expression of affine mappings;
  • - affine transformations of an affine space, fix points and eigenvectors;
  • - homotheties;
  • - basic affine mappings, decomposition of an affine mapping into basic affine mappings.
  • Isometric mappings:
  • - coordinate expression of isometric mappings;
  • - group of isometric transformations, symmetries with respect to subspaces;
  • - decomposition of isometries by reflections;
  • - classification of isometries in plane and space.
  • Similar mappings.
  • - coordinate representation of similar mappings;
  • - a group of similarities;
  • - decomposition of similar mappings to homothetic transformations and isometriess.
  • Circle inversion and its using to solve planimetric problems.
Study resources and literature
    recommended literature
  • SEKANINA, Milan. Geometrie. 1. vyd. Praha: Státní pedagogické nakladatelství, 1986, 197 s. URL info
    not specified
  • JANYŠKA, Josef. Geometrická zobrazení. Online. 2024.
  • BOČEK, Leo and Jaroslav ŠEDIVÝ. Grupy geometrických zobrazení. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1979, 213 s. info
  • SEKANINA, Milan. Geometrie. 1. vyd. Praha: Státní pedagogické nakladatelství, 1988, 307 s. info
  • LEISCHNER, Pavel. Geometrická zobrazení. Vyd. 1. V Českých Budějovicích: Jihočeská univerzita, 2010, 120 s. ISBN 9788073942434. info
  • JANYŠKA, Josef. Geometrická zobrazení - sbírka příkladů. Online. 2024.
Approaches, practices, and methods used in teaching
Lectures: theoretical explanations with examples of practical applications.
Exercises: solving problems focused on basic concepts and theorems, individual problem solving by students.
Method of verifying learning outcomes and course completion requirements
Examination consists of two parts: written and oral.
Current requirements: Written tests in exercises.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/spring2026/MUC23