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MAI7166 | 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 | | 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 | Arasınav | 7 | 1 | 7 | Total work load | | | 7 |
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