Group Theory
Faculteit  Science and Engineering 
Jaar  2022/23 
Vakcode  WBMA00505 
Vaknaam  Group Theory 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester I a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Group Theory  
Leerdoelen  At the end of the course, the student is able to: 1. have a firm knowledge of definitions of and relations between basic notions and structures in abstract group theory, combined with an ability to recognize (a necessity of the use of) such concepts. 2. follow and reproduce the proofs which are given during the lectures. 3. design their own proofs of hypotheses which are offered in exercises or which are elaborated individually by a student. 4. apply this knowledge to the calculation of mathematical properties of the structures within this course. 

Omschrijving  Abstract groups are one of the basic concepts in linear algebra but they are also used, e.g., in cryptography in the context of decomposition of large numbers into prime factors. However, the notion of a group is essential in almost all branches of abstract mathematics. It also has many applications in fundamental physics, where groups arise in the context of symmetry or invariance of models for elementary particles. The crystallographic groups are of interest in chemistry, physical chemistry, and solid state physics. Regarding applications in physics, It must be noted that group theory is not the same as their representation theory, which is a separate subject. Besides giving students a solid background in the theory of groups and how to apply it to solve specific problems, the aim of this course is to develop the students' ability to design their own rigorous proofs of abstract statements. 

Uren per week  
Onderwijsvorm  Hoorcollege (LC), Opdracht (ASM), Werkcollege (T)  
Toetsvorm 
Opdracht (AST), Schriftelijk tentamen (WE), Tussentoets (IT)
(The final grade is determined by the exam grade E, the average homework grade H and the average quiz grade Q. Specifically, the grade is Max(E, 0.85*E + 0.15*H, 0.75*E + 0.15*H + 0.1*Q). A student fails the course if this is less than 5.5, otherwise they pass.) 

Vaksoort  bachelor  
Coördinator  P. Kilicer, PhD.  
Docent(en)  P. Kilicer, PhD. , M.W. Lüdtke, PhD.  
Verplichte literatuur 


Entreevoorwaarden  The course assumes knowledge from Linear Algebra.  
Opmerkingen  The course prepares for the courses Algebraic Structures, Advanced Algebraic Structures, Security & Coding and Caput Algebra and Geometry.  
Opgenomen in 
