FI:MB008 Algebra I - Course Information

MB008 Algebra I

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)
RNDr. Václav Brožek, Ph.D. (seminar tutor)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor)

Guaranteed by

doc. RNDr. Libor Polák, CSc.
Faculty of Informatics

Timetable

Mon 14:00–15:50 A107

Prerequisites

MB005 Foundations of mathematics || MB101 Mathematics 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

• Informatics (programme FI, B-IN)
• Mathematical Informatics (programme FI, B-IN)
• Parallel and Distributed Systems (programme FI, B-IN)
• Computer Networks and Communication (programme FI, B-IN)
• Embedded Systems (programme FI, N-IN)
• Service Science, Management and Engineering (programme FI, N-AP)
• Artificial Intelligence and Natural Language Processing (programme FI, B-IN)

Course objectives

We introduce here the basic algebraic structures: monoids, groups, rings, fields and we study their properties. We pay attention to calculations with polynomials.

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.

Language of instruction

Czech

Follow-Up Courses

• MA009 Algebra II

Further comments (probably available only in Czech)

Study Materials
The course is taught annually.

Teacher's information

http://www.math.muni.cz/~polak/algebra-I.html

• Enrolment Statistics (Autumn 2009, recent)
  
• Permalink: https://is.muni.cz/course/fi/autumn2009/MB008