| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | IMO4012013331 | ELEMENTARY THEORY OF NUMBERS | Compulsory | 4 | 7 | 6 |
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| Level of Course Unit |
| First Cycle |
| Objectives of the Course |
| To explain simple and undecipherable problems with giving integers basic arithmetic properties, have an opinion about some generilazations, have basic knowledge about numbrsand arithmetic, solve actual arithmetic problems with using clasic theories |
| Name of Lecturer(s) |
| Yrd.Doç.Dr. Tolga AKTÜRK |
| Learning Outcomes |
| 1 | Students shall know about the causes of the properties will be taught in school integer factorization, GCD and LCM. | | 2 | Student shall realize some basic features of prime numbers. | | 3 | Student shall express the properties of primitive roots and indexes and solve related problems. |
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| Mode of Delivery |
| Formal Education |
| Prerequisites and co-requisities |
| None |
| Recommended Optional Programme Components |
| None |
| Course Contents |
| Divisibility in whole numbers, Prime numbers, the significant function in the Numbers theory, congruences, Linear congruence, the uniqueness of the division of the whole numbers into prime multipliers, Primitive roots and indexes, quadratic rezidular (secondary) , coding subjects and their applications in the daily life, continuous fractions. |
| Weekly Detailed Course Contents |
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| 1 | Induction Principle | | | | 2 | Division in Integers | | | | 3 | The Greatest Common Divisor and Basic Properties | | | | 4 | Relatively Prime Numbers and Basic Properties | | | | 5 | Polynomials | | | | 6 | The Number of Positive Divisors and The Sum of Positive Divisors | | | | 7 | The Least Common Multiple and Basic Properties | | | | 8 | Euler Theorem and Some Properties | | | | 9 | Modular Arithmetic | | | | 10 | Midterm Exam | | | | 11 | Euler, Fermat and Wilson Theorems | | | | 12 | Linear Congruence | | | | 13 | The System of Linear Congruence | | | | 14 | Polynomial Congruence | | | | 15 | Final Exam | | | | 16 | | | |
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| Recommended or Required Reading |
| Bayraktar, M. 2006. Soyut Cebir ve Sayılar Teorisi. Gazi Kitabevi |
| Planned Learning Activities and Teaching Methods |
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| 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 |
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| Workload Calculation |
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| Midterm Examination | 1 | 1 | 1 |
| Final Examination | 1 | 2 | 2 |
| Attending Lectures | 14 | 5 | 70 |
| Tutorial | 14 | 5 | 70 |
| Self Study | 12 | 3 | 36 |
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| Contribution of Learning Outcomes to Programme Outcomes |
| LO1 | 5 | 1 | 1 | 1 | 1 | 5 | 5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | | LO2 | 5 | 1 | 1 | 1 | 1 | 5 | 5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | | LO3 | 5 | 1 | 1 | 1 | 1 | 5 | 5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
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| * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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