1	Course Title:	ANALYTIC NUMBER THEROY
2	Course Code:	MAT3052
3	Type of Course:	Optional
4	Level of Course:	First Cycle
5	Year of Study:	3
6	Semester:	6
7	ECTS Credits Allocated:	5
8	Theoretical (hour/week):	3
9	Practice (hour/week) :	0
10	Laboratory (hour/week) :	0
11	Prerequisites:	None
12	Recommended optional programme components:	None
13	Language:	Turkish
14	Mode of Delivery:	Face to face
15	Course Coordinator:	Prof. Dr. İSMAİL NACİ CANGÜL
16	Course Lecturers:	Doç. Dr. Ahmet TEKCAN, Yrd. Doç. Dr. Musa DEMİRCİ, Yrd. Doç. Dr. Hacer ÖZDEN
17	Contactinformation of the Course Coordinator:	cangul@uludag.edu.tr, 0224 2941756, Fen-Edebiyat Fakültesi, Matematik Bölümü, 16059, Görükle / Bursa
18	Website:	http://www.ismailnacicangul.com/
19	Objective of the Course:	To obtain results concerning the distribution of prime numbers and to make an introduction to analytic numbers
20	Contribution of the Course to Professional Development

21

Learning Outcomes:

1 Can define prime numbers and state the known results on their distribution; 2 Can establish relations between aritmetic functions; 3 Can apply the theorems on the distribution of prime numbers ;

22	Course Content:

Week	Theoretical	Practical
1	Prime number theorem
2	Results of the prime number theorem
3	The analytic proof of prime number theorem
4	Fundamental theorem of arithmetic
5	Arithmetic functions
6	Dirichlet Product of Arithmetic functions
7	Mobious inversion Formula
8	Applications of Mobious inversion Formula
9	Relations between aritmetic functions
10	Primitive roots
11	Quadratic reciprocity law
12	Legendre symbol
13	Quadratic congruences
14	Riemann-Zeta function

23	Textbooks, References and/or Other Materials:	1. Tom M. Apostol, Introduction to Analytic Number Theory, Springer, 2000 2. Kiran Sridhara Kedlaya, Analytic Number Theory, (Ders notları) MIT, 2006 3. Paul T. Bateman and Harold G. Diamond, Analytic Number Theory an Introductory Course, world Scientific, 2009
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	0	0
Quiz	0	0
Homeworks, Performances	2	50
Final Exam	1	50
Total	3	100
Contribution of Term (Year) Learning Activities to Success Grade		50
Contribution of Final Exam to Success Grade		50
Total		100
Measurement and Evaluation Techniques Used in the Course
Information

25

ECTS / WORK LOAD TABLE

Activites	NUMBER	TIME [Hour]	Total WorkLoad [Hour]
Theoretical	14	3	42
Practicals/Labs	0	0	0
Self Study and Preparation	14	4	56
Homeworks, Performances	2	20	40
Projects	0	0	0
Field Studies	0	0	0
Midtermexams	0	0	0
Others	0	0	0
Final Exams	1	15	15
Total WorkLoad			153
Total workload/ 30 hr			5,1
ECTS Credit of the Course			5

26	CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS
PQ1 PQ2 PQ3 PQ4 PQ5 PQ6 PQ7 PQ8 PQ9 PQ10 LO1 5 0 0 0 0 0 0 3 0 0 LO2 0 4 0 0 5 0 0 3 0 0 LO3 0 4 0 0 5 0 3 3 0 0

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High