| Course title | Algebra 4 |
|---|---|
| Course code | KMT/KAL4@ |
| Organizational form of instruction | Lecture |
| Level of course | Bachelor |
| Year of study | not specified |
| Semester | Summer |
| Number of ECTS credits | 3 |
| Language of instruction | Czech |
| Status of course | Compulsory |
| Form of instruction | Face-to-face |
| Work placements | This is not an internship |
| Recommended optional programme components | None |
| Lecturer(s) |
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| Course content |
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Matrices and their algebraic properties, matrix operations, regular and inverse matrices. Systems of linear equations, Gauss-Jordan elimination, Frobenius theorem on solvability. Determinants, their properties, Laplace expansion, and Cramer's rule. Vector spaces and subspaces, linear independence, basis, and dimension. Linear mappings, kernel and image of a mapping. Euclidean vector spaces, inner products, and orthogonalization.
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| Learning activities and teaching methods |
| Lecture |
| Learning outcomes |
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The course aims to introduce students to the fundamental concepts and methods of linear algebra. Emphasis is placed on understanding the relationships between matrices, systems of linear equations, and vector spaces. Students will master techniques for solving algebraic problems, ranging from elementary row operations to advanced studies of the properties of finite-dimensional Euclidean spaces.
Upon completion, the student will be able to: Perform matrix operations (addition, multiplication, transposition) and determine their properties. Efficiently solve systems of linear equations using the Gauss-Jordan elimination method and Cramer's rule. Calculate determinants of matrices and use them to determine regularity and calculate inverse matrices. Work with vector spaces and subspaces, and determine their basis and dimension. |
| Prerequisites |
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Algebra 3.
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| Assessment methods and criteria |
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Mark
Active knowledge of the course subject matter. Specific requirements (including individual assignments for term papers) are specified in the respective MS Teams group. Regarding active physical attendance, a minimum of 49% is required for both full-time and part-time students. For students with an Individual Study Plan (ISP), the minimum attendance is 20% (specific ISP requirements must be consulted in person with the instructor at the beginning of the semester). |
| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester | |
|---|---|---|---|---|
| Faculty: Faculty of Education | Study plan (Version): Mathematics focused on education (BB25) | Category: Pedagogy, teacher training and social care | 2 | Recommended year of study:2, Recommended semester: Summer |
| Faculty: Faculty of Education | Study plan (Version): Mathematics: teaching focus (BB23) | Category: Pedagogy, teacher training and social care | 2 | Recommended year of study:2, Recommended semester: Summer |
| Faculty: Faculty of Education | Study plan (Version): Mathematics focused on education (BB21) | Category: Pedagogy, teacher training and social care | 2 | Recommended year of study:2, Recommended semester: Summer |
| Faculty: Faculty of Education | Study plan (Version): Mathematics: teaching focus (BB21) | Category: Pedagogy, teacher training and social care | 2 | Recommended year of study:2, Recommended semester: Summer |
| Faculty: Faculty of Education | Study plan (Version): Mathematics focused on education (BB24) | Category: Pedagogy, teacher training and social care | 2 | Recommended year of study:2, Recommended semester: Summer |
| Faculty: Faculty of Education | Study plan (Version): Mathematics focused on education (BB19) | Category: Pedagogy, teacher training and social care | 2 | Recommended year of study:2, Recommended semester: Summer |
| Faculty: Faculty of Education | Study plan (Version): Mathematics: teaching focus (BB24) | Category: Pedagogy, teacher training and social care | 2 | Recommended year of study:2, Recommended semester: Summer |
| Faculty: Faculty of Education | Study plan (Version): Mathematics focused on education (BB22) | Category: Pedagogy, teacher training and social care | 2 | Recommended year of study:2, Recommended semester: Summer |
| Faculty: Faculty of Education | Study plan (Version): Mathematics focused on education (BB23) | Category: Pedagogy, teacher training and social care | 2 | Recommended year of study:2, Recommended semester: Summer |
| Faculty: Faculty of Education | Study plan (Version): Mathematics focused on education (BB20) | Category: Pedagogy, teacher training and social care | 2 | Recommended year of study:2, Recommended semester: Summer |
| Faculty: Faculty of Education | Study plan (Version): Mathematics: teaching focus (BB20) | Category: Pedagogy, teacher training and social care | 2 | Recommended year of study:2, Recommended semester: Summer |
| Faculty: Faculty of Education | Study plan (Version): Mathematics: teaching focus (BB19) | Category: Pedagogy, teacher training and social care | 2 | Recommended year of study:2, Recommended semester: Summer |
| Faculty: Faculty of Education | Study plan (Version): Mathematics: teaching focus (BB25) | Category: Pedagogy, teacher training and social care | 2 | Recommended year of study:2, Recommended semester: Summer |
| Faculty: Faculty of Education | Study plan (Version): Mathematics: teaching focus (BB22) | Category: Pedagogy, teacher training and social care | 2 | Recommended year of study:2, Recommended semester: Summer |