Ordu 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
MAT40420121310	NUMBERS THEORY-II	Elective	4	8	5

Level of Course Unit

First Cycle

Objectives of the Course

To develop the ability to think and to interpret correctly and to give people basic information about mathematics.

Name of Lecturer(s)

Yrd.Doç.Dr. Yıldıray ÇELİK

Learning Outcomes

1	Have the basic knowledge about linear congruences in more than one unknown and congruences of higher degree, and solve problems related to these subjects.
2	Prove the theorems on the Theory of Primitive Roots and determine all composite numbers having primitive roots and investigate all the primitive roots of them.
3	Prove the theorems about the theory of indices and apply this theory to the solutions of various problems.
4	Know the theory of concept of quadratic residue, and determine whether a given integer is a quadratic residue of a number and, research the solvability of quadratic congruences.

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

The expression of integers in any base. The fundamental theorem of arithmetic. Integers divisibility. Prime numbers and the distribution of prime numbers. Euclidean division algorithm and its applications. Unique factorization of integers. Multiplicative and additive functions. Diophantine equations. Congrue

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Linear Congruences in More Than One Unknown.
2	Congruences of Higer Degree.
3	Congruences with Prime Moduli, Primitive Roots.
4	Primitive Roots for Primes.
5	Composite Numbers having Primitive Roots.
6	The Theory of Indices.
7	Euler’s Criterion.
8	Midterm exam
9	Legendre Symb
10	Gauss’ Lemma
11	Quadratic Reciprocity, Jacobi Symbol.
12	Quadratic Congruences with Composite Moduli
13	Numbers of Special Form, Perfect Numbers.
14	Mersenne and Fermat Numbers
15	Final exam
16	Final exam

Recommended or Required Reading

1 Fethi Çallıalp, SaYearar Teorisi, İstanbul, 1999 2 Arif Kaya, Sayılar Kuramına Giriş, İzmir, 1988 3 Ivan Niven, Herbert S. Zuckerman, Number theory, John Wiley&sons. Inc., 1966

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
SUM		0
End Of Term (or Year) Learning Activities	Quantity	Weight
SUM		0
Yarıyıl (Yıl) İçi Etkinlikleri		40
Yarıyıl (Yıl) Sonu Etkinlikleri		60
SUM		100

Language of Instruction

Turkish

Work Placement(s)

None

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	2	2
Final Examination	1	2	2
Makeup Examination	1	2	2
Attending Lectures	14	4	56
Problem Solving	10	4	40
Brain Storming	10	4	40
TOTAL WORKLOAD (hours)			142

Contribution of Learning Outcomes to Programme Outcomes

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7
LO1	2	2	2	4	3	3	3
LO2	3	3	3	4	4	4	4
LO3	2	2	2	3	3	3	3
LO4	2	2	2	4	3	3	4

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