| Course title | Mathematics 1 |
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| Course code | KAG/YMAT1 |
| Organizational form of instruction | Lecture |
| Level of course | Bachelor |
| Year of study | not specified |
| Semester | Summer |
| Number of ECTS credits | 9 |
| Language of instruction | Czech |
| Status of course | unspecified |
| 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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<lo> <li> Sets, relations between sets; properties of relations; mappings. Ordered sets, equivalence relations, decompositions. <li> Structures with a single operation and their substructures ? groupoids, halfgroups, neutral element, inverse element, subgroupoids. Groups, subgroups. <li> Structures with two operations and their substructures ? rings, subrings, domains. Fields, subfields, numbers fields. <li> Vector spaces over number fields ? subspaces; subspaces generated by vectors. Linear combination of vectors, linear hull; dimension and basis of a vector space, vector coordinates. <li> Matrices and determinants ? definitions, computing rules for determinants. Sum of matrices, scalar multiple of a matrix, matrix multiplication. Inverse of a matrix and its computing, rank of a matrix . <li> Systems of linear equations ? introduction, solvability. Gauss elimination method, The Frobenius Theorem, Cramer?s rule. Homogeneous systems of linear equations. </lo>
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| Learning activities and teaching methods |
| Lecture |
| Learning outcomes |
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The course is an introduction to algebra. It is targeted at Computer Science Teaching students
Knowledge |
| Prerequisites |
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unspecified
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| Assessment methods and criteria |
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Mark
Credit: from seminars. Exam: written. |
| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester |
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