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| MAT5050 | Advanced Algebra | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Second Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Prof. Dr. Sultan YAMAK | | Co-Lecturer | Assoc. Doç. Dr. Gül Deniz ÇAYLI | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The course introduces fundamental concepts of advanced algebra which are indispensable in all branches of basic sciences. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | Introduce the concept of modules and understand some of the fundamental theorems. | | | | PO - 2 : | Be introduced to the basic techniques of module theory. | | | | PO - 3 : | Apply the theory to simple problems and intepret results. | | | | 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, Functors, Products and Coproducts, Modules, Submodules, Internal Direct Sums, Factor modules and factor Rings, Generators, Cogenerators, Functorial Properties of Hom, Exact Sequences, Direct products, Direct sums, Free modules, Free and Divisible Abelian Groups, Monoid Rings |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Categories | | | Week 2 | Modules, submodules and examples | | | Week 3 | Internal direct sums | | | Week 4 | Factor modules and Factor rings | | | Week 5 | Homomorphisms of Modules and Rings | | | Week 6 | Generators and Cogenerators | | | Week 7 | Functorial Properties of Hom | | | Week 8 | Mid-term exam | | | Week 9 | Exact Sequences | | | Week 10 | Direct products, Direct sums | | | Week 11 | Free modules | | | Week 12 | Free and divisible Abelian groups | | | Week 13 | Monoid rings | | | Week 14 | Homomorphisms of direct products and sums | | | Week 15 | Exercises | | | Week 16 | End-of-term exam | | | |
| 1 | Thomas. W.Hungerford (1996)Algebra, Published by Springer-Verlag Berlin and Heidelberg GmbH & Co. K, | | | |
| 1 | Kasch, F. (1982), Modules and Ring. London Mathematical Society Monograph, 17, Academic Press, London, New York, Paris. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 12/11/2024 | 2 | 20 | | In-term studies (second mid-term exam) | 12 | 04/12/2024 | 2 | 30 | | End-of-term exam | 16 | 03/01/2025 | 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 | 6 | 14 | 84 | | Arasınav için hazırlık | 7 | 1 | 7 | | Arasınav | 4 | 2 | 8 | | Dönem sonu sınavı için hazırlık | 14 | 1 | 14 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 157 |
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