ECTS - Galois Theory
Galois Theory (MATH546) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Galois Theory | MATH546 | Area Elective | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| 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 aims to give the fundamentals of field extensions and Galois theory and some applications of Galois theory. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Characteristic of a field, the Frobenius morphism, field extensions, algebraic extensions, primitive elements, Galois extensions, automorphisms, normal extensions, separable and inseparable extensions, the fundamental theorem of Galois theory, finite fields, cyclotomic extensions, norms and traces, cyclic extensions, discriminants, polynomials of d |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Field Extensions | Read related sections in references |
| 2 | Automorphisms | Read related sections in references |
| 3 | Normal Extensions | Read related sections in references |
| 4 | Separable and Inseparable Extensions | Read related sections in references |
| 5 | Review | |
| 6 | Midterm Exam 1 | |
| 7 | The Fundamental Theorem of Galois Theory | Read related sections in references |
| 8 | Finite Fields | Read related sections in references |
| 9 | Cyclotomic Extensions | Read related sections in references |
| 10 | Norms and Traces | Read related sections in references |
| 11 | Review | |
| 12 | Midterm Exam 2 | |
| 13 | Cyclic Extensions | Read related sections in references |
| 14 | Discriminants | Read related sections in references |
| 15 | Review | |
| 16 | Final Exam |
Sources
| Course Book | 1. P. Morandi, Field and Galois Theory, Springer-Verlag, New York, 1996 |
|---|---|
| Other Sources | 2. J. S. Milne, Fields and Galois Theory, Lecture Notes, 1998, avaliable at: http://www.jmilne.org/math/CourseNotes/FT.pdf |
| 3. J-P. Escofier, Galois Theory, Springer-Verlag, New York, 2001 | |
| 4. E. Artin, Galois Theory, Dover Publications, 1998 |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 4 | 10 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 50 |
| 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 | ||
| 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 | |||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | |||
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 14 | 3 | 42 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 4 | 3 | 12 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 7 | 14 |
| Prepration of Final Exams/Final Jury | 1 | 9 | 9 |
| Total Workload | 77 | ||