MV008 Algebra I

Faculty of Informatics
Autumn 2016
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Ondřej Klíma, Ph.D. (lecturer)
Mgr. Radka Penčevová (seminar tutor)
doc. Mgr. Michal Kunc, Ph.D. (assistant)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Tue 14:00–15:50 A318
  • Timetable of Seminar Groups:
MV008/01: Mon 12:00–13:50 A320, O. Klíma
MV008/02: Thu 18:00–19:50 A320, R. Penčevová
Prerequisites (in Czech)
( MB005 Foundations of mathematics || MB101 Linear models || MB201 Linear models B ) && ! MB008 Algebra I
Znalost základů teorie čísel v rozsahu předmětu MB104.
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
Course objectives
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
Written examination: it is necessary to get at least 50 out of 100 points.
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 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2016, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2016/MV008