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| MAT3007 | Abstract Algebra | 4+2+0 | ECTS:6 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures and 2 hours of practicals per week | | Lecturer | Doç. Dr. Gül Deniz ÇAYLI | | Co-Lecturer | PROF. DR. Sultan YAMAK, | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | This course aims to teach students the basic concepts of Abstract Algebra. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | The students will be able to learn the concepts of group, normal subgroup, and quotient group.
| | 1, | | LO - 2 : | The students will be able to examine the structure of private groups. | | 1, | | LO - 3 : | The students will be able to introduce Euclidean regions, principal ideal regions, and unique factorization domains. | | 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), LO : Learning Outcome | | |
| Groups, Subgroups and Normal subgroups, Cyclic groups, Lagrange's Theorem, Group Homomorphisms, Group isomorphic Theorems, Rings, Factor Rings, Ring Homomorphisms, Ring Isomorphism Theorems, Prime and Maximal Ideals, Completeness Regions, Fields, Fraction Objects, Euclidian Regions, Principal Ideal Region, One kind of fragmentation regions. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Groups and Subgroups | | | Week 2 | Cyclic Groups, Finite Groups | | | Week 3 | Normal Subgroups, Quotient Groups | | | Week 4 | Lagrange's Theorem | | | Week 5 | Group Homomorphisms | | | Week 6 | Ring Theory | | | Week 7 | Subrings and Ideals | | | Week 8 | Factor Rings and Ring Homomorphisms | | | Week 9 | Midterm | | | Week 10 | Ring Isomorphisms | | | Week 11 | Prime and Maximal Ideals | | | Week 12 | Ring of Polynomials | | | Week 13 | Principal Ideal Domain | | | Week 14 | Euclidean Domain | | | Week 15 | Finite Fields | | | Week 16 | General Review of Topics | | | |
| 1 | Hungerford, T.W., Algebra, Springer, 1974. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 20-28/11/2021 | 2 saat | 50 | | End-of-term exam | 17 | 10-23/01/2022 | 2 saat | 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 | 6 | 14 | 84 | | Sınıf dışı çalışma | 4 | 14 | 56 | | Laboratuar çalışması | 0 | 0 | 0 | | Arasınav için hazırlık | 4 | 3 | 12 | | Arasınav | 2 | 1 | 2 | | Uygulama | 0 | 0 | 0 | | Klinik Uygulama | 0 | 0 | 0 | | Ödev | 0 | 0 | 0 | | Proje | 0 | 0 | 0 | | Kısa sınav | 0 | 0 | 0 | | Dönem sonu sınavı için hazırlık | 4 | 2 | 8 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 0 | 0 | 0 | | Diğer 2 | 0 | 0 | 0 | | Total work load | | | 164 |
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