MA0005 Algebra 2

Faculty of Education
Autumn 2018
Extent and Intensity
2/2/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Břetislav Fajmon, Ph.D. (lecturer)
Mgr. Helena Durnová, Ph.D. (seminar tutor)
doc. Mgr. Vojtěch Žádník, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Břetislav Fajmon, Ph.D.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
Timetable
Thu 10:00–11:50 učebna 37
  • Timetable of Seminar Groups:
MA0005/01: Wed 8:00–9:50 učebna 7, H. Durnová
MA0005/02: Thu 12:00–13:50 učebna 24, V. Žádník
Prerequisites
The subject is aimed at systematic acquiring of the knowledge of fundamental concepts in the theory of vector spaces and Euclidian spaces, linear algebraic methods, including the notions of linear and orthogonal mapping. The SS will actively use the concepts in problem solving, in their follow-up study at the faculty and in their own lessons as school teachers.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The objective of the subject is to impart fundamental knowledge of the theory of vector and Euclidian spaces and linear algebra. After a successful completion the SS will know and explain basic concepts of the following areas: Vector spaces, matrices and determinants, systems of linear equations, and thier solution, Euclidian spaces, linear and orthogonal mapping. All the notions will be actively used by the SS in mathematical problem solving and applied in the context of other parts of higher matthematics.
Learning outcomes
After the completion of the course, the SS will be able to a) work with some basic concepts of linear algebra, such as matrix, determinant, system of linear equations; b) tell the difference between homogeneous and nonhomogeneous solution of a linear system of equations. c) work with some basic linear transformations in plane and space, including orthogonal mapping which keeps the deviation of vectors.
Syllabus
  • 1. Definition of a vector space and its subspace.
  • 2. Linearly dependent and independent vectors, linear closure in a vector space.
  • 3. Basis and dimension of a vector space.
  • 4. Order and permutation, determinant.
  • 5. Computation of a determinant, Saruss's rule, Laplace's theorem.
  • 6. Matrices and matrix algebra. Finding an inverse of a matrix.
  • 7. System of linear equations, Cramer's rule, Jordan's method.
  • 8. Homogeneous systems of linear equations.
  • 9. Scalar product, Euclidian spaces, Gramm-Schmidt orthonormalising process.
  • 10.Linear mapping, linear transform, and its matrix.
  • 11.Eigenvalues and eigenvectors of a linear transform, use and appication of linear transforms.
  • 12.Orthogonal mapping and orthogonal transform.
Literature
    recommended literature
  • HORÁK, Pavel. Cvičení z algebry a teoretické aritmetiky. 3. vyd. Brno: Masarykova univerzita, 2006, 221 s. ISBN 8021039701. info
Teaching methods
Teaching methods chosen will reflect the contents of the subject and the level of students.
Assessment methods
Tests in the course of semestr checking theoretical knowledge and practical skills.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2019, autumn 2020, Autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2018, recent)
  • Permalink: https://is.muni.cz/course/ped/autumn2018/MA0005