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| SEC 422 | some titles from group theory | 4+0+0 | ECTS:6 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Osman KAZANCI | | Co-Lecturer | Assoc. Prof. Dr. Osman Kazancı | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | |
know the concepts of semigroup, group, normal subgroup and quotient group, know the fundemental theorems and isomorphism theorems for these structures andknow the applications of these theorems, know the concept of 'action of a group on a set' and know the applications of it, know the sylow theorems and their applications, know the concepts of normal serie, resolvable group and nilpotent group, know their basic theorems, know the applications of these theorems. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | know the concepts of semigroup, group, normal subgroup and quotient group | | | | LO - 2 : | know the isomorphism theorems and make their applications | | | | LO - 3 : | know the concept of 'action of a group on a set' and know its applications | | | | LO - 4 : | know the concept of symmetric group and its basic theorems | | | | LO - 5 : | know the sylow theorems and make their applications | | | | LO - 6 : | know the concepts of normal serie, resolvable group and nilpotent group, know their basic theorems and make the applications of these theorems | | | | 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), LO : Learning Outcome | | |
| Semigroups and groups, normal subgroups, quotient groups and isomorphism theorems, action of a group on a set, symmetric groups, sylow theorems, normal series, resolvable and nilpotent groups.
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | semigroups | | | Week 2 | groups | | | Week 3 | normal subgroups | | | Week 4 | quotient groups | | | Week 5 | isomorphism theorems | | | Week 6 | action of a group on a set | | | Week 7 | symmetric groups | | | Week 9 | sylow theorems | | | Week 10 | sylow theorems | | | Week 11 | sylow theorems | | | Week 12 | normal series | | | Week 13 | resolvable groups | | | Week 14 | nilpotent groups | | | Week 15 | nilpotent groups | | | |
| 1 | Algebra, Thomas W. Hungerford, 1974. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 10/04/2016 | 2 | 50 | | End-of-term exam | 16 | 29/05/2016 | 2,0 | 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 | 4 | 14 | 56 | | Sınıf dışı çalışma | 5 | 14 | 70 | | Arasınav için hazırlık | 9 | 1 | 9 | | Arasınav | 2 | 1 | 2 | | Kısa sınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 10 | 1 | 10 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 151 |
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