## MUC23 Analytical Geometry 2

Faculty of Science
Spring 2022
Extent and Intensity
2/2/0. 4 credit(s). Type of Completion: zk (examination).
Taught in person.
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
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
there are 7 fields of study the course is directly associated with, display
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. II. 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. I. 1. vyd. Praha: Státní pedagogické nakladatelství, 1986. 197 s. info
• KADLEČEK, Jiří and Jan TROJÁK. Geometrie. III, Geometrická zobrazení : přehled látky s řešenými příklady. 1. vyd. Praha: Univerzita Karlova, 1984. 249 s. info
• BOČEK, Leo and Jaroslav ŠEDIVÝ. Grupy geometrických zobrazení. 1. vyd. Praha: Státní pedagogické nakladatelství, 1979. 213 s. info
• ŠMARDA, Bohumil. Analytická geometrie [Šmarda, 1978]. 1. vyd. 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)
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2020, Spring 2021.
• Enrolment Statistics (Spring 2022, recent)