| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Elementary Number Theory | IME 306 | 6 | 3 + 0 | 3 | 3 |
| Ön Koşul Dersleri | |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | Lisans |
| Dersin Türü | Zorunlu |
| Dersin Koordinatörü | Doç.Dr. ERCAN MASAL |
| Dersi Verenler | Doç.Dr. ERCAN MASAL, |
| Dersin Yardımcıları | Res.Assist.Emine Nur BİLGİÇ |
| Dersin Kategorisi | Alanına Uygun Temel Öğretim |
| Dersin Amacı | To give detailed information to students of elementary education about divisibility on integers, products on integers. Intoduce relations among congruents and some applcation fields, primitive roots and indexes and groups. To give relations among continuous fraction and rational and irrational numbers. |
| Dersin İçeriği | Divisibility on integers, prime numbers, important functions on number theories, congruents, linear congruents, seperating prime products on integers, primitive roots and indexes, quadric residues (second degree), cryptography subjects and usage areas in real life, continuous fractions. |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | Explain divisibility rules on integers | Lecture, Drilland Practice, | Testing, Homework, |
| 2 | Explain the relation between prime numbers and products on integers and express division on integers, highest common factor (H.C.F.), lowest common multiple (L.C.M.) by the help of this relation | Drilland Practice, Lecture, | Testing, Homework, |
| 3 | Explain special functions on number theory | Lecture, Drilland Practice, | Homework, Testing, |
| 4 | Explain the concept of congruents and solve problems related congruents | Lecture, Drilland Practice, | Testing, Homework, |
| 5 | Explain the solution of linear and higher order congruents | Drilland Practice, Lecture, | Homework, Testing, |
| 6 | Express the properties of primitive roots and indexes and solve related problems | Lecture, Drilland Practice, | Testing, Homework, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | Divisibility on integers | |
| 2 | Prime numbers and products on integers | |
| 3 | Euler’s function | |
| 4 | Congruents | |
| 5 | Linear congruents | |
| 6 | Chinese remainder theorem | |
| 7 | Higher order congruents | |
| 8 | Primitive roots | |
| 9 | Mid –Term Exam | |
| 10 | Indexes | |
| 11 | Quadric residues | |
| 12 | Cryptography | |
| 13 | Continuous fractions | |
| 14 | Arithmetic functions |
| Kaynaklar | |
|---|---|
| Ders Notu | |
| Ders Kaynakları | |
| Sıra | Program Çıktıları | Katkı Düzeyi | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Have general information about basic concept, theory and applicaitons on mathematics | X | |||||
| 2 | Have ability of mathematical thinking and apply to real life | X | |||||
| 3 | Classify a problem systematically also create comprehensible, understandable and objective solutions | X | |||||
| 4 | Establish relationship among events looked different | X | |||||
| 5 | Get clear and exact ideas about relationships among time, place and numbers | X | |||||
| 6 | Use principles of scientific method on problem solving | X | |||||
| 7 | Have character on explorer, impartial, disinterested, give sound decisions, open mind and believe that spreading information is needed | X | |||||
| 8 | Think creative and critical | X | |||||
| 9 | Improve methods as fast, understandable and practical to faced problems | X | |||||
| 10 | Have information about national and international modern problems | ||||||
| 11 | Get life long learning behaviour | ||||||
| 12 | Know and apply approach, aim, goal, principle and techniques of teaching program on special field with basic value and principles of Turkish National Education System | ||||||
| 13 | Evaluate development and learning of students, provide to evaluate self-assessment and other students. Use the assessment results to better instruction; share the results with student, parent, administrators and teachers. | ||||||
| 14 | Endeavor for constant development by making self-evaluation. Open the new knowledge and ideas, have a role to develop himself/herself and his/her institution. Have enough knowledge and conscious to protection subjects on society values and environment. | ||||||
| 15 | Interrogator ( get habit to find source of knowledge by asking “Why?” question instead of direct acceptance to given knowledges ) | X | |||||
| Değerlendirme Sistemi | |
|---|---|
| Yarıyıl Çalışmaları | Katkı Oranı |
| 1. Ödev | 10 |
| 1. Ara Sınav | 50 |
| 1. Kısa Sınav | 20 |
| 2. Kısa Sınav | 20 |
| Toplam | 100 |
| 1. Yıl İçinin Başarıya | 50 |
| 1. Final | 50 |
| Toplam | 100 |
| AKTS - İş Yükü Etkinlik | Sayı | Süre (Saat) | Toplam İş Yükü (Saat) |
|---|---|---|---|
| Course Duration (Including the exam week: 16x Total course hours) | 16 | 3 | 48 |
| Hours for off-the-classroom study (Pre-study, practice) | 16 | 1 | 16 |
| Mid-terms | 1 | 10 | 10 |
| Quiz | 2 | 1 | 2 |
| Assignment | 1 | 3 | 3 |
| Final examination | 1 | 8 | 8 |
| Toplam İş Yükü | 87 | ||
| Toplam İş Yükü / 25 (Saat) | 3,48 | ||
| Dersin AKTS Kredisi | 3 | ||