470-2204/01 – Algebra (ALG)

Gurantor departmentDepartment of Applied MathematicsCredits4
Subject guarantorRNDr. Pavel Jahoda, Ph.D.Subject version guarantorRNDr. Pavel Jahoda, Ph.D.
Study levelundergraduate or graduateRequirementOptional
Year2Semestersummer
Study languageCzech
Year of introduction2013/2014Year 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
Combined 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

Lectures
Tutorials

Summary

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

Credit test and oral examination.

E-learning

Další požadavky na studenta

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.

Prerequisities

Subject has no prerequisities.

Co-requisities

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

Combined form (validity from: 2013/2014 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 30  15
        Examination Examination 70  36
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 2 Optional study plan
2019/2020 (B2647) Information and Communication Technology (2601R013) Telecommunication Technology P Czech Ostrava 2 Optional study plan
2019/2020 (B2647) Information and Communication Technology (2612R025) Computer Science and Technology P Czech Ostrava 2 Optional study plan
2019/2020 (B2647) Information and Communication Technology (2612R059) Mobile Technology P Czech Ostrava 2 Optional study plan
2019/2020 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 2 Optional study plan
2019/2020 (B2647) Information and Communication Technology (2601R013) Telecommunication Technology K Czech Ostrava 2 Optional study plan
2019/2020 (B2647) Information and Communication Technology (2612R025) Computer Science and Technology K Czech Ostrava 2 Optional study plan
2019/2020 (B2647) Information and Communication Technology (2612R059) Mobile Technology K Czech Ostrava 2 Optional study plan
2018/2019 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 2 Optional study plan
2018/2019 (B2647) Information and Communication Technology (2601R013) Telecommunication Technology P Czech Ostrava 2 Optional study plan
2018/2019 (B2647) Information and Communication Technology (2612R025) Computer Science and Technology P Czech Ostrava 2 Optional study plan
2018/2019 (B2647) Information and Communication Technology (2612R059) Mobile Technology P Czech Ostrava 2 Optional study plan
2018/2019 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 2 Optional study plan
2018/2019 (B2647) Information and Communication Technology (2601R013) Telecommunication Technology K Czech Ostrava 2 Optional study plan
2018/2019 (B2647) Information and Communication Technology (2612R025) Computer Science and Technology K Czech Ostrava 2 Optional study plan
2018/2019 (B2647) Information and Communication Technology (2612R059) Mobile Technology K Czech Ostrava 2 Optional study plan
2017/2018 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 2 Optional study plan
2017/2018 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 2 Optional study plan
2017/2018 (B2647) Information and Communication Technology (2601R013) Telecommunication Technology P Czech Ostrava 2 Optional study plan
2017/2018 (B2647) Information and Communication Technology (2601R013) Telecommunication Technology K Czech Ostrava 2 Optional study plan
2017/2018 (B2647) Information and Communication Technology (2612R025) Computer Science and Technology P Czech Ostrava 2 Optional study plan
2017/2018 (B2647) Information and Communication Technology (2612R025) Computer Science and Technology K Czech Ostrava 2 Optional study plan
2017/2018 (B2647) Information and Communication Technology (2612R059) Mobile Technology P Czech Ostrava 2 Optional study plan
2017/2018 (B2647) Information and Communication Technology (2612R059) Mobile Technology K Czech Ostrava 2 Optional study plan
2016/2017 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 2 Optional study plan
2016/2017 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 2 Optional study plan
2016/2017 (B2647) Information and Communication Technology (2601R013) Telecommunication Technology P Czech Ostrava 2 Optional study plan
2016/2017 (B2647) Information and Communication Technology (2601R013) Telecommunication Technology K Czech Ostrava 2 Optional study plan
2016/2017 (B2647) Information and Communication Technology (2612R025) Computer Science and Technology P Czech Ostrava 2 Optional study plan
2016/2017 (B2647) Information and Communication Technology (2612R025) Computer Science and Technology K Czech Ostrava 2 Optional study plan
2016/2017 (B2647) Information and Communication Technology (2612R059) Mobile Technology P Czech Ostrava 2 Optional study plan
2016/2017 (B2647) Information and Communication Technology (2612R059) Mobile Technology K Czech Ostrava 2 Optional study plan
2015/2016 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 2 Optional study plan
2015/2016 (B2647) Information and Communication Technology (2601R013) Telecommunication Technology P Czech Ostrava 2 Optional study plan
2015/2016 (B2647) Information and Communication Technology (2612R025) Computer Science and Technology P Czech Ostrava 2 Optional study plan
2015/2016 (B2647) Information and Communication Technology (2612R059) Mobile Technology P Czech Ostrava 2 Optional study plan
2015/2016 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 2 Optional study plan
2015/2016 (B2647) Information and Communication Technology (2601R013) Telecommunication Technology K Czech Ostrava 2 Optional study plan
2015/2016 (B2647) Information and Communication Technology (2612R059) Mobile Technology K Czech Ostrava 2 Optional study plan
2015/2016 (B2647) Information and Communication Technology (2612R025) Computer Science and Technology K Czech Ostrava 2 Optional study plan
2014/2015 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 2 Optional study plan
2014/2015 (B2647) Information and Communication Technology (2601R013) Telecommunication Technology P Czech Ostrava 2 Optional study plan
2014/2015 (B2647) Information and Communication Technology (2612R025) Computer Science and Technology P Czech Ostrava 2 Optional study plan
2014/2015 (B2647) Information and Communication Technology (2612R059) Mobile Technology P Czech Ostrava 2 Optional study plan
2014/2015 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 2 Optional study plan
2014/2015 (B2647) Information and Communication Technology (2601R013) Telecommunication Technology K Czech Ostrava 2 Optional study plan
2014/2015 (B2647) Information and Communication Technology (2612R025) Computer Science and Technology K Czech Ostrava 2 Optional study plan
2014/2015 (B2647) Information and Communication Technology (2612R059) Mobile Technology K Czech Ostrava 2 Optional study plan
2013/2014 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 2 Optional study plan
2013/2014 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 2 Optional study plan
2013/2014 (B2647) Information and Communication Technology (2601R013) Telecommunication Technology P Czech Ostrava 2 Optional study plan
2013/2014 (B2647) Information and Communication Technology (2601R013) Telecommunication Technology K Czech Ostrava 2 Optional study plan
2013/2014 (B2647) Information and Communication Technology (2612R025) Computer Science and Technology P Czech Ostrava 2 Optional study plan
2013/2014 (B2647) Information and Communication Technology (2612R025) Computer Science and Technology K Czech Ostrava 2 Optional study plan
2013/2014 (B2647) Information and Communication Technology (2612R059) Mobile Technology P Czech Ostrava 2 Optional study plan
2013/2014 (B2647) Information and Communication Technology (2612R059) Mobile Technology K Czech Ostrava 2 Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner