Information Package / Course Catalogue - Adnan Menderes University

General Information Unit Staff Academic Information Programme Outcomes Course Structure Diagram Contact Information

Person Responsible for Information Package

Prof. Adnan MELEKOĞLU

Prof. Hülya İNCEBOZ

Prof. İnci EGE

Prof. Semra DOĞRUÖZ

Assoc. Prof. Berna ARSLAN

Assoc. Prof. Emrah YILDIRIM

Assoc. Prof. Korhan GÜNEL

Ins. Nihal GÜNEL

Lec. Ahmet GENÇ

Lec. Dilek AÇIKGÖZ KAYA

Lec. Erdal ÖZYURT

Lec. Muhammet Ali OKUR

Lec. Okan ARSLAN

Lec. Rıfat AŞLIYAN

Lec. Sibel KOÇER

Res. Assist. İclal GÖR

Res. Assist. Mehmet Soner PEHLİVAN

Number Theory

Course Code	: MAT315
Course Type	: Required
Couse Group	: First Cycle (Bachelor's Degree)
Education Language	: Turkish
Work Placement	: N/A

Theory	: 2
Prt.	: 2
Credit	: 3
Lab	: 0
ECTS	: 6

Objectives of the Course

The main objective of this course is to provide the foundations of elementary Number Theory. It aims to provide the ability to analyze and solve some problems that can be encountered frequently in daily life. In addition, the relationship between Number Theory and Cryptography is explained through basic cryptosystems and this is aimed to form the basis for advanced cryptosystems.

Course Content

Divisibility. Prime numbers. Congruences. Congruence equations. Polynomial Congruences. Multiplicative functions, Number theory and Cryptology, Primitive roots and applications, Quadratic residues.

Name of Lecturer(s)

Learning Outcomes

1.	Ability to understand the source of some well known properties of the ring of integers, and be able to relate these facts with daily life utilization areas
2.	To be able to comprehend the basic topics of Number Theory, which has a wide range of applications in mathematics.
3.	To be able to interpret the relationships between the mathematical concepts learned.
4.	To be able to apply the established mathematical relationships to solve problems that may be encountered.
5.	To be able to develop analytical skills and apply to problems

Recommended or Required Reading

1.	Elemantary Number Theory,, Kenneth H. Rosen, Addison-Wesley, 2011.
2.	Sayılar Kuramına Giriş, Prof. Dr. Arif Kaya, Ege Üniversitesi Yayınları, 1988.

Weekly Detailed Course Contents

Week 1 - Theoretical & Practice

Integers, Mathematical Induction

Week 2 - Theoretical & Practice

Divisibility, Representations of Integers

Week 3 - Theoretical & Practice

Prime Numbers, Sieve of Eratosthenes

Week 4 - Theoretical & Practice

Greates Common Divisor and its Properties

Week 5 - Theoretical & Practice

Euclidean Algorithm, Fundamental Theorem of Arithmetic

Week 6 - Theoretical & Practice

Linear Diophantine Equations

Week 7 - Theoretical & Practice

Congruences, Linear Congruences

Week 8 - Theoretical & Practice

Chinese Remainder Theorem

Week 9 - Theoretical & Practice

Polynomial Congruences

Week 10 - Theoretical & Practice

Some Special Congruences

Week 11 - Theoretical & Practice

Multiplicative Functions

Week 12 - Theoretical & Practice

Number Theory and Cryptography

Week 13 - Theoretical & Practice

Primitive Roots and its Applications

Week 14 - Theoretical & Practice

Quadratic Residues and Law of Quadratic Reciprocity

Assessment Methods and Criteria

Type of Assessment	Count	Percent
Assignment	1	%5
Term Assignment	1	%5
Midterm Examination	1	%30
Final Examination	1	%60

Workload Calculation

Activities	Count	Preparation	Time	Total Work Load (hours)
Lecture - Theory	14	1	2	42
Lecture - Practice	14	1	2	42
Assignment	1	6	1	7
Term Project	1	6	1	7
Individual Work	14	0	1	14
Midterm Examination	1	13	2	15
Final Examination	1	21	2	23
TOTAL WORKLOAD (hours)				150

Contribution of Learning Outcomes to Programme Outcomes

	PÇ-1	PÇ-2	PÇ-3	PÇ-4	PÇ-5	PÇ-6	PÇ-7	PÇ-8	PÇ-9	PÇ-10	PÇ-11	PÇ-12	PÇ-13	PÇ-14	PÇ-15	PÇ-16	PÇ-17	PÇ-18
OÇ-1	3		2		3				3	3	2	4
OÇ-2	3		3		3		2		4	3	3	2
OÇ-3					3		3		4	3	3	3
OÇ-4	3		4		4				4	3	3
OÇ-5	3		4		3					4	4