NWI-WP030
Group Theory
Course infoSchedule
Course moduleNWI-WP030
Credits (ECTS)6
CategoryPB (Propaedeutic)
Language of instructionDutch
Offered byRadboud University; Faculty of Science; Wiskunde, Natuur- en Sterrenkunde;
Lecturer(s)
Contactperson for the course
dr. M.S. Solleveld
Other course modules lecturer
Coordinator
dr. M.S. Solleveld
Other course modules lecturer
Examiner
dr. M.S. Solleveld
Other course modules lecturer
Lecturer
dr. M.S. Solleveld
Other course modules lecturer
Academic year2023
Period
KW3-KW4  (29/01/2024 to 31/08/2024)
Starting block
KW3
Course mode
full-time
Remarks-
Registration using OSIRISYes
Course open to students from other facultiesYes
Pre-registrationNo
Waiting listNo
Placement procedure-
Aims
  • 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.
Content
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
Level

Presumed foreknowledge
Wiskunde B (level VWO)
Test information
Written exam. Homework exercises account for a small part of the grade.
Specifics

Required materials
Reader
Dutch lecture notes "Groepentheorie", available on Blackboard

Instructional modes
Course

Tests
Tentamen
Test weight1
Test typeExam
OpportunitiesBlock KW4, Block KW4