FI:MV008 Algebra I - Course Information
MV008 Algebra I
Faculty of InformaticsAutumn 2024
- 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)
Mgr. Pavel Francírek, Ph.D. (seminar tutor)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor)
Mgr. Radka Penčevová (seminar tutor) - 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
- Thu 19. 9. to Thu 12. 12. Thu 8:00–9:50 D2
- Timetable of Seminar Groups:
MV008/02: Fri 20. 9. to Fri 13. 12. Fri 8:00–9:50 B204, P. Francírek - Prerequisites (in Czech)
- MB151 Linear models
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
- Informatics (programme FI, B-INF) (2)
- Informatics in education (programme FI, B-IVV) (2)
- Programming and development (programme FI, B-PVA)
- 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
- GILBERT, William J. and W. Keith NICHOLSON. Modern algebra with applications. 2nd ed. Hoboken, N.J.: Wiley-Interscience, 2004, xvii, 330. ISBN 9780471469889. 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.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course is taught annually.
General note: Předmět byl dříve vypisován pod kódem MB008.
- Enrolment Statistics (recent)
- Permalink: https://is.muni.cz/course/fi/autumn2024/MV008