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Course detail

Groups and Rings

Course unit code: FSI-SG0
Academic year: 2016/2017
Type of course unit: optional (voluntary)
Level of course unit: Bachelor's (1st cycle)
Year of study: 2
Semester: winter
Number of ECTS credits:
Learning outcomes of the course unit:
The course makes access to mastering in a wide range of results of algebra.
Mode of delivery:
90 % face-to-face, 10 % distance learning
Prerequisites:
Linear algebra, general algebra
Co-requisites:
Not applicable.
Recommended optional programme components:
Not applicable.
Course contents (annotation):
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.
Recommended or required reading:
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
G. Bini and F. Flamini, Finite Commutative Rings and Their Applications, Springer 2002
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
Work placements:
Not applicable.
Course curriculum:
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

Type of course unit:

Lecture: 26 hours, 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

The study programmes with the given course