Course detail
Groups and Rings
FSI-SG0 Acad. year: 2023/2024 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
Supervisor
Department
Entry knowledge
Linear algebra, general algebra
Rules for evaluation and completion of the course
Course credit: the attendance, satisfactory solutions of homeworks
Lectures: recommended
Aims
Students will be made familiar with advanced algebra, in particular group theory and ring theory.
The course makes access to mastering in a wide range of results of algebra.
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