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COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
MAT 585RECURRENCE RELATIONS, FIBONACCI AND LUCAS NUMBERS3 + 01st Semester7,5

COURSE DESCRIPTION
Course Level Doctorate Degree
Course Type Elective
Course Objective The aim of this course is to teach the linear homogen recurrence relations and the properties of the numbers which are the results of these recurrence relations. To emphasize the algebraic and combinatorial importance in other sciences.
Course Content Linear Homogen Recurrence Relations, Fibonacci, Lucas, Pell amd Bernoulli Numbers, Fibonacci Lucas Identities, Generalized Fibonacci Numbers and Euclid Algorithm, Divisibility Properties of Fibonacci and Lucas numbers, Congruences, Periods of Fibonacci and Lucas numbers, Generating Functions, Continued Fractions, Golden Ratio
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.
Mode of Delivery Face to Face

COURSE LEARNING OUTCOMES
1Knows the linear homogen recurrence relations and their solutions.
2Learns the Fibonacci, Lucas, Pell ve Bernoulli numbers.
3Learns the divisibility properties and peridicity of the Fibonacci and Lucas numbers.
4Learns to find the generating functions.
5Learns the concept of the continued fractions and the relations between the Fibonacci numbers.
6Knows the golden ratio and the applications in the nature.

COURSE'S CONTRIBUTION TO PROGRAM
PO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08
LO 001        
LO 002        
LO 003        
LO 004        
LO 005        
LO 006        
Sub Total        
Contribution00000000

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
ActivitiesQuantityDuration (Hour)Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)14342
Hours for off-the-classroom study (Pre-study, practice)14798
Assignments155
Mid-terms11515
Final examination13535
Total Work Load

ECTS Credit of the Course






195

7,5
COURSE DETAILS
 Select Year   


 Course TermNoInstructors
Details 2023-2024 Spring1MUSTAFA AŞCI
Details 2022-2023 Spring1MUSTAFA AŞCI
Details 2021-2022 Spring1MUSTAFA AŞCI
Details 2017-2018 Fall1MUSTAFA AŞCI
Details 2015-2016 Fall1MUSTAFA AŞCI
Details 2014-2015 Fall1MUSTAFA AŞCI
Details 2013-2014 Fall1MUSTAFA AŞCI
Details 2012-2013 Fall1MUSTAFA AŞCI


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Course Details
Course Code Course Title L+P Hour Course Code Language Of Instruction Course Semester
MAT 585 RECURRENCE RELATIONS, FIBONACCI AND LUCAS NUMBERS 3 + 0 1 Turkish 2023-2024 Spring
Course Coordinator  E-Mail  Phone Number  Course Location Attendance
Prof. Dr. MUSTAFA AŞCI masci@pau.edu.tr FEN A0204 %70
Goals The aim of this course is to teach the linear homogen recurrence relations and the properties of the numbers which are the results of these recurrence relations. To emphasize the algebraic and combinatorial importance in other sciences.
Content Linear Homogen Recurrence Relations, Fibonacci, Lucas, Pell amd Bernoulli Numbers, Fibonacci Lucas Identities, Generalized Fibonacci Numbers and Euclid Algorithm, Divisibility Properties of Fibonacci and Lucas numbers, Congruences, Periods of Fibonacci and Lucas numbers, Generating Functions, Continued Fractions, Golden Ratio
Topics
WeeksTopics
1 Linear Homogen Recurrence Relations
2 Fibonacci and Lucas Numbers
3 Pell amd Bernoulli Numbers
4 Fibonacci Lucas Identities
5 Generalized Fibonacci Numbers
6 Euclid Algorithm
7 Divisibility Properties of Fibonacci and Lucas numbers
8 Fibonacci Determinants
9 Congruences
10 Periods of Fibonacci and Lucas numbers
11 Generating Functions
12 Continued Fractions
13 Golden Ratio
14 Final Examination
Materials
Materials are not specified.
Resources
ResourcesResources Language
FIBONCCI AND LUCAS NUMBERS WITH APPLICATIONS THOMAS KOSHY, Wiley-Interscience Publication, New York, 2001Türkçe
Course Assessment
Assesment MethodsPercentage (%)Assesment Methods Title
Final Exam50Final Exam
Midterm Exam50Midterm Exam
L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes