470-2204/03 – Algebra (ALG)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantorRNDr. Pavel Jahoda, Ph.D.Subject version guarantordoc. Mgr. Petr Kovář, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFEIIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
JAH02 RNDr. Pavel Jahoda, Ph.D.
KOV16 doc. Mgr. Petr Kovář, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time Credit and Examination 10+10

Subject aims expressed by acquired skills and competences

After passing the course the student will be familiar with the definitions of basic concepts selected theory of algebraic structures and relationships between them. He will understand their significance and will be able to take advantage of their knowledge to solve simple algebraic structures theory tasks. He will also understand the importance of these concepts for the solution of the selected application roles, so that he could formulate a practical role in the language of group theory, solve the problem using theory and tools to interpret the outcome in the context of the original task.

Teaching methods



Selected topics of general algebra constitute content of course Algebra. Possibilities of using this knowledges to solve some practical problems are demonstrated here. Students have the opportunity to obtain basic familiarity with mathematical apparatus, which stands behind the above mentioned applications. So they can understand how these applications work in practice.

Compulsory literature:

J. GALLIAN: Contemporary Abstract Algebra, Cengage Learning; 8 edition (2012), ISBN13 978-1133599708.

Recommended literature:

J. Gallian, Contemporary Abstract Algebra, Cengage Learning; 8 edition (2012), ISBN13 978-1133599708. LANG, S.: Undergraduate Algebra, Springer, 1990, ISBN 0-387-97279-X. GALLIAN, J.: Contemporary Abstract Algebra, Houghton Mifflin, Boston 2002, ISBN 0-618-122141

Way of continuous check of knowledge in the course of semester

Midterm test and a final exam.


Other requirements

The student attending the course of Algebra is expected to be of decent behavior, to be attentive at the lectures and exercises and we expect his busy preparation for the exam.


Subject has no prerequisities.


Subject has no co-requisities.

Subject syllabus:

Lectures 1) introduction to the group theory: symmetry and dihedral groups 2) group: definition, basic properties 3) finite groups and subgroups, examples 4) cyclic groups, classification 5) group of permutations, definitions, cycles, properties and use 6) normal subgroups and Lagrange's theorem 7) factor groups 8) homomorphisms of groups, definitions, examples 9) isomorfisms: motivation, properties, Cayley's theorem 10) direct product of groups, definitions, examples, applications 11) rings and fields: definitions, finite and infinite examples, applications 12) fields, algebraic extensions, examples, applications 13) vector spaces: definition and examples, subspaces, linear independence Cvičení: 1) examples of dihedral groups, geometric meaning, examples 2) examples of groups, verification of the axioms of groups 3) subgroups, examples, design and verification 4) cyclic groups, examples, properties, verification 5) group of permutations, cycles, solving the practical examples 6) factorisation the group by its subgroup 7) examples of factor groups, construction and verification 8) homomorfisms of groups, definitions, examples 9) isomorfisms, examples and counterexamples, verification of axioms 10) direct product of groups, examples 11) homomorfisms og groups 12) rings and fields: examples, verification 13) vector spaces: finite and infinite examples, verification of linear independence

Conditions for subject completion

Part-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30  15
        Examination Examination 70  35
Mandatory attendence parzicipation: participation at all exercises is obligatory, absence of 20% can be excused participation at all lectures is expected

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Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2020/2021 (B0541A170008) Computational and Applied Mathematics AM P Czech Ostrava 3 Compulsory study plan
2020/2021 (B0541A170008) Computational and Applied Mathematics AM K Czech Ostrava 3 Compulsory study plan
2019/2020 (B0541A170008) Computational and Applied Mathematics AM P Czech Ostrava 3 Compulsory study plan
2019/2020 (B0541A170008) Computational and Applied Mathematics AM K Czech Ostrava 3 Compulsory study plan

Occurrence in special blocks

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