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| MAT3008 | Number Theory | 4+0+0 | ECTS:6 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Dr. Öğr. Üyesi Şerife YILMAZ | | Co-Lecturer | Prof. Dr. Osman Kazancı | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The purpose of the course is to give a simple account of classical number theory, prepare students to graduate-level courses in number theory and algebra, and to demonstrate applications of number theory (such as public-key cryptography) |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | learn to solve problems by usnig learned technicmethods. | 1 | 1 | | LO - 2 : | learn to solve linear Diophantine equations | 1,2 | 1 | | LO - 3 : | learn to compute powers and roots modulo-n | 3 | 1 | | LO - 4 : | learn to determine the differences between legendre symbol and Quadratic Resiprocity Theorem. | 3,4 | 1 | | LO - 5 : | learn to determine primitive roots; and compute quadratic residues and solve the congruans, | 4 | 1 | | LO - 6 : | learn to use the jacobi sympol to solve quadratic congruences, | 4,5 | 1 | | LO - 7 : | learn to determine the differences between legendre symbol and Quadratic Resiprocity Theorem. | 5,6 | 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), LO : Learning Outcome | | |
| Linear Congruences, High Degree Congruence, Prime Modules, Power Resudies, Quadradic Resudies, The Legendre Symbol, The Quadratic Resiprocity Theorem, The Jacobi Symbol, Multiplicative Functions, Diophantine Equation. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Definitions, Linear Congruences | | | Week 2 | Non-linear Congruences | | | Week 3 | Prime Modules | | | Week 4 | Power Resudies | | | Week 5 | Quadradic Resudies | | | Week 6 | The Legendre Symbol | | | Week 7 | Primitive roots | | | Week 8 | Mid-term exam | | | Week 9 | The Quadratic Resiprocity Theorem | | | Week 10 | The Quadratic Resiprocity Theorem | | | Week 11 | The Jacobi Symbol | | | Week 12 | Applications of Jacobi Symbol | | | Week 13 | Some special function | | | Week 14 | Multiplicative Functions | | | Week 15 | Diophantine Equation
| | | Week 16 | End-of-term exam | | | |
| 1 | Rose, H.E., 1998, A Course in Number Theory Clarendon Press. Oxford | | | |
| 1 | Kumanduri, R.,Romero, C., 1998, Number Theory with Computer Applications A Viacom Company Upper Saddle River, New Jersey. | | | 2 | Burton D. M., 2002, Elementary number theory, The McGraw-Hill Companies. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 20/11/2021 | 2 | 50 | | End-of-term exam | 16 | 10/01/2021 | 2 | 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 | 5 | 14 | 70 | | Arasınav için hazırlık | 10 | 1 | 10 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 8 | 1 | 8 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 148 |
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