    Course module   NWIWP030  Category   PB (Propaedeutic)  Language of instruction   Dutch  Offered by   Radboud University; Faculty of Science; Wiskunde, Natuur en Sterrenkunde;  Lecturer(s)     Academic year   2023   Period   KW3KW4  (29/01/2024 to 31/08/2024) 
 Starting block   KW3  
 Course mode   fulltime  
 Remarks     Registration using OSIRIS   Yes  Course open to students from other faculties   Yes  Preregistration   No  Waiting list   No  Placement procedure    
     
 The student has a thorough knowledge of the basic concepts of group theory.
 The student is able to work with the abstract axioms and to deduce from this simple conclusions about the structure of groups.
 The student knows a number of examples of groups and homomorphisms and is able to apply the abstract results in the context of these examples.
 The student is able to apply the theory of actions of groups; he/she understands the relationship between orbits and cosets of a stabilizer subgroup. He / she is able to apply this, e.g. to combinatorial problems.
 The student is able to use the theory of quotients, both in an abstract context and in practical examples. In particular, this involves the uses of the homomorphism and isomorphism theorems.
 The student knows some basic concepts and results of group theory, is able to recognize these in examples, and is able to apply the abstract result to the analysis of new examples. These include concepts like subgroup, normal subgroup, center, commutator subgroup, kernel and image of a homomorphism, the order of an element and the theorems of Lagrange and Cauchy.



This course is intended as an introduction to group theory, one of the corner stones of modern mathematics and also essential for other disciplines. Initially the emphasis will be on the basic definitions and concepts like group, homomorphism, subgroup and normal subgroup. At the same time we will see examples such as modular arithmetic, permutations and dihedral groups. Then we will treat quotient groups and group actions. Finally we will derive some fundamental structure theorems.
Instructional Modes

   Written exam. Homework exercises account for a small part of the grade. 
 


   Required materialsReaderDutch lecture notes "Groepentheorie", available on Blackboard 


Instructional modesTestsTentamenTest weight   1 
Test type   Exam 
Opportunities   Block KW4, Block KW4 


  
 
 