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
170300401803	NUMBER THEORY II	Compulsory	4	8	6

Level of Course Unit

First Cycle

Objectives of the Course

The aim of this course is to gain the ability to pose and solve problems.

Name of Lecturer(s)

Dr. Öğr. Üyesi Ezgi KAYA

Learning Outcomes

1	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.
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.

Mode of Delivery

Daytime Class

Prerequisites and co-requisities

Recommended Optional Programme Components

Course Contents

Quadratic residues, Square sums and Fermat's last theorem, Arithmetic Functions, Continuous fractions, Fibonacci and Lucas Numbers

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Quadratic residues
2	Quadratic equations
3	Legendre Symbol
4	Gauss’ quadratic reciprocity law
5	Frame Totals
6	Fermat's last theorem
7	Arithmetic Functions
8	Midterm exam
9	Möbius Function and Mobius Inversion Formula
10	Dirichlet Product
11	Continuous Fractions
12	Representation of Numbers by Continuous Fractions
13	Fibonacci Numbers
14	Lucas Numbers

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	3	42
Problem Solving	14	2	28
Brain Storming	14	1	14
Self Study	14	3	42
Individual Study for Homework Problems	14	1	14
Individual Study for Mid term Examination	1	15	15
Individual Study for Final Examination	1	20	20
TOTAL WORKLOAD (hours)			178

Contribution of Learning Outcomes to Programme Outcomes

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