| Course title | Algebra 1 |
|---|---|
| Course code | KAG/A1M |
| Organizational form of instruction | Lecture + Lesson |
| Level of course | Bachelor |
| Year of study | 2 |
| Semester | Summer |
| Number of ECTS credits | 4 |
| Language of instruction | Czech |
| Status of course | Compulsory, Optional |
| 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. Groups, basic examples of groups. Subgroups, partitions. Normal subgroups, quotient groups. Homomorphisms, congruences, the relationship between homomorphisms, congruences and normal subgroups. The centre of a group, inner authomorphisms. The homomorphism theorem, the isomorphism theorems. Direct products. Cyclic groups. Finite abelian groups. Permutation groups, Cayley's theorem. 2. Rings, division rings and integral domains, basic examples. Subrings, ideals, quotient rings. Homomorphisms, congruences, the relationship between homomorphisms, congruences and ideals. The homomorphism theorem. Prime ideals and maximal ideals. Direct products. The characteristic of a ring.
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| Learning activities and teaching methods |
| Lecture, Monologic Lecture(Interpretation, Training) |
| Learning outcomes |
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To understand the rudiments of the theory of groups and rings.
Students are familiar with basic concepts and theorems, including their proofs. |
| Prerequisites |
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unspecified
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| Assessment methods and criteria |
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Written exam
Credit: attendance at seminars and/or written test (according to the instructor's discretion). |
| 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): Mathematics (2020) | Category: Mathematics courses | 2 | Recommended year of study:2, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Applied Mathematics - Specialization in Business Mathematics (2026) | Category: Mathematics courses | 2 | Recommended year of study:2, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Applied Mathematics - Specialization in Data Science (2026) | Category: Mathematics courses | 2 | Recommended year of study:2, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Applied Mathematics - Specialization in Industrial Mathematics (2026) | Category: Mathematics courses | 2 | Recommended year of study:2, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Applied Mathematics - Specialization in Mathematics for Sustainable Innovation (2026) | Category: Mathematics courses | 2 | Recommended year of study:2, Recommended semester: Summer |