# Algebraic Number Theory (MATH542) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Algebraic Number Theory MATH542 Area Elective 3 0 0 3 5
Pre-requisite Course(s)
Consent of the Department
Course Language English Elective Courses Ph.D. Face To Face Lecture, Question and Answer. This course is designed to give the essential elements of algebraic number theory. The students who succeeded in this course; understand the main theorems in algebraic number theory define and construct examples of number theoretic structures given in the content of the course be able to apply the main theorems of algebraic number theory be able to reproduce simple proofs of some theorems in algebric number theory. Integers, norm, trace, discriminant, algebraic integers, quadratic integers, Dedekind domains, valuations, ramification in an extension of Dedekind domains, different, ramification in Galois extensions, ramification and arithmetic in quadratic fields, the quadratic reciprocity law, ramification and integers in cyclotomic fields, Kronecker-Weber the

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Integers, Norm, Trace
2 Discriminant, Algebraic integers,
4 Dedekind domains, Valuations
5 Ramification in an extension of Dedekind domains,
6 Different, Ramification in Galois extensions
7 Ramification and arithmetic in quadratic fields,
9 Ramification and integers in cyclotomic fields
10 The Kronecker-Weber Theorem on Abelian extensions
11 The Dirichlet’s Theorem on the finiteness of the class group
12 The Dirichlet’s Theorem on units
13 Hermite-Minkowski Theorem
14 Fermat’s Last Theorem.
15 Review
16 Final Exam

### Sources

Course Book 1. Algebraic Number Theory, I.N. Stewart and D.O. Tall, Chapman & Hall, 1995 2. Algebraic Number Fields, Gerald J. Janusz, AMS,1996 3. Number Theory: Algebraic Numbers and Functions, H.Koch, AMS,2005

### Evaluation System

Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 5 30
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 1 30
Final Exam/Final Jury 1 40
Toplam 7 100
 Percentage of Semester Work 60 40 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Ability to carry out advanced research activities, both individual and as a member of a team
2 Ability to evaluate research topics and comment with scientific reasoning
3 Ability to initiate and create new methodologies, implement them on novel research areas and topics
4 Ability to produce experimental and/or analytical data in systematic manner, discuss and evaluate data to lead scintific conclusions
5 Ability to apply scientific philosophy on analysis, modelling and design of engineering systems
6 Ability to synthesis available knowledge on his/her domain to initiate, to carry, complete and present novel research at international level
7 Contribute scientific and technological advancements on engineering domain of his/her interest area
8 Contribute industrial and scientific advancements to improve the society through research activities

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours) 16 3 48
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 14 3 42
Presentation/Seminar Prepration
Project
Report
Homework Assignments 5 3 15
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 1 10 10
Prepration of Final Exams/Final Jury 1 10 10