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| MATL5600 | Group Theory | 3+0+0 | ECTS:5 | | Year / Semester | Fall Semester | | Level of Course | Second Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | -- | | Co-Lecturer | Assistant Prof. Dr. Sultan YAMAK | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The purpose of the course is to give a general knowledge of group theory. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | learn the basic properties of groups | 1,2 | 1 | | PO - 2 : | learn the relationship between direct sum and direct product | 1,2 | 1 | | PO - 3 : | learn the structure finitely gererated abelian groups andbasic properties. | 1,3 | 1 | | PO - 4 : | learn the basic knowledge about the sylow theorems | 1,2 | 1 | | PO - 5 : | learn the relationship between nilpotent and solvable groups | 1,3 | 1 | | PO - 6 : | learn the jordan-hölder theorem and the charactetrizations of nilpotent and solvable groups | 1,2 | 1 | | 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 | | |
| Categories, Direct products and direct sums, Free groups, Free abelian groups, Clasification of finite groups Nilpotent and sovable groups, normal and subnormal series. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Introduction to group theory | | | Week 2 | The basic properties of groups | | | Week 3 | Categories and free objecs | | | Week 4 | Direct products and direct sums | | | Week 5 | Free groups and free products | | | Week 6 | Generators and relations | | | Week 7 | Free abelian groups | | | Week 8 | Mid-term exam | | | Week 9 | Finitely gererated abelian groups | | | Week 10 | The sylow theorems | | | Week 11 | Clasification of finite groups | | | Week 12 | Nilpotent | | | Week 13 | Sovable groups | | | Week 14 | Normal and subnormal series. | | | Week 15 | Applications | | | Week 16 | End-of-term exam | | | |
| 1 | Bhattacharya, P.B.,Jain, S.K, Nagpaul S.R, 1994, Basic Abstract Algebra, Cabbridge University Press, Second edition. | | | 2 | A First Courcse in Abstract Algebra, Addison-wesley Publishıng Company. | | | 3 | Hunderford, T.W., 1987, Algebra, Springer-verlag New York. Heidelberk Berlin | | | |
| 1 | Bayar, E., 1986, Soyut Cebir, K.T.Ü. Fen-Ed.Fak. Yayınları No: 41. Trabzon. | | | 2 | Bilhan, M., Güloğlu, İ., Koç,C., 1991, Soyut Cebir, Anadolu Üniversitesi Yayınları No:113. | | | 3 | Çallıalp, F., 2001, Örneklerle Soyut Cebir, Birsen Yayınevi, İstanbul. | | | 4 | Karakaş, H.İ., 2009, Cebir Dersleri, Tüba Yayınları, Ankara. | | | 5 | Asar, A.O., Arıkan, A., Arıkan A., 2009, Cebir, Eflatun Yayınevi, Ankara. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 8 | 11-NOV-10 | 2 | 30 | | Quiz | 13 | 08/11/2010 | 1,30 | 20 | | End-of-term exam | 16 | 07-JAN-11 | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 8 | 14 | 112 | | Arasınav için hazırlık | 12 | 1 | 12 | | Arasınav | 2 | 1 | 2 | | Uygulama | 3 | 2 | 6 | | Kısa sınav | 1.3 | 1 | 1.3 | | Dönem sonu sınavı için hazırlık | 12 | 1 | 12 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 189.3 |
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