Iğdır University Lifelong Learning Programme

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type of Course Unit	Year of Study	Semester	Number of ECTS Credits
170300401703	NUMBER THEORY I	Compulsory	4	7	6

Level of Course Unit

First Cycle

Objectives of the Course

To teach divisibility, congruences, linear Diophant equations, arithmetic functions, and also the applications of those together with the origins of the notions

Name of Lecturer(s)

Dr. Öğr. Üyesi Ezgi KAYA

Learning Outcomes

1	Knows the Notion of divisibility on the ring of integers and related notions.
2	Knows the corresponding English meanings of the main notions.
3	Differentiates between prime and composite numbers and knows the reasons of different situations.
4	Knows daily applications of congruences.

Mode of Delivery

Daytime Class

Prerequisites and co-requisities

Recommended Optional Programme Components

Course Contents

Divisibility Properties of Integers, Euler's Function, Diophantine Equations, Congruences and Congruence Systems, Properties of Prime Numbers.

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Divisibility on Integers
2	Euclid Algorithm
3	Fundamental Theorem of Arithmetic
4	Euler's phi Function
5	Diophantine Equations
6	Integers and Modular Arithmetic
7	Linear congruences with one variable
8	Midterm exam
9	Linear congruences and linear Diophantine equations
10	Examples of linear congruences, Relation between linear congruences and linear Diophantine equations
11	Congruence systems
12	Solution of congruence systems
13	Distribution of Prime Numbers
14	Prime Number Properties

Recommended or Required Reading

1. Sayılar Teorisi, İsmail Naci Cangül , 2015 2. Sayılar Teorisi Problemleri, İsmail Naci Cangül & Basri Çelik, 2005

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
Midterm Examination	1	100
SUM		100
End Of Term (or Year) Learning Activities	Quantity	Weight
Final Examination	1	100
SUM		100
Term (or Year) Learning Activities		40
End Of Term (or Year) Learning Activities		60
SUM		100

Language of Instruction

Turkish

Work Placement(s)

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	1	1
Final Examination	1	2	2
Attending Lectures	14	2	28
Problem Solving	14	2	28
Self Study	14	3	42
Individual Study for Homework Problems	14	1	14
Individual Study for Mid term Examination	1	20	20
Individual Study for Final Examination	1	30	30
Homework	7	2	14
TOTAL WORKLOAD (hours)			179

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
LO1	4	4	3	3	5	2	2	3	4	4
LO2	2	3	3	3	3	4	3	2	3	4
LO3	4	4	4	3	5	3	3	3	4	3
LO4	4	4	5	3	4	3	2	3	4	5

* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High