PřF:MUC23 Analytical Geometry 2 - Course Information
MUC23 Analytical Geometry 2
Faculty of ScienceSpring 2023
- Extent and Intensity
- 2/2/0. 4 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Josef Janyška, DSc. (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
- Tue 12:00–13:50 M1,01017
- Timetable of Seminar Groups:
MUC23/02: Mon 8:00–9:50 M5,01013, P. Šišma - Prerequisites
- Knowledge of M1500 Algebra 1, M2500 Algebra 2 and M3521 Geometry 2.
- 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
- Mathematics with a view to Education (programme PřF, B-EB)
- Mathematics with a view to Education (programme PřF, B-FY)
- Mathematics with a view to Education (programme PřF, B-GE)
- Mathematics with a view to Education (programme PřF, B-GK)
- Mathematics with a view to Education (programme PřF, B-CH)
- Mathematics with a view to Education (programme PřF, B-IO)
- Mathematics with a view to Education (programme PřF, B-MA)
- Course objectives
- 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. - Syllabus
- 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.
- Literature
- recommended literature
- JANYŠKA, Josef. Geometrická zobrazení, Učební text, jarní semestr 2017
- not specified
- SEKANINA, Milan. Geometrie. 1. vyd. Praha: Státní pedagogické nakladatelství, 1988, 307 s. info
- HORÁK, Pavel and Josef JANYŠKA. Analytická geometrie. Brno: Masarykova univerzita v Brně, 1997, 151 s. ISBN 80-210-1623-X. info
- SEKANINA, Milan. Geometrie. 1. vyd. Praha: Státní pedagogické nakladatelství, 1986, 197 s. URL info
- KADLEČEK, Jiří and Jan TROJÁK. Geometrie. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1984, 249 s. info
- BOČEK, Leo and Jaroslav ŠEDIVÝ. Grupy geometrických zobrazení. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1979, 213 s. info
- ŠMARDA, Bohumil. Analytická geometrie. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1978, 157 s. info
- Teaching methods
- Lectures: theoretical explanations with examples of practical applications.
Exercises: solving problems focused on basic concepts and theorems, individual problem solving by students. - Assessment methods
- 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
- Enrolment Statistics (Spring 2023, recent)
- Permalink: https://is.muni.cz/course/sci/spring2023/MUC23