MA0003 Algebra 1

Faculty of Education
Spring 2018
Extent and Intensity
2/2/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
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
Tue 16:40–18:20 D20 učebna
  • Timetable of Seminar Groups:
MA0003/01: Thu 9:20–11:00 D16 učebna, H. Durnová
MA0003/02: Thu 13:55–15:35 D212 učebna, H. Durnová
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
Abstract
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
After the completion of the course the students will a) have knowledge of fundamental concepts in the theory of arithmetics, such as addition, product, intersection, union, infimum, supremum, operations with classes of decomposition of the set of all integers; b) have skills in solving algebraic equations in different areas of mathematics; c) know some methods of mathematical reasoning for binary operations and their properties; d) be acquainted with the syllabus of mathematics for classes 6 and 7 in Czech elementary schools.
Key topics
  • 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.
Study resources and literature
    recommended literature
  • PINTER, Charles C. A book of abstract algebra. Second edition. Mineola, New York: Dover Publications, 2010, xiv, 384. ISBN 9780486474175. info
  • HORÁK, Pavel. Cvičení z algebry a teoretické aritmetiky I. 2. vyd. Brno: Masarykova univerzita, 1998, 221 s. ISBN 8021018534. info
Approaches, practices, and methods used in teaching
Teaching methods chosen will reflect the contents of the subject and the level of students as newcomers to the university.
Method of verifying learning outcomes and course completion requirements
The final mark comprises several parts all of which must be completed: a) practical part - one or two tests; b) theoretical part - testing during the semester; c) final written test
Language of instruction
Czech
Teacher's information
Použitá literatura:
Charles C. Pinter: The Book of Abstract Algebra. Dover Publications 2010, reprint of the second edition from 1990.
Horák, P. (1998) Cvičení z algebry a teoretické aritmetiky I. (ISBN 80-210-1853-4). Brno: MU.
Horák, P. (2013) M1125 Základy matematiky - učební text Přírodovědecké fakulty MU (dostupný na internetu).
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025, Spring 2026, Spring 2027.
  • Enrolment Statistics (Spring 2018, recent)
  • Permalink: https://is.muni.cz/course/ped/spring2018/MA0003