MB008 Algebra I

Faculty of Informatics
Autumn 2012
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
Fri 14:00–15:50 G101
Prerequisites
MB005 Foundations of mathematics || MB101 Linear models
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 9 fields of study the course is directly associated with, display
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
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
The course is also listed under the following terms Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011.
  • Enrolment Statistics (recent)
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