Generalized Fibonacci Numbers and Applications
Mathematics
Institute of Natural and Applied Sciences
Second Cycle (Master's Degree)
| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Generalized Fibonacci Numbers and Applications | MAT508 | Elective | Master's degree | 1 | Fall | 8 |
Name of Lecturer(s)
Prof. Dr. Neşe ÖMÜR
Associate Prof. Dr. Yücel TÜRKER ULUTAŞ
Learning Outcomes of the Course Unit
1) Gaining the skills required for effective study.
2) Explain the generating functions and weighted Fibonacci and Lucas Sums.
3) Remember the Tribonacci numbers.
4) Develop theoretical concepts.
5) Reinforce the knowledge about the number theory.
6) Make the correct interpreting and gain the knowledge in plain.
Program Competencies-Learning Outcomes Relation
| Program Competencies | ||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
| Learning Outcomes | ||||||||
| 1 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 2 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 3 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 4 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 5 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 6 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
Mode of Delivery
Face to Face
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
Number Theory
Course Contents
This course provides candidates with in-depth knowledge on Fibonacci Numbers, Fibonacci and Lucas identities, generalized Fibonacci numbers, additional Fibonacci and Lucas formulas, the Euclidean Algorithm, solving recurrence relations, completeness theorems, Pascal's triangle, Pascal-like triangle, Hosoya's triangle, divisibility properties, generating functions, continued fractions, weighted Fibonacci and Lucas sums, Fibonacci matrices, Fibonacci determinants, Fibonacci and Lucas congruences, Fibonacci and Lucas series, Fibonacci and Lucas polynomials, Tribonacci numbers.
Weekly Schedule
1) Fibonacci Numbers, Fibonacci and Lucas Identities2) Generalized Fibonacci Numbers, Additional Fibonacci and Lucas Formulas
3) The Euclidean Algorithm, Solving Recurrence Relations, Completeness Theorems
4) Pascal Triangle, Pascal-like Triangle, Hosoya's Triangle
5) Divisibility Properties
6) Generalized Fibonacci Numbers Revisited, Generating Functions
7) Continued Fractions
8) Midterm examination/Assessment
9) Weighted Fibonacci and Lucas Sums
10) Fibonacci Matrices
11) Fibonacci Determinants
12) Fibonacci and Lucas Series
13) Fibonacci and Lucas Polynomials
14) Fibonacci and Lucas Congruences
15) Tribonacci Numbers
16) Final examination
Recommended or Required Reading
Planned Learning Activities and Teaching Methods
1) Lecture
2) Discussion
3) Demonstration
4) Group Study
5) Problem Solving
Assessment Methods and Criteria
Contribution of Semester Studies to Course Grade |
40% |
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Contribution of Final Examination to Course Grade |
60% |
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Total | 100% | ||||||||||||||
Language of Instruction
Turkish
Work Placement(s)
Not Required