| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | 210300408101 | NUMBER THEORY – II | Compulsory | 4 | 8 | 6 |
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| Level of Course Unit |
| First Cycle |
| Objectives of the Course |
| The aim of this course is to gain the ability to pose and solve problems. |
| Name of Lecturer(s) |
| Dr. Öğr. Üyesi Ezgi AYDEMİR |
| Learning Outcomes |
| 1 | Know the theory of concept of quadratic residue, and determine whether a given integer is a quadratic residue of a number and, research the solvability of quadratic congruences. | | 2 | Prove the theorems on the Theory of Primitive Roots and determine all composite numbers having primitive roots and investigate all the primitive roots of them. | | 3 | Defines the concepts of arithmetic functions. | | 4 | Explain the applications of number theory. | | 5 | Knows the reasons for the first emergence of concepts and their historical development. | | 6 | Knows the English equivalents of the basic concepts used. |
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| Mode of Delivery |
| Daytime Class |
| Prerequisites and co-requisities |
| - |
| Recommended Optional Programme Components |
| - |
| Course Contents |
| Quadratic residues, Square sums and Fermat's last theorem, Arithmetic Functions, Continuous fractions, Fibonacci and Lucas Numbers |
| Weekly Detailed Course Contents |
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| 1 | Quadratic residues | | | | 2 | Quadratic equations | | | | 3 | Legendre Symbol | | | | 4 | Gauss’ quadratic reciprocity law | | | | 5 | Frame Totals | | | | 6 | Fermat's last theorem | | | | 7 | Arithmetic Functions | | | | 8 | Midterm exam | | | | 9 | Möbius Function and Mobius Inversion Formula | | | | 10 | Dirichlet Product | | | | 11 | Continuous Fractions | | | | 12 | Representation of Numbers by Continuous Fractions | | | | 13 | Fibonacci Numbers | | | | 14 | Lucas Numbers | | |
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| Recommended or Required Reading |
| 1. Sayılar Teorisi, İsmail Naci Cangül , 2015
2. Sayılar Teorisi Problemleri, İsmail Naci Cangül & Basri Çelik, 2005 |
| Planned Learning Activities and Teaching Methods |
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| Assessment Methods and Criteria | |
| Midterm Examination | 1 | 70 | | Homework | 1 | 30 | | SUM | 100 | |
| Final Examination | 1 | 100 | | SUM | 100 | | Term (or Year) Learning Activities | 50 | | End Of Term (or Year) Learning Activities | 50 | | SUM | 100 |
| | Language of Instruction | | Turkish | | Work Placement(s) | | - |
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| Workload Calculation |
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| Midterm Examination | 1 | 1 | 1 |
| Final Examination | 1 | 2 | 2 |
| Attending Lectures | 14 | 2 | 28 |
| Problem Solving | 10 | 2 | 20 |
| Question-Answer | 14 | 2 | 28 |
| Brain Storming | 10 | 2 | 20 |
| Individual Study for Mid term Examination | 1 | 20 | 20 |
| Individual Study for Final Examination | 1 | 30 | 30 |
| Homework | 1 | 20 | 20 |
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| Contribution of Learning Outcomes to Programme Outcomes |
| LO1 | 3 | 3 | 3 | 4 | 5 | 3 | 3 | 4 | 4 | 3 | | LO2 | 3 | 3 | 3 | 4 | 4 | 3 | 3 | 4 | 2 | 3 | | LO3 | 4 | 4 | 3 | 4 | 4 | 3 | 3 | 4 | 2 | 3 | | LO4 | 5 | 4 | 4 | 4 | 5 | 5 | 4 | 4 | 5 | 4 | | LO5 | 4 | 4 | 4 | 5 | 4 | 5 | 4 | 4 | 4 | 4 | | LO6 | 4 | 3 | 4 | 5 | 4 | 4 | 3 | 4 | 3 | 3 |
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| * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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Iğdır University, Iğdır / TURKEY • Tel (pbx): +90 476
226 13 14 • e-mail: info@igdir.edu.tr
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