MV008 Algebra I

Faculty of Informatics
Autumn 2021
Extent and Intensity
2/2/0. 3 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Michal Kunc, Ph.D. (lecturer)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor)
Mgr. Radka Penčevová (seminar tutor)
Mgr. Pavel Francírek, Ph.D. (assistant)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Computer Science – Faculty of Informatics
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 15. 9. to Wed 15. 12. Wed 12:00–13:50 D3
  • Timetable of Seminar Groups:
MV008/01: Tue 14. 9. to Tue 14. 12. Tue 18:00–19:50 A320, O. Klíma
MV008/02: Mon 13. 9. to Mon 13. 12. Mon 10:00–11:50 A320, O. Klíma
MV008/03: Mon 13. 9. to Mon 13. 12. Mon 10:00–11:50 B204, M. Kunc
Prerequisites (in Czech)
( MB005 Foundations of mathematics || MB101 Mathematics I || MB201 Linear models B || MB151 Linear models ) && ! MB008 Algebra I
Znalost základů teorie čísel v rozsahu předmětu MB154.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 13 fields of study the course is directly associated with, display
Course objectives
The aim of the course is to become familiar with basic algebraic terminology, demonstrated on monoids, groups and rings, and with its usage for instance in modular arithmetics or for calculations with permutations and numbers.
Learning outcomes
After passing the course, students will be able to: use the basic notions of the theory of monoids, groups and rings; define and understand basic properties of these structures; verify simple algebraic statements; apply theoretical results to algorithmic calculations with numbers, mappings and polynomials.
Syllabus
  • Semigroups: monoids, subsemigroups and submonoids, homomorphisms and isomorphisms, Cayley's representation, transition monoids of automata, direct products of semigroups, invertible elements.
  • Groups: basic properties, subgroups, homomorphisms and isomorphisms, cyclic groups, Cayley's representation, direct products of groups, cosets of a subgroup, Lagrange's theorem, normal subgroups, quotient groups.
  • Polynomials: polynomials over complex, real, rational and integer numbers, polynomials over residue classes, divisibility, irreducible polynomials, roots, minimal polynomials of numbers.
  • Rings: basic properties, subrings, homomorphisms and isomorphisms, direct products of rings, integral domains, fields, fields of fractions, divisibility, polynomials over a field, ideals, quotient rings, field extensions, finite fields.
Literature
  • ROSICKÝ, J. Algebra, grupy a okruhy. 3rd ed. Brno: Masarykova univerzita, 2000, 140 pp. ISBN 80-210-2303-1. info
  • PROCHÁZKA, Ladislav. Algebra. 1. vyd. Praha: Academia, 1990, 560 s. info
Teaching methods
Lectures: theoretical explanation. Exercises: solving problems with the aim of understanding basic concepts and theorems.
Assessment methods
The examination consists of a compulsory written part (pass mark 50%) and an optional oral part. The requirements will be adjusted according to the epidemiological situation and current restrictions.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
General note: Předmět byl dříve vypisován pod kódem MB008.
The course is also listed under the following terms Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2021, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2021/MV008