Erciyes University - Info Package

Course unit title	Level of course unit	Course unit code	Type of course unit	Semester of course unit	Local credit	ECTS credit	Syllabus
GROUP THEORY- II	Second cycle	MAT 542		2	7.50	7.50	Print

Description of course unit

Prerequisites and course requisities	No
Language of instruction	Turkish
Coordinator	Prof. dr. Himmet CAN
Lecturer(s)	Prof. dr. Himmet CAN
Teaching assitant(s)	No
Mode of delivery	Face to face
Course objective	The objective of the course is to provide the students with the knowledge about more advanced topics in group theory. Students must have a background on the basic group theory.
Course description	The fundamental concepts of the group theory such as free groups, generators and relation, direct sums, group actions, orbits and stabilizers, Burnside's lemma, Sylow's theorems, Nilpotent and solvable groups, Topological groups, Krull topology.

Course contents

1	Free groups
2	Generators and relations
3	Free abelian groups
4	Direct sums
5	Group actions
6	Orbits and stabilizers
7	Burnside''s lemma
8	Class equation
9	Sylow''s theorems
10	Nilpotent and solvable groups
11	Topological groups
12	Topological subgroups
13	Krull topology
14	Applications of Topological groups
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Learning outcomes of the course unit

1	Definition of the free groups and their examples
2	To have the basic concepts of generators and relation, direct sums of subgroups
3	To comprehend the groups actions, orbits and stabilizers
4	To learn the Burnside's lemma
5	To reinforce the concept of class equation
6	To comprehend the Sylow's theorems, nilpotent and solvable groups.
7	To have the fundamental concepts of topological groups
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*Contribution level of the course unit to the key learning outcomes

1	Gain fundamental knowledges of theoritical framework
2	Gain fundamental knowledges of practical framework
3	Tracing worldwide evolutions in theoritical and pratical frameweork
4	Acquire the ability of working in a teamwork
5	Gain the abilities of taking initiatives, improving creative solutions and considering analytically.
6	Gain the abilities of reaching to the people or groups who are in the theoritical or/and the pratical area.
7	Acquire the abilities of speaking a foreign language to reach to the people or groups who are in the theoritical or/and the pratical area.
8	Acquire the abilities of using some software or hardware in the area.
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Number of stars refer to level of contribution from 1 (the least) to 5 (the most)

Planned learning activities, teaching methods and ECTS work load

	Quantity	Time (hour)	Quantity*Time (hour)
Lectures (face to face teaching)	14	3	42
Study hours out of classroom (study before and after the class)	14	7	98
Homework	0	0	0
Presentation / seminar	0	0	0
Quiz	0	0	0
Preparation for midterm exams	1	20	20
Midterm exams	1	2	2
Project (term paper)	0	0	0
Laboratuar	0	0	0
Field study	0	0	0
Preparation for final exam	1	18	18
Final exam	1	2	2
Research	1	5	5
Total work load			187
ECTS			7.50

Assessment methods and criteria

Evaluation during semester	Quantity	Percentage
Midterm exam	1	40
Quiz	0	0
Homework	0	0
Semester total		40
Contribution ratio of evaluation during semester to success		40
Contribution ratio of final exam to success		60
General total		100

Recommended and required reading

Textbook	K. Spindler, Abstract algebra with applications, Marcel Dekker, New York, 1994.
Additional references	Y. Chow, Modern abstract algebra, Gordon and Breach Science Inc., New York, 1976.

Files related to the course unit