Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
GENERALIZED FIBONACCI AND LUCAS SEQUENCES MAT 581 0 3 + 0 3 6
 Dersin Dili Türkçe Dersin Seviyesi Yüksek Lisans Dersin Türü SECMELI Dersin Koordinatörü Prof.Dr. REFİK KESKİN Dersi Verenler Prof.Dr. REFİK KESKİN Dersin Yardımcıları Dersin Kategorisi Dersin Amacı TO INVESTIGATE THE GENERALIZED FIBONACCI AND LUCAS SEQUENCES. Dersin İçeriği TO INVESTIGATE THE GENERALIZED FIBONACCI AND LUCAS SEQUENCES.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/ she describes the Fibonacci numbers. 1 - 4 - 15 - A - C - F - 2 - He/ she describes the Lucas numbers. 1 - 4 - 15 - A - C - F - 3 - He/ she learns the properties of Fibonacci and Lucas numbers. 1 - 15 - A - C - F - 4 - He/ she learns related with some properties of Fibonacci and Lucas numbers. 1 - 4 - 15 - A - C - F - 5 - He/ she finds the generating functions of Fibonacci and Lucas numbers 1 - 4 - 15 - A - C - F - 6 - He/ she learns Fibonacci and Lucas polynomials 1 - 4 - 15 - A - C - F - 7 - He/ she learns some properties Fibonacci and Lucas polynomials 1 - 4 - 15 - A - C - F - 8 - He/ she learns the Binet forms of Fibonacci and Lucas polynomials 1 - 4 - 15 - A - C - F - 9 - He/ she learns Fibonacci and Lucas series 1 - 4 - 15 - A - C - F - 10 - He/ she learns Fibonacci and Lucas matrices 1 - 4 - 15 - A - C - F - 11 - He/ she learns Fibonacci and Lucas determinants 1 - 4 - 15 - A - C - F - 12 - He/ she learns Tribonacci polynomials 1 - 4 - 15 - A - C - F - 13 - He/ she learns Jacobsthal polynomials 1 - 4 - 15 - A - C - F - 14 - He/ she learns the roots of Fibonacci and Lucas polynomials 1 - 4 - 15 - A - C - F - 15 - He/ she learns Gaussian Fibonacci polynomials 1 - 4 - 15 - A - C - F -
 Öğretim Yöntemleri: 1:Lecture 4:Drilland Practice 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework F:Performance Task

#### Ders Akışı

Hafta Konular ÖnHazırlık
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.

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 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

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 70
Odev 1 30
Toplam 100
Yıliçinin Başarıya Oranı 50
Finalin Başarıya Oranı 50
Toplam 100

#### AKTS - İş Yükü

Etkinlik Sayısı Süresi(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(s) 6.36
Dersin AKTS Kredisi 6.36
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