| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | FMA635 | ALGEBRA I | Compulsory | 1 | 1 | 6 |
|
| Level of Course Unit |
| Second Cycle |
| Objectives of the Course |
| The purpose of this course is to give general knowledge about concepts of groups and rings, Sylow Theorems and its applications, Nilpotent and Solvable groups, Factorization in rings,localization, simple and primitive rings, semisimple rings, Simple and Primitive rings, Prime and Semiprime rings. |
| Name of Lecturer(s) |
| Assist. Prof. Dr. Yıldıray ÇELİK |
| Learning Outcomes |
| 1 | State the Theorems of Sylows. | | 2 | Apply the Sylows Theorems to questions. | | 3 | Express characterizations of nilpotent and solvable groups. | | 4 | Factorize the polynomial rings over commutative rings. | | 5 | Identify the radicals of some rings. | | 6 | Define the prime and primitive rings. |
|
| Mode of Delivery |
| Formal Education |
| Prerequisites and co-requisities |
| None |
| Recommended Optional Programme Components |
| None |
| Course Contents |
| Groups, Sylow Theorems and its applications , Characterization of Nilpotent and Solvable Groups, Rings, Rings, concepts of F[x] polynomial rings, Factorization ın commutative rings, Simple and Primitive Rings, Prime and Semiprime Rings, Localization of Rings, Semisimple Rings, Prime Radical, Concepts of Prime and Primitive Rings. |
| Weekly Detailed Course Contents |
|
| 1 | Groups, Subgroups, Cyclic groups, quotient groups | | | | 2 | Homomorphism Theorems | | | | 3 | Lagrange Theorem and its applications | | | | 4 | Finitely generated groups | | | | 5 | Group actions over set | | | | 6 | Sylows Toerems and its appliations | | | | 7 | Nilpotent Groups and its charaterization | | | | 8 | Midterm exam | | | | 9 | Solvable Groups and its charaterization | | | | 10 | Rings, Subrings, İdeals, Division Rings | | | | 11 | Structure of the ring F[X] | | | | 12 | Factorization of polynomials over commutative rings | | | | 13 | Localization | | | | 14 | Semisimple Rings and Radicals | | | | 15 | Prime, Primitive Rings and their characterization | | | | 16 | Final exam | | |
|
| Recommended or Required Reading |
|
| Planned Learning Activities and Teaching Methods |
|
| 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 |
|
| Workload Calculation |
|
| Midterm Examination | 1 | 2 | 2 |
| Final Examination | 1 | 2 | 2 |
| Attending Lectures | 14 | 3 | 42 |
| Practice | 14 | 3 | 42 |
| Problem Solving | 5 | 2 | 10 |
| Self Study | 14 | 5 | 70 |
| Individual Study for Homework Problems | 10 | 2 | 20 |
| Individual Study for Mid term Examination | 7 | 2 | 14 |
| Individual Study for Final Examination | 14 | 2 | 28 |
|
| Contribution of Learning Outcomes to Programme Outcomes |
| LO1 | 4 | 3 | 4 | 3 | 4 | 4 | 4 | | LO2 | 4 | 3 | 4 | 3 | 3 | 4 | 4 | | LO3 | 4 | 3 | 3 | 3 | 3 | 3 | 4 | | LO4 | 4 | 3 | 3 | 3 | 3 | 3 | 3 | | LO5 | 4 | 3 | 3 | 3 | 3 | 3 | 3 | | LO6 | 4 | 3 | 4 | 3 | 3 | 4 | 3 |
|
| * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
|
|
|
|
Ordu University Rectorate Building ,Cumhuriyet Campus , Center / ORDU / TURKEY • Tel: +90 452 226 52 00
|