MA0005 Algebra 2

Faculty of Education
Autumn 2023
Extent and Intensity
2/2/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
Mgr. Helena Durnová, Ph.D. (lecturer)
RNDr. Břetislav Fajmon, Ph.D. (lecturer)
RNDr. Petra Antošová, Ph.D. (seminar tutor)
Mgr. Irena Budínová, Ph.D. (seminar tutor)
Mgr. Lukáš Másilko (seminar tutor)
Guaranteed by
RNDr. Břetislav Fajmon, Ph.D.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
Timetable
Tue 8:00–9:50 učebna 30
  • Timetable of Seminar Groups:
MA0005/01: Thu 12:00–13:50 učebna 1, L. Másilko
MA0005/02: Thu 10:00–11:50 učebna 1, L. Másilko
MA0005/03: Thu 14:00–15:50 učebna 30, P. Antošová
Prerequisites
Fundamental knowledge, not necessarily the finished exam in subjects MA0001, MA0003. Finished subject MA0015 is an advantage, because the students will follow up with the contents of the subject.
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
Course objectives
The subject serves as a preliminary, algebraic look at geometry. The contents of the subject will be followed up in Geometry 2 (MA0009).
Learning outcomes
Having completed the course, the students will a) know some basic concepts in the theory of vector spaces and affine spaces (vector coordinates, affine coordinates, basis, dimension, etc.); b) have skills in working with matrices (computation of a determinant, solution of linear system of equations, transformation of coordinates, vector and scalar product of vectors); c) know and use mathematical notation in the area of linear and affine mappings; d) be acquainted with some parts of analytical geometry, and thus they will be prepared for the follow-up subject Geometry 2.
Syllabus
  • 1. Determinant and its properties, Cramer's Rule.
  • 2. Laplace expansion of a determinant. Linear property, determinant of an echelon form.
  • 3. Vector space (basis, dimension, coordinates), systems of linear equations.
  • 4. Mutual position of vector subspaces.
  • 5. Matrix operation, inverse matrix, matrix method in solving linear systems.
  • 6. Homogeneous and nonhomogeneous linear systems, superposition rule.
  • 7. Linear mapping between vector spaces.
  • 8. Transitoin matrix, composition of linear mappings.
  • 9. Scalar product, norm of a vector.
  • 10. Ortogonal vectors, ortogonal projection of a vector onto a vector subspace.
  • 11. Eigenvalies and eigenvectors.
  • 12. Vector product.
Teaching methods
Teaching methods chosen will reflect the contents of the subject and the level of students.
Assessment methods
Two tests during the semester with the obligation to complete 60 per cent of the contents. The final oral exam.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
Materials and requirements in English will be given by the teacher.
The course is also listed under the following terms Autumn 2018, Autumn 2019, autumn 2020, Autumn 2021, Autumn 2022, Autumn 2024.
  • Enrolment Statistics (Autumn 2023, recent)
  • Permalink: https://is.muni.cz/course/ped/autumn2023/MA0005