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Main menu for Browse IS/STAG
Course info
KMA / ZA
:
Course description
Department/Unit / Abbreviation
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KMA
/
ZA
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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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Fundamentals of Algebra
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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,
4
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
2
[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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5 / -
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3 / -
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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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0 / -
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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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Summer semester
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Semester taught
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Summer 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 |
No
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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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N/A
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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 subject is dedicated to the study of basics of algebra - ordered set, lattices, groups, fields.
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Requirements on student
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Knowledge, understanding and aplications of algebraic structures.
Credit - individual assigment.
Exam - orals: 3 topics (semigroups, groups, rings and fields).
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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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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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Undergraduate study programme term essay (20-40)
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30
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Preparation for an examination (30-60)
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45
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Contact hours
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39
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Total
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114
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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: |
využívat znalosti v rozsahu středoškolského učiva |
orientovat se v základech matematické logiky |
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 |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
ovládat pojmy ekvivalence, rozkladu množiny na třídy ekvivalence |
ovládat pojmy z teorie pologrup |
ovládat pojmy z teorie grup |
Skills - skills resulting from the course: |
aplikovat základní vlastnosti grup na konkrétní modely |
umět rozpoznat strukturu okruhu a tělesa |
řešit jednoduché úlohy v aritmetikách modulo k |
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 |
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: |
Lecture supplemented with a discussion |
Skills - the following training methods are used to achieve the required skills: |
Lecture supplemented with a discussion |
Competences - the following training methods are used to achieve the required competences: |
Lecture supplemented with a discussion |
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