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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 | Face to face | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Funda KARAÇAL | | Co-Lecturer | Prof. Dr. Sultan YAMAK | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | To present the Concepts of Ring and Module theory. To provide students with the supporting knowledge necessary for ring and module theory. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | Know the basic concepts of modules. | 1,2,3,4,5,6,7,8 | 1,3 | | LO - 2 : | Have some knowledge of homomorphisms. | 1,2,3,4,5,6,7,8 | 1,3 | | LO - 3 : | Know the basic properties of Free modules and vector spaces. | 1,2,3,4,5,6,7,8 | 1,3 | | LO - 4 : | Have some knowledge of types Modules. | 1,2,3,4,5,6,7,8 | 1,3 | | 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, finite generation modules, cyclic modules, irreducible modules, non-separable modules, semisimple modules, Artinian and Noetherian modules. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Fundamental Concepts | | | Week 2 | Modules and sub modules | | | Week 3 | The intersection and sum of submodules | | | Week 4 | spans modüles by a set | | | Week 5 | homomorphisms of modules and factor modules | | | Week 6 | Properties of homomorphs | | | Week 7 | Free modules | | | Week 8 | Finite generation modules | | | Week 9 | Midterm Examination | | | Week 10 | Cyclic Modüles | | | Week 11 | simple modules | | | Week 12 | Maximal and minimal submodules | | | Week 13 | Semisimple modules | | | Week 14 | properties of Semisimple modules | | | Week 15 | properties of Semisimple modules | | | Week 16 | Artinian and Noetherian modules | | | |
| 1 | Modules and Rings, Kasch F., Academic Press, 1982 | | | |
| 1 | Algebra,Thomas V. Hungerdford, Springer,1987. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 10 | 11/04/2022 | 2 | 50 | | End-of-term exam | 16 | 16/05/2022 | 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 | 2 | 14 | 28 | | Arasınav için hazırlık | 4 | 2 | 8 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 4 | 3 | 12 | | Dönem sonu sınavı | 2 | 2 | 4 | | Total work load | | | 110 |
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