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| MATL7461 | Some Properties of Fibonacci and Lucas Numbers | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Doç. Dr. Ali Hikmet DEĞER | | Co-Lecturer | None | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The aim of this course is to give some interesting properties of Fibonacci and Lucas numbers and to examine the relation between them. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | recognize Fibonacci and Lucas numbers. | 3,8 | 1, | | PO - 2 : | learn the relationship between Fibonacci and Lucas numbers and continuous fractions. | 3,8 | 1, | | PO - 3 : | discover the golden ratio and geometry. | 3,8 | 1, | | PO - 4 : | discover the Fibonacci numbers in the nature. | 3,8 | 1, | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| History, Rabbits, Fibonacci numbers, and Lucas numbers, The golden section and Fibonacci quadratic equation, Some geometry related to the golden section, Some Fibonacci algebra, Shortcuts to large F_n and L_n, Divisibility properties of the Fibonacci and Lucas numbers, Periodicity of the Fibonacci and Lucas numbers, Pascal's triangle and the Fibonacci numbers, Selected identities involving the Fibonacci and Lucas numbers, Two-by-two matrices related to the Fibonacci numbers, Representation theorems, Fibonacci numbers in nature. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Introduction and History. | | | Week 2 | Fibonacci and Lucas numbers with born history of Rabbits. | | | Week 3 | The golden section and Fibonacci quadratic equation. | | | Week 4 | Some geometry applications related to the golden section. | | | Week 5 | Some Fibonacci algebra and applications. | | | Week 6 | Shortcuts to determine large F_n and L_n numbers. | | | Week 7 | Divisibility properties of the Fibonacci and Lucas numbers and applications. | | | Week 8 | Periodicity of the Fibonacci and Lucas numbers. | | | Week 9 | Mid-term exam. | | | Week 10 | Pascal's triangle and the Fibonacci numbers. | | | Week 11 | Selected identities involving the Fibonacci and Lucas numbers. | | | Week 12 | Applications of selected identities involving the Fibonacci and Lucas numbers. | | | Week 13 | Two-by-two matrices related to the Fibonacci numbers. | | | Week 14 | Representation theorems. | | | Week 15 | Fibonacci numbers in nature. | | | Week 16 | Final exam. | | | |
| 1 | Fibonacci and Lucas Numbers, Verner E. Hoggatt, Jr., The Fibonacci Association, University of Santa Clara, 1969. | | | |
| 1 | A Primer for the Fibonacci Numbers, Verner E. Hoggatt, Jr., The Fibonacci Association, University of Santa Clara, 1973. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 15/03/2024 | 2 | 30 | | Quiz | 12 | 15/04/2024 | 1 | 20 | | End-of-term exam | 16 | 06/06/2024 | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 10 | 14 | 140 | | Arasınav için hazırlık | 6 | 1 | 6 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 10 | 1 | 10 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 202 |
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