1	Course Title:	GALOIS THEORY
2	Course Code:	MAT4061
3	Type of Course:	Optional
4	Level of Course:	First Cycle
5	Year of Study:	4
6	Semester:	7
7	ECTS Credits Allocated:	5
8	Theoretical (hour/week):	3
9	Practice (hour/week) :	0
10	Laboratory (hour/week) :	0
11	Prerequisites:	None
12	Recommended optional programme components:	None
13	Language:	Turkish
14	Mode of Delivery:	Face to face
15	Course Coordinator:	Prof. Dr. İSMAİL NACİ CANGÜL
16	Course Lecturers:	Yrd. Doç. Dr. Musa DEMİRCİ Yrd. Doç. Dr. Hacer ÖZDEN
17	Contactinformation of the Course Coordinator:	cangul@uludag.edu.tr, 0 224 2941657, Fen-Edebiyat Fakültesi Matematik Bölümü
18	Website:
19	Objective of the Course:	The aim of this course is to give students some basic concepts of Galois Theory, to teach the techniques related to the solutions of polynomial equations.
20	Contribution of the Course to Professional Development

21

Learning Outcomes:

1 to be able to solve the 2nd, 3rd and 4th order polynomial equations; 2 to be able to state the fundamental theorem of Galois theory; 3 to be able to state the relations between groups, rings and polynomials; 4 to be able to classify domains, fields, subrings, subfields and ideals and give examples of those; 5 to let the students know the differences between rings, fields and domains;

22	Course Content:

Week	Theoretical	Practical
1	Rings
2	Integral Domains and Fields
3	Homomorphism and Ideals
4	Quotient rings
5	Polinomial rings
6	Prime and maximal ideals
7	Irreducible polinomials
8	The general solution methods fort the third and fourth order equations
9	Field extensions and finite fields
10	Midterm exam and general review
11	Galois group
12	The roots of the unit and fields extensions
13	The fundamental theorem Galois Theory
14	Quadratic, cubic and quartic Galois groups

23	Textbooks, References and/or Other Materials:	J. ROTMAN, Galois Theory, Springer, 1998; İ. N. CANGÜL, Galois Theory Lecture Notes
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	1	40
Quiz	0	0
Homeworks, Performances	0	0
Final Exam	1	60
Total	2	100
Contribution of Term (Year) Learning Activities to Success Grade		40
Contribution of Final Exam to Success Grade		60
Total		100
Measurement and Evaluation Techniques Used in the Course
Information

25

ECTS / WORK LOAD TABLE

Activites	NUMBER	TIME [Hour]	Total WorkLoad [Hour]
Theoretical	14	3	42
Practicals/Labs	0	0	0
Self Study and Preparation	14	4	56
Homeworks, Performances	0	0	0
Projects	0	0	0
Field Studies	0	0	0
Midtermexams	1	20	20
Others	0	0	0
Final Exams	1	30	30
Total WorkLoad			148
Total workload/ 30 hr			4,93
ECTS Credit of the Course			5

26	CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS
PQ1 PQ2 PQ3 PQ4 PQ5 PQ6 PQ7 PQ8 PQ9 PQ10 LO1 5 0 0 0 0 0 0 0 0 0 LO2 2 4 0 0 4 0 0 5 0 0 LO3 0 4 0 0 5 0 0 5 0 0 LO4 0 0 0 0 5 0 0 0 0 0 LO5 0 0 0 0 4 0 0 4 0 0

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High