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Main menu for Browse IS/STAG
Course info
KMA / ARI
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Course description
Department/Unit / Abbreviation
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KMA
/
ARI
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Theoretical Arithmetic
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
5
Cred.
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Type of completion
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Combined
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Type of completion
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Combined
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Time requirements
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Lecture
3
[Hours/Week]
Tutorial
1
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
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Yes
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Automatic acceptance of credit before examination
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No
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Included in study average
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YES
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Language of instruction
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Czech
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Occ/max
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Automatic acceptance of credit before examination
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No
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Summer semester
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0 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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5 / -
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0 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Winter semester
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Semester taught
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Winter semester
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Minimum (B + C) students
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1
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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Czech
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Internship duration
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0
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No. of hours of on-premise lessons |
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Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
No
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Fundamental course |
Yes
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Fundamental theoretical course |
No
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Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
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None
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Preclusive courses
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N/A
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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KMA/AGM, KMA/ALS
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Histogram of students' grades over the years:
Graphic PNG
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XLS
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Course objectives:
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The course aims at introducing the students to axiomatic definition of number systems and to divisibility in integral domains.
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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. Pean?s axioms of postive integers.
Week 2. Development of integral number system and their properties
Week 3. Field of fraction for an integral domain and definition of rational numbers
Week 5. Development of real numbers, Dedekind?s method by cuts
Week 6. Properties of the real and complex number systems
Week 7. Ring of polynomials, algebraic and transcendental numbers.
Week 8. Divisibility in integral domain, basic properties
Week 9. Gauss integral domains, basic properties
Week 10. Integral domain of principal ideals
Week 11. Euclidian integral domains, theirs properties, Gauss integers
Week 12. relationship between the gauss integral domains, integral domain of principal ideals and Euclidian integral domain
Week 13. Gauss integral domains of polynomials
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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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-
Recommended:
Algebra
(Saunders M. L., Birkhoff G.)
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Recommended:
Algebra : Celost. vysokošk. učebnice pro stud. matematicko-fyzikálních a přírodovědeckých fakult, stud. oborů matematické vědy. 1. vyd. Praha : Academia, 1990. ISBN 80-200-0301-0.
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Recommended:
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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Recommended:
Blažek, Jaroslav. Algebra a teoretická aritmetika. I.. Praha : Státní pedagogické nakladatelství, 1979.
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Recommended:
Katriňák,T. a kol. Algebra a teoretická aritmetika (1). Bratislava, 1985.
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On-line library catalogues
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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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Contact hours
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52
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Preparation for an examination (30-60)
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45
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Graduate study programme term essay (40-50)
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40
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Total
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137
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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 |
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: |
definovat axiomaticky pojem přirozeného čísla a formulovat vlastnosti množiny přirozených čísel |
odvodit zavedení celých čísel a formulovat vlastnosti oboru integrity celých čísel |
popsat podílové podílové těleso oboru integrity a tím zavést čísla racionální |
metodou řezů formulovat čísla reálná a jejich vlastnosti |
popsat těleso komplexních čísel |
formulovat pojem dělitelnosti v oboru integrity |
shrnout vlastnosti oborů integrity hlavních ideálů a euklidovských oborů integrity |
Skills - skills resulting from the course: |
dělat celočíselné rozklady v oborech. integrity |
aplikovat souvislosti mezi jednotlivými obory integrity |
Competences - competences resulting from the course: |
N/A |
samostatně získávají další odborné znalosti, na základě praktické zkušenosti a jejího vyhodnocení a samostatným studiem teoretických poznatků oboru |
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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: |
Interactive lecture |
Individual study |
Discussion |
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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