456-0905/01 – Theory of Relational and Algebraic Structures (TRAS)

Gurantor departmentDepartment of Computer ScienceCredits10
Subject guarantorprof. RNDr. Václav Snášel, CSc.Subject version guarantorprof. RNDr. Václav Snášel, CSc.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction1997/1998Year of cancellation2009/2010
Intended for the facultiesFEIIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
SNA57 prof. RNDr. Václav Snášel, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+0
Part-time Credit and Examination 3+0

Subject aims expressed by acquired skills and competences

Teaching methods

Summary

The course deals with fundamentals of system theory and modern algebra. It covers the following main topics: general relational systems, mapping, equivalence relation, ordering relation, general algebraic systems, morphisms, congruence relation and quotient algebras, grupoids, semigroups, monoids, groups, lattices, Boolean lattices, rings, sigma algebras and abstract data types.

Compulsory literature:

Recommended literature:

Way of continuous check of knowledge in the course of semester

E-learning

Other requirements

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Přednášky: Obecný pojem relačního a algebraického systému. Relace, operace a jejich signatury. Typy relací, operace s relacemi. Korespondence. Relace typu zobrazení. Elementární vlastnosti a základní typy homogenních binárních relací. Kvaziuspořádání. Relace typu uspořádání. Relace typu ekvivalence, rozklady množin, faktorová množina. Direktní součiny relací. Uzávěry relací. Souvislost teorie grafů a teorie relací. Obecný pojem algebry. Morfismy algeber, kongruence na algebrách, direktní součiny algeber. Algebry s jedinou základní binární operací: grupoidy, pologrupy, monoidy, grupy, Abelovy grupy. Elementy teorie grup. Struktura grup a reprezentace grup. Algebry se dvěma základními binárními duálními operacemi: svazy, úplné svazy, distributivní a komplementární svazy, Booleovy svazy /algebry/. Elementy teorie Booleových algeber. Reprezentace Booleových algeber, souvislost s teorii množin a výrokovou logikou. Algebry se dvěma základními neduálními operacemi: okruhy, obory integrity, tělesa, pole. Vícedruhové /heterogenní/ algebry. Abstraktní datové typy a jejich algebraická specifikace.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester, validity until: 2012/2013 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Exercises evaluation and Examination Credit and Examination 100 (145) 51 3
        Examination Examination 100  0 3
        Exercises evaluation Credit 45  0 3
Mandatory attendence participation:

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Conditions for subject completion and attendance at the exercises within ISP:

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Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2009/2010 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2009/2010 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2646) Information Technology K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2007/2008 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2006/2007 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2005/2006 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction

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