Information Package / Course Catalogue
Groups and Symmetry
Course Code: MTK559
Course Type: Area Elective
Couse Group: Second Cycle (Master's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 8
Objectives of the Course

The purpose of this course is to introduce students to the topics in the course content.

Course Content

Groups, cyclic and dihedral groups, finite groups, permutations, matrix groups, group action, orbit and stabiliser of a point, symmetry groups of regular polygons and regular polytopes, finite rotation groups, isometries of the Euclidean plane.

Name of Lecturer(s)
Learning Outcomes
1.Ability to define the concepts of a group
2.Ability to explain the concepts of cyclic and dihedral groups
3.Ability to explain the concept of group action
4.Ability to determine the symmetry groups of regular polygons and regular polytopes
5.Ability to explain the isometries of the Euclidean plane
Recommended or Required Reading
1.Armstrong, M.A. (1988) Groups and Symmetry, Springer
2.Farmer, D. (1996) Groups and Symmetry, American Mathematical Society
Weekly Detailed Course Contents
Week 1 - Theoretical
Groups and subgroups
Week 2 - Theoretical
Cyclic and dihedral groups
Week 3 - Theoretical
Finite groups
Week 4 - Theoretical
Permutations
Week 5 - Theoretical
Symmetric and alternating groups
Week 6 - Theoretical
Matrix groups
Week 7 - Theoretical
Group action
Week 8 - Theoretical
Orbit and stabiliser of a point, Midterm exam
Week 9 - Theoretical
Symmetry groups of regular polygons
Week 10 - Theoretical
Symmetry groups of regular polytopes
Week 11 - Theoretical
Finite rotation groups
Week 12 - Theoretical
Isometries of the Euclidean plane
Week 13 - Theoretical
Euclidean groups and Euclidean surfaces
Week 14 - Theoretical
Compact Euclidean surfaces
Assessment Methods and Criteria
Type of AssessmentCountPercent
Midterm Examination1%30
Final Examination1%70
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory140342
Individual Work140570
Midterm Examination116218
Final Examination118220
TOTAL WORKLOAD (hours)150
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
PÇ-14
PÇ-15
OÇ-1
3
4
3
4
2
3
1
2
3
OÇ-2
3
4
3
4
2
3
1
2
3
OÇ-3
3
4
3
4
2
3
1
2
3
OÇ-4
3
4
3
4
2
3
1
2
3
OÇ-5
3
4
3
4
2
3
1
2
3
Adnan Menderes University - Information Package / Course Catalogue
2026