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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 5024 ALGEBRAIC 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 Mathematics

Course Objective

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

Learning Outcomes of the Course Unit

1   Will be able to use the structure of number fields and rings of integers. 2   Will be able to use Gaussian integers, Quadratic number fields and Dedekind domains. 3   Will be able to use the properties of Class group and the finiteness of the class number. 4   Will be able to use the Dirichlet s unit theorem and its applications. 5   Will be able to use the Dedekind zeta function. Kummer s approach to Fermat s last theorem.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Number fields. 2 Ring of integers. 3 Gaussian integers, Integrality, Ideals. 4 Norms and Traces, The discriminant. 5 Quadratic number fields. 6 Dedekind domains, Fractional ideals, Unique factorization of ideals, Some arithmetic in Dedekind domains. 7 Geometry of numbers. 8 The ideal class group, Lattices. 9 Midterm 10 Minkowski Theory, Finiteness of the class number. 11 Dirichlet Unit Theorem and Its Applications, Units in quadratic fields. 12 Dedekind Zeta Function. 13 Kummer approach to Fermat last theorem. 14 p-adic integers and p-adic numbers, The p-adic valuation.

Recomended or Required Reading

Textbook(s): [1] Samuel, Pierre, Algebraic Theory of Numbers, Dover publications, 2008 [2] Jarvis, Frazer, Algebraic Number Theory, Springer, 2014 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