TYPE OF COURSE UNIT	Elective Course
LEVEL OF COURSE UNIT	Bachelor's Degree
YEAR OF STUDY	-
SEMESTER	-
NUMBER OF ECTS CREDITS ALLOCATED	4
NAME OF LECTURER(S)	-
LEARNING OUTCOMES OF THE COURSE UNIT	At the end of this course, the students; 1) will be able to introduce Numbers and integers, Greatest common divisors 2) will be able explain Divisibility and remainders 3) will be able to use the basic results of Modular arithmetic 4) will be able to solve congruences with Chinese remainder theorem, 5) will be able to explain new methods for solving diophantine equations
MODE OF DELIVERY	Face to face
PRE-REQUISITES OF THE COURSE	No
RECOMMENDED OPTIONAL PROGRAMME COMPONENT	No
COURSE DEFINITION	Divisibility of integers, prime numbers, important functions in number theory, congruences, linear congruence, uniqueness of prime factorization of integers, primitive roots and indices, quadratic residues (quadratic), cryptography and applications in daily life, continued fractions.
COURSE CONTENTS	WEEK TOPICS 1st Week Properties of Set of Integers, Divisibility, Division Algorithm 2nd Week Modular arithmetic, basic theories and results Numbers, obeb, okek and various results 3rd Week Euclidean Algorithm, Factorization techniques 4th Week Congruences, Linear Congruences 5th Week Linear Equation systems and Chinese Remainder Theorem 6th Week Higher order congruences 7th Week Diafont equations and their solution with Bezaut's lemma 8th Week Midterm Exam 9th Week Continuing (chain) fractions 10th Week Quadratic Congruences and solutions 11th Week Arithmetic functions Euler function 12th Week Legendre symbol, Wilson's theorem 13th Week Primitive Roots 14th Week General review
RECOMENDED 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 WORKLOAD	Activities Number Hours Workload Midterm exam 1 2 2 Preparation for Quiz Individual or group work 1 5 5 Preparation for Final exam 1 10 10 Course hours 14 2 28 Preparation for Midterm exam 1 7 7 Laboratory (including preparation) Final exam 1 2,5 2,5 Homework Performance Practice 13 3 39 Total Workload 93,5 Total Workload / 30 3,11 ECTS Credits of the Course 4
LANGUAGE OF INSTRUCTION	Turkish
WORK PLACEMENT(S)	No