Course objectives:
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The course aims at introducing the students to divisibility in integral domains and their application in solving basic problems.
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Requirements on student
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Knowledge, understanding and aplications of algebraic structures.
Credit - individual assigment.
Exam - test + oral.
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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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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Preparation for an examination (30-60)
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40
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Undergraduate study programme term essay (20-40)
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30
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Contact hours
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39
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Total
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109
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
orientovat se v základech matematické logiky, algebry a teorie grup |
využívat znalosti v rozsahu středoškolského učiva |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
aplikovat principy matematických důkazů |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
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 - skills resulting from the course: |
dělat celočíselné rozklady v oborech integrity |
používat euklidův algoritmus |
aplikovat souvislosti mezi jednotlivými obory integrity |
Competences - competences resulting from the course: |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
Seminar work |
Individual presentation at a seminar |
Skills - skills achieved by taking this course are verified by the following means: |
Seminar work |
Competences - competence achieved by taking this course are verified by the following means: |
Seminar work |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Individual study |
Interactive lecture |
Skills - the following training methods are used to achieve the required skills: |
Individual study |
Competences - the following training methods are used to achieve the required competences: |
Individual study |
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