Semester  Course Unit Code  Course Unit Title  L+P  Credit  Number of ECTS Credits 
7  MATH443  INTRODUCTION TO ANALYTIC NUMBER THEORY  3+0  3  6 
Language of Instruction

English

Level of Course Unit

First Cycle

Department / Program

MATHEMATICS

Mode of Delivery

Face to Face

Type of Course Unit

Elective

Objectives of the Course

This course aims to study number theory via analysis.

Course Content

Arithmetical functions, Dirichlet multiplication, averages of arithmetical functions, distribution of prime numbers, Dirichlet’s theorem

Course Methods and Techniques


Prerequisites and corequisities

None

Course Coordinator

None

Name of Lecturers

Dr.Öğr.Üyesi Haydar Göral

Assistants

None

Work Placement(s)

No

Recommended or Required Reading
Resources

Introduction to Analytic Number Theory, Tom M. Apostol


Introduction to Analytic Number Theory, Tom M. Apostol








Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"
Assessment Methods and Criteria
InTerm Studies

Midterm exams

2

%
60

Quizzes

0

%
0

Homeworks

0

%
0

Other activities

0

%
0

Laboratory works

0

%
0

Projects

0

%
0

Final examination

1

%
40

Total

3

%
100

ECTS Allocated Based on Student Workload
Activities

Total Work Load

Weekly Course Time

3

14

42

Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.)

4

14

56

Exams and Exam Preparations

7

12

84

Total Work Load
 

Number of ECTS Credits 6
182

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
No  Learning Outcomes 
1
 to become comfortable with arithmetical functions 
2
 to gain an understanding of averages of arithmetical functions 
3
 understanding the distribution of prime numbers 
Weekly Detailed Course Contents
Week  Topics  Study Materials  Materials 
1 
prime numbers



2 
some arithmetical functions



3 
Dirichlet product



4 
divisor functions



5 
averages



6 
some elementary asymptotic formulas



7 
The average order of Möbius and Mangoldt



8 
Chebyshev functions



9 
prime counting function



10 
Tauberian theorems



11 
partial sums of reciprocals of the primes



12 
Dirichlet characters



13 
Dirichlet theorem



14 
primes in arithmetic progressions



Contribution of Learning Outcomes to Programme Outcomes
Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant
https://obs.iyte.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=227343&lang=en