Course detail
Groups and Rings
FSI-SG0 Acad. year: 2021/2022 Winter semester
In the course Groups and rings, students are familiarised with selected topics of algebra. The acquired knowledge is a starting point not only for further study of algebra and other mathematical disciplines, but also a necessary assumption for a use of algebraic methods in a practical solving of number of problems.
Supervisor
Department
Learning outcomes of the course unit
The course makes access to mastering in a wide range of results of algebra.
Prerequisites
Linear algebra, general algebra
Planned learning activities and teaching methods
The course is taught through lectures explaining the basic principles and theory of the discipline.
Assesment methods and criteria linked to learning outcomes
Course credit: the attendance, satisfactory solutions of homeworks
Language of instruction
Czech
Aims
Students will be made familiar with advanced algebra, in particular group theory and ring theory.
Specification of controlled education, way of implementation and compensation for absences
Lectures: recommended
The study programmes with the given course
Programme B-MAI-P: Mathematical Engineering, Bachelor's
branch ---: no specialisation, 2 credits, elective
Programme B-FIN-P: Physical Engineering and Nanotechnology, Bachelor's
branch ---: no specialisation, 2 credits, elective
Type of course unit
Lecture
26 hours, optionally
Teacher / Lecturer
Syllabus
1. Groups, subgroups, factor groups
2. Group homomorphisms, group actions on a set, group products
3. Topological, Lie and algebraic groups
4. Jets of mappings, jet groups
5. Rings and ideals
6. Euclidean rings, PID and UFD
7. Monoid a group rings
8. Gradede rings, R-algebras
9. Polynomials and polynomial morphisms
10. Modules and representations
11. Finite group and rings
12. Quaternionic algebras
13. Reserve – the topic to be specified