MA2BP_PAL1 Algebra 1

Faculty of Education
Autumn 2017
Extent and Intensity
2/0/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jaroslav Beránek, CSc. (lecturer)
Mgr. Helena Durnová, Ph.D. (lecturer)
RNDr. Břetislav Fajmon, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Jaroslav Beránek, CSc.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
Prerequisites
Anotation: The subject is aimed at acquiring basic knowledge and skills in the theory of binary algebraic operations, algebraic structures and their morphisms. An integral part is the theory of cyclic groups and factor structures.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
At the end of the course students should be able to understand and explain the following: Binary algebraic operations on a set, their properties. Algebraic structures with one operation, their substructures and homomorphisms. Algebraic structures with two operations, their substructures and homomorphisms. Cyclic groups. Factor structures (generating partition, left and right cosets for a subgroup, normal subgroup, quotient group, ideal, cosets for an ideal, quotient rings).
Syllabus
  • 1. The congruence relation for integers, quotient cosets. 2. Binary and algebraic operations and their properties, part 1. 3. Binary and algebraic operations and their properties, part 2. 4. Algebraic structures with one operation. 5. Substructures and homomorphisms of algebraic structures with one operation. 6. Algebraic structures with two operations. 7. Substructures and homomorphisms of algebraic structures with two operations. 8. Group generators, cyclic groups, part 1. 9. Group generators, cyclic groups, part 2. 10. Fundamentals of the partition structures (generating partition, the grupoid congruence). 11. Left and right cosets for a subgroup, normal subgroup. 12. Ideal, cosets for an ideal, quotient rings.
Literature
    recommended literature
  • BIRKHOFF, Garrett and Saunders MAC LANE. Prehľad modernej algebry. Translated by Štefan Znám - Jaroslav Smítal. 1. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1979, 468 s. info
    not specified
  • HORÁK, Pavel. Cvičení z algebry a teoretické aritmetiky I. 2. vyd. Brno: Masarykova univerzita, 1998, 221 s. ISBN 8021018534. info
  • HORÁK, Pavel. Algebra a teoretická aritmetika. 2. vyd. Brno: Masarykova univerzita, 1993, 145 s. ISBN 8021008164. info
  • KATRIŇÁK, Tibor. Algebra a teoretická aritmetika. 1. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1985, 349 s. info
  • Cvičení z algebry. Edited by Yvona Coufalová. Vyd. 1. Brno: UJEP Brno, 1985, 168 s. info
  • BLAŽEK, Jaroslav. Algebra a teoretická aritmetika. 1. vyd. Praha: Státní pedagogické nakladatelství, 1983, 278 s. URL info
Teaching methods
Lectures.
Assessment methods
Written test and oral exam. Required percentage of correct answers in the written test: 60 %.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
Information on completion of the course: Podmínkou pro konání zkoušky je získání zápočtu z disciplíny MA2BP_CAL1.
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/ped/autumn2017/MA2BP_PAL1