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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 5009 ANALYTIC NUMBER THEORY ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

Offered to

Mathematics (English) Mathematics (English)

Course Objective

The aim of this course is to introduce the fundamental concepts in analytic number theory, and show its usage in the whole body of mathematics.

Learning Outcomes of the Course Unit

1   Will be able to use aritmetical functions and their averages, multiplicative and additive functions, Dirichlet multiplication, Moebius inversion. 2   Will be able to use Dirichlet series, Euler product. 3   Will be able to use the properties of the Riemann Zeta function. 4   Will be able to use the Prime number theorem. 5   Will be able to use the Sieve methods.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Arithmetical functions, multiplicative and additive functions. 2 Dirichlet product, Moebius inversion. 3 Partial summation and averages. 4 Distribution of prime numbers. 5 Primes in arithmetic progressions. 6 L-functions. 7 Euler product 8 Midterm 9 The Riemann Zeta function. 10 Dirichlet series. 11 Prime number theorem. 12 Sieve methods. 13 Additive number theory. 14 Sums over primes.

Recomended or Required Reading

Textbook(s): [1] Apostol, T., Introduction to Analytic Number Theory, Springer, 2010. [2] Davenport, H., Multiplicative Number Theory, Springer, 2000. References: Materials: Instructor s notes and presentations

Planned Learning Activities and Teaching Methods

Lecture notes Presentation Problem solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 ASG ASSIGNMENT 3 RPT REPORT 4 FIN FINAL EXAM 5 FCG FINAL COURSE GRADE MTE * 0.30 +ASG +RPT/2 * 0.30 +FIN * 0.40 6 RST RESIT 7 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.30 +ASG +RPT/2 * 0.30 +RST * 0.40 *** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

haydar.goral@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 3 39 Preparations before/after weekly lectures 13 3 39 Preparation for midterm exam 1 15 15 Preparation for final exam 1 25 25 Preparing assignments 10 5 50 Final 1 3 3 Midterm 1 3 3 TOTAL WORKLOAD (hours) 174

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 LO.1 4 3 3 2 2 2 4 3 3 3 LO.2 4 3 3 2 2 2 4 3 3 3 LO.3 4 3 3 2 2 2 4 3 3 3 LO.4 4 3 3 2 2 2 4 3 3 3 LO.5 4 3 3 2 2 2 4 3 3 3