ECTS - Galois Theory
Galois Theory (MATH546) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Galois Theory | MATH546 | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| MATH541 |
| Course Language | English |
|---|---|
| Course Type | N/A |
| Course Level | Natural & Applied Sciences Master's Degree |
| 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 | |
|---|---|
| Major Area Courses | |
| Supportive Courses | X |
| 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 | Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area. | |||||
| 2 | Has the ability to obtain, to evaluate, to interpret and to apply information by doing scientific research. | |||||
| 3 | Can apply gained knowledge and problem solving abilities in inter-disciplinary research. | |||||
| 4 | Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary. | |||||
| 5 | Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study. | |||||
| 6 | Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework. | |||||
| 7 | Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility. | |||||
| 8 | Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation. | |||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | |||||
| 10 | Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge. | |||||
| 11 | Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | |||||
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 | ||