Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 3 / Spring Semester | ||||
| Level of Course | 1st Cycle Degree Programme | ||||
| Type of Course | Compulsory | ||||
| 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) | HATİCE TOPCU, | ||||
| Language of Instruction | Turkish | ||||
| Work Placement(s) | None | ||||
| Objectives of the Course | |||||
| To teach the most general and fundamental notions about the theory of rings and fields. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Can define homomorphisms between rings. |
PO-3 Define the some models of mathematical problems, evaluate with a critical approach, analyze with theoretical and applied knowledge. |
Examination |
| LO-2 | Can understand properties of quotient fields. |
PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data. |
Examination |
| LO-3 | Can know polynomial rings and do arithmetical operations with rings. Do prime factorization. |
PO-5 Develop suitable material for a subject on a mathematical area, to use the knowledge and experience gains with different methods |
Examination |
| LO-4 | Can find prime and maximal ideal of a ring. Know field extensions, normal extensions and Galois extensions . |
PO-10 With the knowledge of foreign language required the field of mathematics, use and follow information technologies by the level of European Language Portfoy B1. |
Examination |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| Ring homomorphisms, Quotient fields, Polynomial rings, Arithmetic in rings, Prime factorizations, Prime and maximal ideals, Field extensions, Normal extensions, Galois extensions | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Ring homomorphisms | problem-solving |
| 2 | Quotient fields | problem-solving |
| 3 | Polynomial rings | problem-solving |
| 4 | Arithmetic in rings | problem-solving |
| 5 | Arithmetic in rings | problem-solving |
| 6 | Prime factorizations | problem-solving |
| 7 | Prime and maximal ideals | problem-solving |
| 8 | mid-term exam | |
| 9 | Prime and maximal ideals | problem-solving |
| 10 | Prime and maximal ideals | problem-solving |
| 11 | Prime and maximal ideals | problem-solving |
| 12 | Normal extensions | problem-solving |
| 13 | Normal extensions | problem-solving |
| 14 | Galois extensions | problem-solving |
| 15 | Galois extensions | problem-solving |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | A First Course in Abstract Algebra , John B. Fraleigh, Addision-Wesley Publishing Company. 1994 | |
| 2 | Algebra, Thomas W. Hungerford, Holtü, Rinehart and Winston, inc. New York Chicago San Francisco, 1974, | |
| 3 | Abstract Algebra David S. Dummit, Richard M. Foote, John Wiley & Sons, inc. 2004. | |
| 4 | Soyut Cebir, D.Taşçı, Ankara 2010. | |
| Required Course instruments and materials | ||
| The books of abstract algebra | ||
| Assessment Methods | |||
| Type of Assessment | Week | Hours | Weight(%) |
| mid-term exam | 8 | 2 | 40 |
| Other assessment methods | |||
| 1.Oral Examination | |||
| 2.Quiz | |||
| 3.Laboratory exam | |||
| 4.Presentation | |||
| 5.Report | |||
| 6.Workshop | |||
| 7.Performance Project | |||
| 8.Term Paper | |||
| 9.Project | |||
| final exam | 16 | 2 | 60 |
| Student Work Load | |||
| Type of Work | Weekly Hours | Number of Weeks | Work Load |
| Weekly Course Hours (Theoretical+Practice) | 4 | 15 | 60 |
| Outside Class | |||
| a) Reading | 2 | 15 | 30 |
| b) Search in internet/Library | 2 | 15 | 30 |
| c) Performance Project | 0 | ||
| d) Prepare a workshop/Presentation/Report | 0 | ||
| e) Term paper/Project | 0 | ||
| Oral Examination | 0 | ||
| Quiz | 0 | ||
| Laboratory exam | 0 | ||
| Own study for mid-term exam | 3 | 7 | 21 |
| mid-term exam | 1 | 2 | 2 |
| Own study for final exam | 3 | 7 | 21 |
| final exam | 1 | 2 | 2 |
| 0 | |||
| 0 | |||
| Total work load; | 166 | ||