Course: Introduction to Group Theory

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Course title Introduction to Group Theory
Course code UMKM/PUTG
Organizational form of instruction Lecture + Lesson
Level of course not specified
Year of study not specified
Semester Winter
Number of ECTS credits 2
Language of instruction Czech
Status of course unspecified
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Seibert Jaroslav, doc. RNDr. CSc.
  • Seinerová Kateřina, Ing.
Course content
Cartesian product of two sets. Relation and its characteristics. Graphics processing. Algebraic structures with one operation. Characteristics of operations. Magma (or grupoid), semigroup, group. Abelian group. Algebraic structures with two operations (circle and solid). Examples of algebraic structures. Permutations. Eclipsing motions. Groups in certain situations in the practice.

Learning activities and teaching methods
Methods of individual activities, Projection, Skills training
Learning outcomes
The course acquaints the students with basic terms and applications of the group theory. The aim of the course is to strengthen reasoning of the students, their ability in the analysis of mathematical problems as well as the ability in structuring the concrete situations.
The course intenzifies ligical thinking ant forming of the competence of mathematical analysis of a given problem. An indispensable part is also the competence of partition of a given situation into particular components.
Prerequisites
Basic knowledge of mathematical logic, linear algebra and mathematical analysis (in extent of the first year of university study)

Assessment methods and criteria
Written examination, Discussion, Systematic monitoring

The assignment is granted upon passing the final written test.
Recommended literature
  • CHAJDA, I. Úvod do algebry (grupoidy a grupy). Olomouc, 2005.
  • MAC LANE,S., BIRKHOFF, G. Algebra. Alfa, 1974.
  • MAREŠ, J. Algebra (Úvod do obecné algebry). ČVUT Praha, 1999.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester