Course detail

Groups and Rings

FSI-SG0 Acad. year: 2022/2023 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.

Language of instruction

Czech

Number of ECTS credits

2

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

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, elective

Programme B-FIN-P: Physical Engineering and Nanotechnology, Bachelor's, 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