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Description of Individual Course Units
| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits |
|---|---|---|---|---|---|
| MAT716 | FIBONACCI AND LUCAS NUMBERS II | 3 | 5 | 5,00 |
Level of Course Unit
Lisans
Language of Instruction
Turkish
Objectives of the Course
To teach Fibonacci, Lucas, Pell and Pell-Lucas polynomials, Binet formulas and properties of these polynomials with their proofs
Name of Lecturer(s)
Learning Outcomes
| 1 | Expresses Fibonacci and Lucas polynomials using Binet's formulas. |
| 2 | Expresses Pell and Pell-Lucas polynomials using Binet's formulas. |
| 3 | Proves the identities that give the relationships between Fibonacci and Lucas polynomials. |
| 4 | Proves the identities that give the relationships between Pell and Pell- Lucas polynomials. |
| 5 | Learns the relationships between the polynomials of special number sequences. |
Mode of Delivery
Formal Education
Prerequisities and Co-Requisities
None
Recommended Optional Programme Components
None
Content of the Course
Definition of Fibonacci, Lucas, Pell, Pell-Lucas polynomials, metallic ratios, Binet formulas, identities related to Fibonacci, Lucas, Pell and Pell-Lucas polynomials
Weekly Detailed Course Contents
| Week | Subjects (Theoretical) | Teaching Methods | Preparatory |
|---|---|---|---|
| 1 | Definition of Fibonacci, Lucas, Pell and Pell-Lucas numbers | ||
| 2 | Golden ratio, silver ratio, bronze ratio | ||
| 3 | Identities involving Fibonacci and Lucas numbers | ||
| 4 | Identities involving Pell and Pell-Lucas numbers | ||
| 5 | Definition of Fibonacci and Lucas polynomials | ||
| 6 | Definition of Pell and Pell-Lucas polynomials | ||
| 7 | Binet formulas | ||
| 8 | Binet formulas | ||
| 9 | Properties of Fibonacci and Lucas polynomials | ||
| 10 | Relationships between Fibonacci and Lucas polynomials | ||
| 11 | Properties of Pell and Pell-Lucas polynomials | ||
| 12 | Relationships between Pell and Pell-Lucas polynomials | ||
| 13 | Chebyshev Polynomials | ||
| 14 | Chebyshev Polynomials |
Text Book / Material / Recommended Resources
Fibonacci and Lucas numbers with applications, T. Koshy, John Wiley and Sons, Proc., New York-Toronto, 2001. Fibonacci and Lucas numbers and the golden section, S. Vajda, Ellis Horwood Limited Publ., England, 1989.
Assessment Methods and Criteria
| Term (or Year) Learning Activities | Quantity | Weight |
|---|---|---|
| Midterm Examination | 1 | 80 |
| Quiz | 1 | 20 |
| Total | 100 | |
| End Of Term (or Year) Learning Activities | Quantity | Weight |
| Final Examination | 1 | 100 |
| Total | 100 | |
| Term (or Year) Learning Activities | 40 | |
| End Of Term (or Year) Learning Activities | 60 | |
Work Pacement(s)
None
Workload Calculation
| Activities | Number | Time (hours) | Total Work Load (hours) |
|---|---|---|---|
| Midterm Examination | 1 | 2 | 2 |
| Final Examination | 1 | 2 | 2 |
| Quiz | 1 | 1 | 1 |
| Attending Lectures | 14 | 2 | 28 |
| Self Study | 14 | 3 | 42 |
| Individual Study for Mid term Examination | 3 | 3 | 9 |
| Individual Study for Final Examination | 4 | 3 | 12 |
| Individual Study for Quiz | 3 | 2 | 6 |
| Homework | 2 | 8 | 16 |
| Total Work Load (hours) | 118 | ||
Contribution of Learning Outcomes to Programme Outcomes
| PO 1 | PO 2 | PO 3 | PO 4 | PO 5 | PO 6 | PO 7 | PO 8 | PO 9 | PO 10 | PO 11 | PO 12 | PO 13 | PO 14 | PO 15 | |
| LO 1 | 5 | ||||||||||||||
| LO 2 | 5 | ||||||||||||||
| LO 3 | 5 | ||||||||||||||
| LO 4 | 5 | ||||||||||||||
| LO 5 | 5 |
* Contribution Level: 1 Very low 2 Low 3 Medium 4 High 5 Very High