Course Name Code Semester T+U Hours Credit ECTS
Generalized Fibonacci and Lucas Sequences MAT 581 0 3 + 0 3 6
Precondition Courses
Recommended Optional Courses
Course Language Turkish
Course Level yuksek_lisans
Course Type Optional
Course Coordinator Prof.Dr. REFİK KESKİN
Course Lecturers
Course Assistants
Course Category
Course Objective TO INVESTIGATE THE GENERALIZED FIBONACCI AND LUCAS SEQUENCES.
Course Content TO INVESTIGATE THE GENERALIZED FIBONACCI AND LUCAS SEQUENCES.
# Course Learning Outcomes Teaching Methods Assessment Methods
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,
Week Course Topics Preliminary Preparation
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
Resources
Course Notes
Course Resources 1-Thomas Koshy, "Fibonacci and Lucas numbers with Applications"John-Wiley, 2001.
2- N. N Vorobiev, "Fibonacci numbers" Birkhauser, 1992.
Order Program Outcomes Level of Contribution
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
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 70
1. Ödev 30
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
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
Total Workload 159
Total Workload / 25 (Hours) 6.36
dersAKTSKredisi 6