Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 1 / Spring 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 some special module structures on non-commutative rings | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Can grasp some special rings |
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. |
Examination |
| LO-2 | To develop some proof techniques over injective and projective modules |
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-13 Ability to use mathematical knowledge in technology. PO-15 To apply mathematical principles to real world problems. PO-17 Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary. |
Examination |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| Free Modules, Projective modules, Injective modules, Tensor product, Radical and socle of a module, CS, C2 and C3 modules | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Free Modules | Teaching |
| 2 | Projective modules | Teaching |
| 3 | Projective modules | Teaching |
| 4 | Injective modules | Teaching |
| 5 | Injective modules | Teaching |
| 6 | Tensor product | Teaching |
| 7 | Flat Modules | Teaching |
| 8 | mid-term exam | |
| 9 | Radical and socle of a module | Teaching |
| 10 | Radical and socle of a module | Teaching |
| 11 | Essential and small submodule | Teaching |
| 12 | Essential and small submodule | Teaching |
| 13 | CS, C2 and C3 modules | Teaching |
| 14 | Lifting, D2 and D3 modules | Teaching |
| 15 | semiperfect modules | 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 | 14 | 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 | ||