PdF:MA0003 Algebra 1 - Course Information
MA0003 Algebra 1
Faculty of EducationSpring 2019
- Extent and Intensity
- 2/2/0. 5 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- Mgr. Jiří Janda, Ph.D. (seminar tutor)
RNDr. Břetislav Fajmon, Ph.D. (lecturer)
Mgr. Helena Durnová, Ph.D. (seminar tutor) - Guaranteed by
- RNDr. Břetislav Fajmon, Ph.D.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education - Timetable
- Mon 17:00–18:50 učebna 35
- Timetable of Seminar Groups:
MA0003/02: Thu 11:00–12:50 učebna 6, J. Janda
MA0003/03: Thu 8:00–9:50 učebna 32, J. Janda - Prerequisites
- The subject is aimed at acquiring knowledge and skills in theory of binary algebraic operations, algebraic structures and their morphisms. Getting acquainted with the theory of cyclic groups and factoring structures forms an integral part. THE PREREQUISITES ARE GOOD SKILLS IN THE SUBJECT "FOUNDATIONS OF MATHEMATICS" (MA0001).
- 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
- Mathematics for Education (programme PdF, B-SPE)
- Course objectives
- At the end of the course the SS will be able to understand and explain the concepts of and solve problems in the following areas: binary algebraic operations on a set, and their properties. Algebraic structures with one operation, their substructures and homomorphisms. Algebraic structures with two operations, their substructures and homomorphisms. Cyclic groups. Factoring structures (generating partition, normal subgroup, quotient group, left and right cosets for a subgroup, cosets for an ideal, quotient ring.
- Learning outcomes
- Po absolvování kursu budou studenti a) mít znalosti základních pojmů v teorii aritmetických operací, jako je sčítání, násobení, průnik, sjednocení, průsek, spojení, sečítání a násobení zbytkových tříd celých čísel; b) mít dovednosti při řešení algebraických rovnic v různých částech matematiky; c) znát důkazové metody a metody matematického usuzování pro některé vlastnosti matematických operací; d) budou seznámeni s osnovami výuky matematiky v 6. a 7 . třídě ZŠ.
- Syllabus
- 1. The congruence relation for integers, remainder 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
- Teaching methods
- Teaching methods chosen will reflect the contents of the subject and the level of students as newcomers to the university.
- Assessment methods
- Written and oral exam.
- Language of instruction
- Czech
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
- Enrolment Statistics (Spring 2019, recent)
- Permalink: https://is.muni.cz/course/ped/spring2019/MA0003