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| MAT4016 | Module 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 | | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Funda KARAÇAL | | Co-Lecturer | Prof. Dr. Sultan Yamak, Doç. Dr. Gül Deniz Çaylı | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | This course aims to introduce the concepts and algebraic structures related to ring and module theory and to give examples. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | The students will learn the basic concepts of module theory. | 1 - 3 - 5 | 1, | | LO - 2 : | The students will stay on top of homomorphisms. | 1 - 3 - 5 | 1, | | LO - 3 : | The students will learn the basic properties of free modules and vector spaces. | 1 - 3 - 5 | 1, | | LO - 4 : | The students will stay on top of the specific modules. | 1 - 3 - 5 | 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 | | |
| Modules, submodules, factor modules, module homomorphisms, free modules, finitely generated modules, cyclic modules, irreducible modules, non-separable modules, semi-simple modules, Artinian and Noetherian modules. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Fundamental concepts | | | Week 2 | Modules and submodules | | | Week 3 | The intersection and sum of submodules | | | Week 4 | Modules generated by a set | | | Week 5 | Homomorphisms of modules and factor modules | | | Week 6 | Properties of homomorphisms | | | Week 7 | Free modules | | | Week 8 | Finitely generated modules | | | Week 9 | Mid-term exam | | | Week 10 | Cyclic modules | | | Week 11 | Simple modules | | | Week 12 | Maximal and minimal submodules | | | Week 13 | Semi-simple modules | | | Week 14 | Properties of semi-simple modules | | | Week 15 | Artinian and Noetherian modules | | | Week 16 | End-of-term exam | | | |
| 1 | Kasch, F. 1982; Modules and Rings, Academic Press, London | | | |
| 1 | Hungerdford, T. W. 1974, Algebra, Springer-Verlag, NewYork | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 19/04/2024 | 2 | 50 | | End-of-term exam | 16 | 04/06/2024 | 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 | 4 | 14 | 56 | | Sınıf dışı çalışma | 6 | 14 | 84 | | Arasınav için hazırlık | 4 | 5 | 20 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 4 | 4 | 16 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 180 |
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