| Course title | Mathematics 1 |
|---|---|
| Course code | KAG/IMAT1 |
| Organizational form of instruction | Lecture + Exercise |
| Level of course | Bachelor |
| Year of study | not specified |
| Semester | Winter |
| Number of ECTS credits | 5 |
| 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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1. Fundamentals of logic, proofs of mathematical propositions. 2. Relations, equivalence and partial order on a set, set mappings, basic algebraic structures. 3. Matrices, operations with matrices (sum, product, real multiple). 4. Order, permutations, determinants. 5. Vector spaces, subspaces, direct sum of subspaces, bases of vector spaces. 6. Eucleidian vector spaces, orthogonal and orthonormal bases, the inequality of Schwarz, Schmidt's orthogonalisation. 7. Rank of a matrix, homogeneous and nonhomogeneous systems of linear equations, Frobenius' theorem, the Gauss method, Cramer's rule. 8. Ring of the square matrices, inverse matrix. 9. Linear mappings and transformations, their matrices, basic properties and examples.
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| Learning activities and teaching methods |
| unspecified |
| Learning outcomes |
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To understand bases of linear algebra, to master solving the typical tasks.
Students obtain ability to apply a knowledge of the linear algebra for solving particular mathematical problems. |
| Prerequisites |
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unspecified
|
| Assessment methods and criteria |
|
unspecified
Credit: from seminars. Exam: oral |
| 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 Science | Study plan (Version): Computer Science (2020) | Category: Informatics courses | 2 | Recommended year of study:2, Recommended semester: Winter |
| Faculty: Faculty of Science | Study plan (Version): Information Technologies (2022) | Category: Informatics courses | 2 | Recommended year of study:2, Recommended semester: Winter |
| Faculty: Faculty of Science | Study plan (Version): Computer Science - Specialization in Programming and Software Development (2021) | Category: Informatics courses | 2 | Recommended year of study:2, Recommended semester: Winter |