Nevşehir Hacı Bektaş Veli University Course Catalogue
|
|||||
| Year/Semester of Study | 1 / Fall Semester | ||||
| Level of Course | 3rd Cycle Degree Programme | ||||
| Type of Course | Optional | ||||
| Department | MATHEMATICS (DOCTORATE DEGREE) | ||||
| 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 teach advanced algebraic topics to be enough to do research. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Can obtain scientific knowledge and study as independent. |
PO-1 Students can design an original issue and explore new, different and / or comprehend complex issues. |
Performance Project Term Paper |
| LO-2 | Can know advanced topics in rings in research level. |
PO-3 Students will be dominated by current issues in mathematics. |
Examination |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
|||
| Course Contents | ||
| Rings and Subrings, Concept of Ideal, Quotient Rings, Ring Homomorphisms and Isomorphism Theorems, Prime and Maximal Ideals, The Field of Quotients of an Integral Domain, Prime and semiprime rings, Polynomial rings, Polynomial rings with multi indeterminates | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Rings: some specific examples of rings. | Topic and Applications |
| 2 | Subrings | Topic and Applications |
| 3 | Ideals | Topic and Applications |
| 4 | Quotient Rings | Topic and Applications |
| 5 | Ring homomorphisms and isomorphism theorems | Topic and Applications |
| 6 | Prime and maximal ideals | Topic and Applications |
| 7 | Principal ideal domain | Topic and Applications |
| 8 | mid-term exam | |
| 9 | The Field of Quotients of an Integral Domain | Topic and Applications |
| 10 | Simple and semisimple rings | Topic and Applications |
| 11 | Prime and semiprime rings | Topic and Applications |
| 12 | Polynomial rings | Topic and Applications |
| 13 | Polynomial rings | Topic and Applications |
| 14 | Polynomial rings with multi indeterminates | Topic and Applications |
| 15 | Polynomial rings with multi indeterminates | Topic and Applications |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | 1-Taşçı, D., (2008), Soyut Cebir, Alp yayınları | |
| 2 | 2- Goldstein, I. N., (1973) Abstract Algebra, Prentice Hall, New York | |
| 3 | 3- Passman, D.S., (2004) A course in Ring Theory, AMS Chelsea Publishing | |
| 4 | 4-Fuller F.W., Anderson R., (1974) Rings and Categories of Modules, Springer-Verlag, New York | |
| Required Course instruments and materials | ||
| The books of lecture. | ||
| 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 | 2 | 10 |
| 8.Term Paper | 14 | 2 | 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 | 8 | 24 |
| d) Prepare a workshop/Presentation/Report | 0 | ||
| e) Term paper/Project | 3 | 8 | 24 |
| Oral Examination | 0 | ||
| Quiz | 0 | ||
| Laboratory exam | 0 | ||
| Own study for mid-term exam | 3 | 7 | 21 |
| mid-term exam | 2 | 1 | 2 |
| Own study for final exam | 3 | 7 | 21 |
| final exam | 2 | 1 | 2 |
| 0 | |||
| 0 | |||
| Total work load; | 192 | ||