Course: Introduction to Group Theory

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Course title Introduction to Group Theory
Course code UMKM/AUTG
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 2
Language of instruction English
Status of course Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Boháčová Hana, Mgr. Ph.D.
Course content
The cartesian product of sets. Relations and their properties. Graphical processing of the exercises. Algebraic structures with one operation. Properties of the algebraic operations. Grupoid, semi-group, group. The Abel groups. Algebraic structures with two operations (ring, field). Examples of algebraic structures. Permutation. Groups in practical situations.

Learning activities and teaching methods
Methods of individual activities, Projection, Skills training
Learning outcomes
The aim of this course is to inform the students about the foundations of the group theory. It should a super-structure which gives an overview in mathematical branches and provides to find the connections and analogies.
Students should be able to do a logical analysis of problems and a partition of a given situation into particular components.
Prerequisites
The basic knowledge of mathematical logic, linear algebra and mathematical analysis (in range ussual for the first university year).

Assessment methods and criteria
Written examination, Discussion, Systematic monitoring

Assignment - passing a final written test.
Recommended literature
  • Birkhoff, G. - Mac Lane, S. Algebra. Chelsea, 1999. ISBN 0-8218-1646-2.
  • Eidelman, Yuli. Functional analysis : an introduction. Providence: American Mathematical Society, 2004. ISBN 0-8218-3646-3.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Economics and Administration Regional and Information Management (2013) Economy 3 Winter