MV008 Algebra I

Faculty of Informatics
Autumn 2013
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Libor Polák, CSc. (lecturer)
doc. Mgr. Michal Kunc, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Libor Polák, CSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Thu 14:00–15:50 G124
Prerequisites
( MB005 Foundations of mathematics || MB101 Linear models || MB201 Linear models B ) && ! MB008 Algebra I
Prerequisites: MB005 Foundations of mathematics.
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 8 fields of study the course is directly associated with, display
Course objectives
After this course a student will be able to deal with the basic algebraic structures like monoids and groups and will understand calculating roots and irreducibility of polynomials. He/she will cope with an application in language theory.
Syllabus
  • Groups (permutation groups, Cayley's theorems, subgroups and normal subgroups, quotient groups, homomorphisms, products, classification of cyclic groups).
  • Polynomials over C, R, Q (multiplicity of zeros and the derivative, irreducible polynomials, Euklid's algorithm).
  • Rings (ideals, factor rings, fields, skewfields).
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
Once a week a standard lecture with a stress on motivation and examples.
Assessment methods
A written exam has tree parts: a completion of a text concerning (on advance) given theoretical issues, a calculation of a transformation monoid, and 3 tests problems where the students show the understanding the basics. It takes two hours. One half of possible points is needed for a success.
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.
Teacher's information
http://www.math.muni.cz/~polak/algebra-I.html
The course is also listed under the following terms Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2013, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2013/MV008