Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 1 / Fall Semester | ||||
| Level of Course | 2nd Cycle Degree Programme | ||||
| Type of Course | Optional | ||||
| Department | MATHEMATICS | ||||
| Pre-requisities and Co-requisites | None | ||||
| Mode of Delivery | Face to Face | ||||
| Teaching Period | 14 Weeks | ||||
| Name of Lecturer | SEZER SORGUN (ssorgun@nevsehir.edu.tr) | ||||
| Name of Lecturer(s) | |||||
| Language of Instruction | Turkish | ||||
| Work Placement(s) | None | ||||
| Objectives of the Course | |||||
| To describe the module structures on non-commutative rings | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Can explain the modul structures |
PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other. |
Examination |
| LO-2 | Can define Artinian ve Noethernian moduls |
PO-1 Fundamental theorems of about some sub-theories of Analysis, Applied Mathematics, Geometry, and Algebra can apply to new problems. PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other. PO-16 Ability to use the approaches and knowledge of other disciplines in Mathematics. |
Examination |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| Rings,Modules and submodules, Module homomorphisms, Categories of modules and exact sequences,Series of modules: Modules of finite composition lenght | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Rings | Teaching |
| 2 | Modules and submodules | Teaching |
| 3 | Module homomorphisms | Teaching |
| 4 | Categories of modules and exact sequences | Teaching |
| 5 | Direct summands | Teaching |
| 6 | Direct sums and products of modules | Teaching |
| 7 | Generating and cogenerating. | Teaching |
| 8 | mid-term exam | |
| 9 | Simple and semisimple modules | Teaching |
| 10 | Finitely generated modules and chain conditions | Teaching |
| 11 | Series of modules: Modules of finite composition lenght | Teaching |
| 12 | Indecomposable decompositions of modules | Teaching |
| 13 | Noetherian and Artinian modules | Teaching |
| 14 | Noetherian and Artinian modules | Teaching |
| 15 | Noetherian and Artinian rings | Teaching |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Second Edition, 13, Springer-Verlag, New York, 1992. | |
| 2 | A. Facchini, Module Theory. Endomorphism rings and direct sum decompositions in some classes of modules, Progress in Math. 167, Birkhauser Verlag, Basel, 1998. | |
| Required Course instruments and materials | ||
| Lecture books | ||
| Assessment Methods | |||
| Type of Assessment | Week | Hours | Weight(%) |
| mid-term exam | 8 | 2 | 30 |
| Other assessment methods | |||
| 1.Oral Examination | |||
| 2.Quiz | |||
| 3.Laboratory exam | |||
| 4.Presentation | |||
| 5.Report | |||
| 6.Workshop | |||
| 7.Performance Project | 7 | 3 | 10 |
| 8.Term Paper | 7 | 3 | 10 |
| 9.Project | |||
| final exam | 16 | 2 | 50 |
| Student Work Load | |||
| Type of Work | Weekly Hours | Number of Weeks | Work Load |
| Weekly Course Hours (Theoretical+Practice) | 3 | 14 | 42 |
| Outside Class | |||
| a) Reading | 2 | 14 | 28 |
| b) Search in internet/Library | 2 | 14 | 28 |
| c) Performance Project | 3 | 7 | 21 |
| d) Prepare a workshop/Presentation/Report | 0 | ||
| e) Term paper/Project | 3 | 7 | 21 |
| Oral Examination | 0 | ||
| Quiz | 0 | ||
| Laboratory exam | 0 | ||
| Own study for mid-term exam | 3 | 8 | 24 |
| mid-term exam | 2 | 1 | 2 |
| Own study for final exam | 3 | 8 | 24 |
| final exam | 2 | 1 | 2 |
| 0 | |||
| 0 | |||
| Total work load; | 192 | ||