MATHEMATICS (TURKISH, PHD)
PhD	TR-NQF-HE: Level 8	QF-EHEA: Third Cycle	EQF-LLL: Level 8

Course Introduction and Application Information

Course Code	Course Name	Semester	Theoretical	Practical	Credit	ECTS
MAT6001	Advanced Algebra I	Spring	3	0	3	8

This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction:	Turkish
Type of course:	Departmental Elective
Course Level:
Mode of Delivery:	Face to face
Course Coordinator :	Assoc. Prof. ATABEY KAYGUN
Recommended Optional Program Components:	None
Course Objectives:	To provide the necessary algebraic tools and techniques to a graduate student who would go into a doctoral program in mathematics.

Learning Outcomes

The students who have succeeded in this course;
A student who finished this course successfully will have acquired the necessary basic knowledge to be able to follow a course in algebra in a doctoral program in mathematics.

Course Content

Groups. Symmetric groups. Matrix groups. Abelian groups. Groups by generators and relations. p-groups. Central series and nilpotent groups. Group actions. Sylow Theorems. Group representations. Finite groups and their characters. Character tables. Commutative rings and fields. Polynomial rings. Rings of matrices. Ideals, subrings and modules. Commutative rings and fields. Polynomial rings. Rings of matrices. Ideals, subrings and modules. Chains of ideals and modules. Artinian and Noetherian rings. Hopkins-Levitzki Theorem. Chains of ideals and modules. Artinian and Noetherian rings. Hopkins-Levitzki Theorem.

Weekly Detailed Course Contents

Week	Subject	Related Preparation
1)	Set theory.
2)	Groups. Symmetric groups. Matrix groups. Abelian groups.
3)	Groups by generators and relations.
4)	p-groups. Central series and nilpotent groups. Group actions. Sylow Theorems.
5)	p-groups. Central series and nilpotent groups. Group actions. Sylow Theorems.
6)	Group representations.
7)	Group representations.
8)	Finite groups and their characters. Character tables.
9)	Finite groups and their characters. Character tables.
10)	Calculations of group character tables.
11)	Commutative rings and fields. Polynomial rings. Rings of matrices. Ideals, subrings and modules.
12)	Commutative rings and fields. Polynomial rings. Rings of matrices. Ideals, subrings and modules.
13)	Chains of ideals and modules. Artinian and Noetherian rings. Hopkins-Levitzki Theorem.
14)	Chains of ideals and modules. Artinian and Noetherian rings. Hopkins-Levitzki Theorem.

Sources

Course Notes / Textbooks:	Instructor's own lectures. S. Lang, "Algebra"
References:

Evaluation System

Semester Requirements	Number of Activities	Level of Contribution
Project	1	% 20
Midterms	2	% 40
Final	1	% 40
Total		% 100
PERCENTAGE OF SEMESTER WORK		% 40
PERCENTAGE OF FINAL WORK		% 60
Total		% 100

ECTS / Workload Table

Activities	Number of Activities	Duration (Hours)	Workload
Course Hours	14	3	42
Study Hours Out of Class	14	7	98
Project	1	33	33
Midterms	2	2	4
Final	1	23	23
Total Workload			200

Contribution of Learning Outcomes to Programme Outcomes

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

Program Outcomes

Level of Contribution