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Lecturer(s)
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Hofman Martin, RNDr. Mgr. Ph.D.
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Course content
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Week 1-3: Divisibility in integral domain, basic properties. Week 4-6: Gauss integral domains, basic properties. Week 7-8: Integral domain of principal ideals. Week 9-11: Euclidian integral domains, theirs properties, Gauss integers Week 12-13: Relationship between the gauss integral domains, integral domain of principal ideals and Euclidian integral domain.
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Learning activities and teaching methods
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Lecture supplemented with a discussion, Lecture with practical applications, Individual study
- Preparation for an examination (30-60)
- 40 hours per semester
- Contact hours
- 39 hours per semester
- Undergraduate study programme term essay (20-40)
- 30 hours per semester
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| prerequisite |
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| Knowledge |
|---|
| orientovat se v základech matematické logiky, algebry a teorie grup |
| využívat znalosti v rozsahu středoškolského učiva |
| Skills |
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| aplikovat principy matematických důkazů |
| Competences |
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| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| define the notion of divisibility in an integral domain |
| summarize the properties of gauss integral domain and apply them to particular integral domains |
| summarize the properties of integral domain of principal ideals and Euclidian integral domains |
| introduce relationships between the specific integral domains a apply them to particular domains |
| Skills |
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| dělat celočíselné rozklady v oborech integrity |
| používat euklidův algoritmus |
| aplikovat souvislosti mezi jednotlivými obory integrity |
| Competences |
|---|
| N/A |
| teaching methods |
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| Knowledge |
|---|
| Individual study |
| Interactive lecture |
| Skills |
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| Individual study |
| Competences |
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| Individual study |
| assessment methods |
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| Knowledge |
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| Combined exam |
| Seminar work |
| Individual presentation at a seminar |
| Skills |
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| Seminar work |
| Competences |
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| Seminar work |
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Recommended literature
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Blažek, Jaroslav. Algebra a teoretická aritmetika. I.. Praha : Státní pedagogické nakladatelství, 1979.
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Blažek, Jaroslav; Koman, Milan; Vojtašková, Blanka. Algebra a teoretická aritmetika : Celost. a vysokošk. učebnice pro stud. matematicko-fyzikálních, přírodověd. a pedagog. fakult. Díl 2.. 1. vyd. Praha : SPN, 1985.
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Katriňák,T. a kol. Algebra a teoretická aritmetika (1). Bratislava, 1985.
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