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Lecturer(s)
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Teska Jakub, RNDr. Mgr. Ph.D.
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Course content
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Week 1-4: Groupoids, monoids, semigroups. Week 5-7: Groups, Abelian Groups, subgroups, Lagrange´s Theorem, normal subgroups, quotient groups. Week 8-9: Homomorphisms of groups, theorem about isomorphism of groups, cyclic groups and their structure. Week 10-11: Rings and fields, subrings, ideals, quotient rings, zero divisors, basic properties of fields. Week 12-13: Associative, commutative rings with an identity.
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Learning activities and teaching methods
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Lecture supplemented with a discussion, Lecture with practical applications, Discussion
- Undergraduate study programme term essay (20-40)
- 30 hours per semester
- Contact hours
- 39 hours per semester
- Preparation for an examination (30-60)
- 45 hours per semester
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| prerequisite |
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| Knowledge |
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| využívat znalosti v rozsahu středoškolského učiva |
| orientovat se v základech matematické logiky |
| Skills |
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| aplikovat principy matematických důkazů |
| Competences |
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| N/A |
| N/A |
| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| ovládat pojmy ekvivalence, rozkladu množiny na třídy ekvivalence |
| ovládat pojmy z teorie pologrup |
| ovládat pojmy z teorie grup |
| Skills |
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| aplikovat základní vlastnosti grup na konkrétní modely |
| umět rozpoznat strukturu okruhu a tělesa |
| řešit jednoduché úlohy v aritmetikách modulo k |
| Competences |
|---|
| N/A |
| teaching methods |
|---|
| Knowledge |
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| Lecture supplemented with a discussion |
| Skills |
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| Lecture supplemented with a discussion |
| Competences |
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| Lecture supplemented with a discussion |
| assessment methods |
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| Knowledge |
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| Combined exam |
| Seminar work |
| Skills |
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| Seminar work |
| Competences |
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| Seminar work |
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Recommended literature
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Beran, Ladislav. Grupy a svazy. Vyd. 1. Praha : SNTL, 1974.
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Cohn, Paul M. Basic algebra : groups, rings and fields. London : Springer, 2003. ISBN 1-85233-587-4.
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Procházka a kol. Algebra. Academia Praha.
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Wallace, David Alexander Ross. Groups, rings and fields. [1st ed.]. London : Springer, 1998. ISBN 3-540-76177-2.
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