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| MAT7166 | Algebraic Number Fields | 3+0+0 | ECTS:7.5 | | Year / Semester | Spring Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Prof. Dr. Mehmet AKBAŞ | | Co-Lecturer | Assoc. Prof. Dr. Ömer Pekşen | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | To extend the results of basic number theory to Algebraic number fields |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | learn some extensions of number theory to Algebraic number fields | 3,4 | 1 | | PO - 2 : | enlarge their views towards other objects | 3,4 | 1 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| Algebraic numbers, basis of an ideal, prime ideals, factorization into prime ideals |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Algebraic number fields, conjugate fields | | | Week 2 | The field polynomial of an element of an Algebraic number field | | | Week 3 | Discriminant of a set of elements | | | Week 4 | Basis of an Ideal | | | Week 5 | Prime ideals in rings of integers | | | Week 6 | Integral basis | | | Week 7 | Integral basis | | | Week 8 | Mid-term exam | | | Week 9 | Minimal integers | | | Week 10 | Some integral basis in cubic fields | | | Week 11 | Index and minimal index | | | Week 12 | Integral basis of a cyclotomic field | | | Week 13 | Dedekind domain, Ideals in a Dedekind domain | | | Week 14 | Factorization into Prime ideals | | | Week 15 | Order of ideals, generators of ideals in a Dedekind domain | | | Week 16 | End-of-term exam | | | |
| 1 | Alaca, Ş. Kenneth, W.S. 2004; Introductory Algebraic Number Theory, CUP | | | |
| 1 | Serge, L. 1986; Algebraic Number Theory, Springer Verlag, New York | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 8 | 05/11/2010 | 1,5 | 30 | | In-term studies (second mid-term exam) | 12 | 09/12/2010 | 1,5 | 20 | | End-of-term exam | 16 | 06/01/2011 | 1,8 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 4 | 14 | 56 | | Sınıf dışı çalışma | 8 | 14 | 112 | | Arasınav için hazırlık | 7 | 1 | 7 | | Arasınav | 7 | 1 | 7 | | Dönem sonu sınavı için hazırlık | 10 | 1 | 10 | | Dönem sonu sınavı | 8 | 1 | 8 | | Total work load | | | 200 |
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