| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | FMA636 | ALGEBRA II | Compulsory | 1 | 2 | 6 |
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| Level of Course Unit |
| Second Cycle |
| Objectives of the Course |
| To develop the ability to think and to interpret correctly and to give people basic information about mathematics. |
| Name of Lecturer(s) |
| Assist. Prof. Yıldıray ÇELİK |
| Learning Outcomes |
| 1 | Students who successfully complete this course will develop the right thinking and the ability to comment and students will gain basic knowledge about mathematics. |
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| Mode of Delivery |
| Formal Education |
| Prerequisites and co-requisities |
| None |
| Recommended Optional Programme Components |
| None |
| Course Contents |
| Rings. Integral domains and fields. Chapter object of a completeness region, Sequential completeness region. Ideals and quotient rings, ring homomorphisms. Characteristic of a ring, maximal and prime ideals. Polynomials over a ring, divisibility of polynomials. Factorization in polynomial rings. The roots of polynomials and irreducibility criteria. |
| Weekly Detailed Course Contents |
|
| 1 | The definition of ring and examples
| | | | 2 | Integral domains and fields
| | | | 3 | Chapter object of a completeness region
| | | | 4 | Sequential completeness region
| | | | 5 | Ideals and quotient rings
| | | | 6 | Ring homomorphisms
| | | | 7 | Characteristic of a ring
| | | | 8 | Midterm exam
| | | | 9 | Maximal and prime ideals
| | | | 10 | Polynomials over a ring
| | | | 11 | Divisibility of polynomials
| | | | 12 | Factorization in polynomial rings
| | | | 13 | The roots of polynomials and irreducibility criteria
| | | | 14 | Polynomials over a ring
| | | | 15 | Euclidean rings and fraction rings, the local rings.
| | | | 16 | Final exam | | |
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| Recommended or Required Reading |
| 1-Algebra, Thomas W. Hungerford
2-Soyut Cebire giriş H.İbrahim KARAKAŞ
3-Soyut Cebir, Ergun BAYAR, Trabzon, 1986.
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| Planned Learning Activities and Teaching Methods |
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| Assessment Methods and Criteria | |
| SUM | 0 | |
| SUM | 0 | | Yarıyıl (Yıl) İçi Etkinlikleri | 40 | | Yarıyıl (Yıl) Sonu Etkinlikleri | 60 | | SUM | 100 |
| | Language of Instruction | | Turkish | | Work Placement(s) | | None |
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| Workload Calculation |
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| Midterm Examination | 1 | 2 | 2 |
| Final Examination | 1 | 2 | 2 |
| Attending Lectures | 14 | 3 | 42 |
| Practice | 14 | 3 | 42 |
| Self Study | 14 | 5 | 70 |
| Individual Study for Homework Problems | 10 | 2 | 20 |
| Individual Study for Mid term Examination | 7 | 2 | 14 |
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| Contribution of Learning Outcomes to Programme Outcomes |
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| * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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