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Main menu for Browse IS/STAG
Courses found, count: 1
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Abbreviation unit / Course abbreviation |
Title |
Variant |
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KAG
/
ALG4
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Algebra 4
Show course
Algebra 4
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2024/2025
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Course info
KAG / ALG4
:
Course description
Department/Unit / Abbreviation
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KAG
/
ALG4
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Academic Year
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2024/2025
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Academic Year
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2024/2025
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Title
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Algebra 4
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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,
3
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
|
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, English
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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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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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not determined
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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, English
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Internship duration
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0
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No. of hours of on-premise lessons |
10
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Evaluation scale |
A|B|C|D|E|F |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
Yes
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Fundamental course |
No
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Fundamental theoretical course |
Yes
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Evaluation scale |
A|B|C|D|E|F |
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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KAG/MALG4
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Prerequisite courses
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KAG/ALG1
and KAG/ALG2
and KAG/MALG3
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Meet all prerequisites before registering
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NO
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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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KAG/ALG5, KAG/SZZMT, KAG/SZZZA
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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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Understand divisibility theory in integral domains and basics of lattice theory.
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Requirements on student
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Credit: attendance at seminars, written test.
Exam: understanding of basics of divisibility theory and lattice thery, ability to prove crucial statements
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Content
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1. Divisibility in integral domains. Units, irreducible and prime elements. Greatest common divisor, least common multiple. Ideal generated by a set, pricipal ideal domains. Euclidean domains, Gaussian domains.
2. Partially ordered sets. Mappings of partially ordered sets: monotone, antitone, isomorphic embedding, isomorphism. Distinguished elements: maximal, minimal, greatest, least. Lower and upper cone of a set, directed sets. Supremum and infimum, semilattices. The Zorn lemma.
3. Lattices: Partially ordered sets and algebras. Complete lattices, the fixed point theorem. Sublattices. Lattice homomorphisms and congruence relations. Quotient lattices, homomorphism theorem. Ideals (and filters) of lattices. Ideal generated by a set, principal ideals.
4. Modullar and distributive lattices. Complements and relative complements, Boolean lattices, generalized Boolean lattices. Correspondence between congruences and ideals. Boolean algebras.
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Activities
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Fields of study
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Studijní texty zveřejněné na stránkách katedry a osobních stánkách vyučujících (kag.upol.cz kag.upol.cz/vizitka/prijmenivyucujiciho/), zadávání a odevzdávání příkladů a prací přes IS STAG, komunikace s vyučujícím e-mailem, domluva osobních konzultací s vyučujícím
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Guarantors and lecturers
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Literature
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Basic:
Chajda. Algebra III. Teorie svazů a univerzální algebra.. UP Olomouc, 1991.
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Basic:
Hort D., Rachůnek J. Algebra1. UP Olomouc, 2003.
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Basic:
Halaš R., Chajda I. Cvičení z algebry. VUP Olomouc, 1999.
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Recommended:
Burris S., Sankappanavar H. P. A Course in Universal Algebra. Springer-Verlag, New York, 1981. ISBN 0-387-90578-2.
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Recommended:
Jukl M. Lineární algebra. Univerzita Palackého Olomouc, 2006. ISBN 80-244-1270-5.
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Recommended:
Bican, L. Lineární algebra a geometrie. Praha, Academia, 2000. ISBN 80-200-0843-8.
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Recommended:
Rachůnek J. Svazy. VUP Olomouc, 2003.
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On-line library catalogues
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Prerequisites - other information about course preconditions |
- |
Competences acquired |
Comprehension of basics of divisibility theory in integral domains and basics of lattice theory. |
Teaching methods |
- Lecture
- Dialogic Lecture (Discussion, Dialog, Brainstorming)
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Assessment methods |
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