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. 3. vyd. 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.
Listed among pre-requisites of other courses
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.
  • Enrolment Statistics (Autumn 2013, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2013/MV008