# 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)
MATH541
Course Language English Elective Courses Ph.D. Face To Face Lecture, Question and Answer. This course aims to give the fundamentals of field extensions and Galois theory and some applications of Galois theory. The students who succeeded in this course; Understand normal and seperable extensions Understand and apply the fundamental theorem of Galois Theory Understand and use norm, trace mappings Understand cyclic extensions Understand and use discriminants 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 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

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 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)
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