| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Generalızed Fıbonaccı and Lucas Sequences | MAT 581 | 0 | 3 + 0 | 3 | 6 |
| Ön Koşul Dersleri | |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | YUKSEK_LISANS |
| Dersin Türü | Seçmeli |
| Dersin Koordinatörü | Prof.Dr. REFİK KESKİN |
| Dersi Verenler | |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Diğer |
| Dersin Amacı | TO INVESTIGATE THE GENERALIZED FIBONACCI AND LUCAS SEQUENCES. |
| Dersin İçeriği | TO INVESTIGATE THE GENERALIZED FIBONACCI AND LUCAS SEQUENCES. |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | He/ she describes the Fibonacci numbers. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, Performance Task, |
| 2 | He/ she describes the Lucas numbers. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, Performance Task, |
| 3 | He/ she learns the properties of Fibonacci and Lucas numbers. | Lecture, Problem Solving, | Testing, Homework, Performance Task, |
| 4 | He/ she learns related with some properties of Fibonacci and Lucas numbers. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, Performance Task, |
| 5 | He/ she finds the generating functions of Fibonacci and Lucas numbers | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, Performance Task, |
| 6 | He/ she learns Fibonacci and Lucas polynomials | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, Performance Task, |
| 7 | He/ she learns some properties Fibonacci and Lucas polynomials | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, Performance Task, |
| 8 | He/ she learns the Binet forms of Fibonacci and Lucas polynomials | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, Performance Task, |
| 9 | He/ she learns Fibonacci and Lucas series | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, Performance Task, |
| 10 | He/ she learns Fibonacci and Lucas matrices | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, Performance Task, |
| 11 | He/ she learns Fibonacci and Lucas determinants | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, Performance Task, |
| 12 | He/ she learns Tribonacci polynomials | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, Performance Task, |
| 13 | He/ she learns Jacobsthal polynomials | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, Performance Task, |
| 14 | He/ she learns the roots of Fibonacci and Lucas polynomials | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, Performance Task, |
| 15 | He/ she learns Gaussian Fibonacci polynomials | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, Performance Task, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | Fibonacci and Lucas numbers. | |
| 2 | Some general properties of the Fibonacci numbers. | |
| 3 | The properties related with the Fibonacci numbers. | |
| 4 | The generating functions of the Fibonacci and Lucas numbers. | |
| 5 | Fibonacci and Lucas Polynomials. | |
| 6 | Some general properties of the Fibonacci Polynomials. | |
| 7 | The Binet forms of the Fibonacci Polynomials | |
| 8 | Fibonacci and Lucas sequences | |
| 9 | Fibonacci and Lucas matrices | |
| 10 | Fibonacci and Lucas determinants | |
| 11 | Fibonacci and Lucas series | |
| 12 | The roots of Fibonacci and Lucas polynomials | |
| 13 | Gaussian Fibonacci and Lucas numbers | |
| 14 | Tribonacci and Jacobsthal numbers |
| Kaynaklar | |
|---|---|
| Ders Notu | |
| Ders Kaynakları | 1-Thomas Koshy, "Fibonacci and Lucas numbers with Applications"John-Wiley, 2001. 2- N. N Vorobiev, "Fibonacci numbers" Birkhauser, 1992. |
| Sıra | Program Çıktıları | Katkı Düzeyi | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 0 | Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise | X | |||||
| 2 | Student follows the current journals in his/her field and puts forward problems. | X | |||||
| 3 | Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics | X | |||||
| 4 | Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. | X | |||||
| 5 | Student uses different proof methods to come to a solution by analyzing the problems encountered. | X | |||||
| 6 | Student determines the problems to be solved within his/her field and if necessary takes the lead. | X | |||||
| 7 | Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. | X | |||||
| 8 | Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters | X | |||||
| 9 | Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. | X | |||||
| 10 | Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. | X | |||||
| 11 | Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. | X | |||||
| Değerlendirme Sistemi | |
|---|---|
| Yarıyıl Çalışmaları | Katkı Oranı |
| 1. Ara Sınav | 70 |
| 1. Ödev | 30 |
| 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 | 6 | 96 |
| Final examination | 1 | 15 | 15 |
| Toplam İş Yükü | 159 | ||
| Toplam İş Yükü / 25 (Saat) | 6,36 | ||
| Dersin AKTS Kredisi | 6 | ||