MA0005 Algebra 2

Faculty of Education
Autumn 2021
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)
Mgr. Irena Budínová, Ph.D. (seminar tutor)
Mgr. Lukáš Másilko (seminar tutor)
RNDr. Petra Antošová, Ph.D. (assistant)
Guaranteed by
RNDr. Břetislav Fajmon, Ph.D.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
Timetable
Wed 22. 9. to Wed 15. 12. Wed 10:00–11:50 učebna 1
  • Timetable of Seminar Groups:
MA0005/01: Tue 21. 9. to Tue 14. 12. Tue 8:00–9:50 učebna 42, L. Másilko
MA0005/02: Tue 21. 9. to Tue 14. 12. Tue 10:00–11:50 učebna 42, L. Másilko
MA0005/03: Mon 20. 9. to Mon 13. 12. Mon 15:00–16:50 učebna 30, I. Budínová
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. Vector space and its subspace, its basis, dimension, coordinates.
  • 2. Affine space and its subspace, its basis, dimension, affine coordinates.
  • 3. Mutual position of vector and affine spaces.
  • 4. Order and permutation, determinant, Cramer rule.
  • 5. Computation and properties of a determinant, Laplace theorem.
  • 6. test-a.
  • 7. Matrices and their operations. The inverse of a matrix, matrix method of solving systems of linear equations.
  • 8. Linear transformation between vector spaces, kernel and image of a linear transformation.
  • 9. Change of basis, eigenvalues and eigenvectors of a linear transformation.
  • 10. Affine transformation between affine spaces.
  • 11. Scalar product = dot product, angle and length of a vector, orthogonalization, projection of a vector into a subspace.
  • 12. test-b.
Literature
    recommended literature
  • HORÁK, Pavel. Cvičení z algebry a teoretické aritmetiky. 3. vyd. Brno: Masarykova univerzita, 2006, 221 s. ISBN 8021039701. info
  • HORÁK, Pavel and Josef JANYŠKA. Analytická geometrie (Analytic geometry). 1. dotisk 1. vydání. Brno: Masarykova univerzita v Brně, 2002, 155 s. ISBN 80-210-1623-X. info
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
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2018, Autumn 2019, autumn 2020, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2021, recent)
  • Permalink: https://is.muni.cz/course/ped/autumn2021/MA0005