ECTS - Algebraic Number Theory
Algebraic Number Theory (MATH542) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Algebraic Number Theory | MATH542 | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| Consent of the Department |
| Course Language | English |
|---|---|
| Course Type | N/A |
| Course Level | Ph.D. |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Question and Answer. |
| Course Lecturer(s) |
|
| Course Objectives | This course is designed to give the essential elements of algebraic number theory. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | 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, | |
| 3 | Quadratic integers, Dedekind domains | |
| 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, | |
| 8 | Quadratic Reciprocity Law | |
| 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 |
|---|---|
| Other Sources | 2. Algebraic Number Fields, Gerald J. Janusz, AMS,1996 |
| 3. Number Theory: Algebraic Numbers and Functions, H.Koch, AMS,2005 |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| 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 |
|---|---|
| Percentage of Final Work | 40 |
| Total | 100 |
Course Category
| Core Courses | X |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
ECTS/Workload Table
| 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 |
| Total Workload | 125 | ||