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GRADUATE INSTITUTE of NATURAL and APPLIED SCIENCES / DEPARTMENT of MATHEMATICS
Doctorate
Course Catalog
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FBE
GRADUATE INSTITUTE of NATURAL and APPLIED SCIENCES / DEPARTMENT of MATHEMATICS / Doctorate
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MATL7380Combinatorial Group Theory3+0+0ECTS:7.5
Year / SemesterSpring Semester
Level of CourseThird Cycle
Status Elective
DepartmentDEPARTMENT of MATHEMATICS
Prerequisites and co-requisitesNone
Mode of DeliveryFace to face
Contact Hours14 weeks - 3 hours of lectures per week
LecturerProf. Dr. Bahadır Özgür GÜLER
Co-Lecturer
Language of instructionTurkish
Professional practise ( internship ) None
 
The aim of the course:
Representations of groups in terms of generators and relations
 
Programme OutcomesCTPOTOA
Upon successful completion of the course, the students will be able to :
PO - 1 : Knowing representations of groups by generators and relations
PO - 2 : Knowing how to examine a group by the graph
PO - 3 : Learning some applications of group theory to combinatorial problems
CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome

 
Contents of the Course
Symmetric, Dihedral, Permutation groups, The action of a group on a set, Applications of group action
 
Course Syllabus
 WeekSubjectRelated Notes / Files
 Week 1Definition of a group and fundamental concepts
 Week 2Symmmetric Groups
 Week 3Dihedral Groups
 Week 4Permutation groups
 Week 5The action of a group on a set
 Week 6The index of permutation groups
 Week 7Transitive action
 Week 8Imprimitive action
 Week 9Mid-exam
 Week 10Action on orbits
 Week 11An application of modular group
 Week 12Applications of congruence subgroups of modular group
 Week 13Applications of group action
 Week 14Burnside theorem
 Week 15Applications of Burnside theorem
 Week 16Final
 
Textbook / Material
1Magnus W., Karrass A., Solitar D., Combinatorial Group Theory, Dover Pub., (1976).
 
Recommended Reading
1Dixon J.D., Mortimer B., Permutation Groups, Springer(Graduate texts), (1996).
2Asar A.O., Arıkan A., Arıkan A., Cebir, Eflatun, (2010).
 
Method of Assessment
Type of assessmentWeek NoDate

Duration (hours)Weight (%)
Mid-term exam 9 2 50
End-of-term exam 16 2 50
 
Student Work Load and its Distribution
Type of workDuration (hours pw)

No of weeks / Number of activity

Hours in total per term
Yüz yüze eğitim 3 14 42
Sınıf dışı çalışma 3 14 42
Arasınav için hazırlık 10 1 10
Arasınav 2 1 2
Dönem sonu sınavı için hazırlık 10 1 10
Dönem sonu sınavı 2 1 2
Total work load108