Mathematics (English)
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code:

MATH321

Course Name:

Group Theory

Semester:

Fall

Course Credits:

ECTS

Language of instruction:

English

Course Condition:

Does the Course Require Work Experience?:

Type of course:

Compulsory Courses

Course Level:

Bachelor

TR-NQF-HE:6. Master`s Degree

QF-EHEA:First Cycle

EQF-LLL:6. Master`s Degree

Mode of Delivery:

Face to face

Course Coordinator:

Prof. Dr. SELÇUK DEMİR

Course Lecturer(s):

Prof. Dr. Ali Nesin

Course Assistants:

Course Objective and Content

Course Objectives:	The aim of the course is to learn the basics of group theory, one of the basic concepts of algebra.
Course Content:	The content of the course consists of groups, symmetries, dihedral groups, permutation groups, direct and semi-direct product of groups, structure of finitely generated abelian groups, factor groups, homomorphism theorems, group actions, Sylow theorems.

Learning Outcomes

The students who have succeeded in this course;
1) Understand dihedal groups, permutations groups and other basic examples of groups with their structure.
2) Understand the structure of cyclic groups, factor groups and homomorphism theorems.
3) Understand the structure of finitely generated abelian groups.
4) Understand basics of group actions.
5) Understand the Sylow Theorem.

Course Flow Plan

Week	Subject	Related Preparation
1)	Groups and examples of groups
2)	Symmetries
3)	Elementary properties of groups, subgroups
4)	The structure of cyclic groups
5)	Group of permutations, dihedral groups
6)	Direct product of groups, semidirect products
7)	The structure of finitely generated abelian groups
8)	Midterm Exam
9)	Factor groups
10)	Homomorphism theorems
11)	Actions of groups
12)	Applications of the group actions to counting: Burnside formula
13)	Sylow theorems
14)	Free abelian groups, the proof of the fundamental theorem of finitely generated abelian groups

Sources

Course Notes / Textbooks:	John B. Fraleigh and Neal Brand - “A First Course in Abstract Algebra”
References:	Lecture notes

Course - Program Learning Outcome Relationship

Course Learning Outcomes	1	2	3	4	5
Program Outcomes
1) Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline.
2) Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems.
3) Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques.
4) Have the ability to think analytically and use the time effectively in the process of deduction.
5) Have the ability to search the literature, understand and interpret scientific articles.
6) Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License.
7) Have the ability to work efficiently in interdisciplinary teams.
8) Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations.
9) Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards.
10) Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria.
11) Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves.

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Average	3 Highest

	Program Outcomes	Level of Contribution
1)	Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline.	2
2)	Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems.
3)	Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques.
4)	Have the ability to think analytically and use the time effectively in the process of deduction.	3
5)	Have the ability to search the literature, understand and interpret scientific articles.
6)	Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License.
7)	Have the ability to work efficiently in interdisciplinary teams.
8)	Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations.
9)	Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards.
10)	Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria.	3
11)	Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves.

Assessment & Grading

Semester Requirements	Number of Activities	Level of Contribution
Midterms	1	% 40
Final	1	% 60
total		% 100
PERCENTAGE OF SEMESTER WORK		% 40
PERCENTAGE OF FINAL WORK		% 60
total		% 100

Workload and ECTS Credit Calculation

Activities	Number of Activities	Preparation for the Activity	Spent for the Activity Itself	Completing the Activity Requirements	Workload
Course Hours	13	0	3		39
Study Hours Out of Class	13	0	3		39
Midterms	1	0	15		15
Final	1	0	25		25
Total Workload					118