Course detail

Groups and Rings

FSI-SG0Acad. year: 2022/2023

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

Mode of study

Not applicable.

Guarantor

doc. RNDr. Miroslav Kureš, Ph.D.

Department

Institute of Mathematics (ÚM)

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

Co-requisites

Not applicable.

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

Course curriculum

Not applicable.

Work placements

Not applicable.

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

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

G. Bini and F. Flamini, Finite Commutative Rings and Their Applications, Springer 2002
M.F. Atiyah and I.G. Macdonald, Introduction To Commutative Algebra, Addison-Wesley series in mathematics, Verlag Sarat Book House, 1996
O. Bogopolski, Introduction to Group Theory, European Mathematical Society 2008

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme B-FIN-P Bachelor's 2 year of study, winter semester, elective
  • Programme B-MAI-P Bachelor's 2 year of study, winter semester, elective

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. RNDr. Miroslav Kureš, Ph.D.

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