ELEMENTARY NUMBER THEORY

EMT430

Course Code: EMT430
Semester: -
Theory+Practice: 3 + 0
ECTS: 4

Course Type

Elective Course

Course Level

Bachelor's Degree

Year of Study

Semester

ECTS

Name of Lecturer(s)

Professor Şeyda Kılıçoğlu

Learning Outcomes

At the end of this course, the students;

Will be able to introduce numbers and integers, greatest common divisors.
Will be able explain Divisibility and remainders.
Will be able to use the basic results of modular arithmetic.
Will be able to solve congruences with chinese remainder theorem.
Will be able to explain new methods for solving diophantine equations.

Mode of Delivery

Face to face

Prerequisites

Recommended Optional Programme Components

Course Description

The course content includes the following topics: divisibility of integers, prime numbers, significant functions in number theory, congruences, linear congruence, the uniqueness of prime factorization of integers, primitive roots and indices, quadratic residues (quadratic), cryptography and its applications in daily life, and continued fractions.

Course Contents

WEEK	TOPICS
1^st Week	Properties of set of integers, divisibility, division algorithm
2^nd Week	Modular arithmetic, basic theories and results numbers, OBEB, OKEK and various results
3^rd Week	Euclidean algorithm, factorization techniques
4^th Week	Congruences, linear congruences
5^th Week	Linear equation systems and chinese Remainder theorem
6^th Week	Higher order congruences
7^th Week	Midterm
8^th Week	Diafont equations and their solution with Bezaut's lemma
9^th Week	Continuing (chain) fractions
10^th Week	Quadratic congruences and solutions
11^th Week	Arithmetic functions Euler function
12^th Week	Legendre symbol, Wilson's theorem
13^th Week	Primitive roots
14^th Week	Primitive roots
15^th Week	General review

Recommended or Required Reading

A. Kaya, "Sayılar Kuramına Giriş", Ege Üniversitesi Yayınları, No: 112, 1988, İzmir.
H. Griffin, "Elementary Theory of Numbers", McGraw Hill, 1954.
Sait Akkaş ,. Hacısalihoğlu Hilmi ,Zühtü Özel, Arif Sabuncuoğlu Soyut Matematik
Nasibov H.Ferhat, Hacısalihoğlu Hilmi, Kılıçoğlu Şeyda .Sayılar Teorisi 2010

Planned Learning Activities and Teaching Methods

Lecture
Practice
Other

Assessment Methods and Criteria

	Quantity	Percentage (%)
Mid-term	1	40
Practice	1	5
Attendance	1	5
Total(%)		50
Contribution of In-term Studies to Overall Grade(%)		50
Contribution of Final Examination to Overall Grade(%)		50
Total(%)		100

ECTS Allocated Based on Student Workload

Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Midterm exam	1	2	2
Preparation for Quiz
Individual or group work	13	2	26
Preparation for Final exam	1	18	18
Course hours	13	3	39
Preparation for Midterm exam	1	15	15
Laboratory (including preparation)
Final exam	1	2	2
Homework
Performance Practice	1	18	18
Total Work Load			120
Total Work Load / 30 (h)			4
ECTS Credit of the Course			4

Language of Instruction

Turkish

Work Placement(s)

Programme Qualifications / Learning Outcomes

	LO1	LO2	LO3	LO4	LO5
K1
K2
K3
K4
K5
K6
K7
K8
K9	X	X	X	X	X
K10	X	X	X	X	X