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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 | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Prof. Dr. Sultan YAMAK | | Co-Lecturer | Assoc. Prof. Dr. Osman Kazancı | | 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. | 1 - 2 | 1,3, | | PO - 2 : | be introduced to the basic techniques of module theory | 2 - 3 | 1,3, | | PO - 3 : | apply the theory to simple problems and interpret results. | 1 - 4 | 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), 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 | Funxctorial Properties of Hom | | | Week 8 | Mid-term exam | | | Week 9 | Exact Sequences | | | Week 10 | Direct product, 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 | 16/4/2024 | 2 | 20 | | In-term studies (second mid-term exam) | 12 | 14/5/2024 | 2 | 30 | | End-of-term exam | 16 | 06/4/2024 | 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 | 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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