Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits

Course Details
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 co-requisities 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

Course Category

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
In-Term Studies Quantity Percentage
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
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration 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:
NoLearning 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
WeekTopicsStudy MaterialsMaterials
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
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 4 4 4
C2 4 4 4
C3 4 4 4 4

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant