Graduate
Institute of Graduate Studies
Mathematics And Computer Science
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Theory of Groups

Course CodeSemester Course Name LE/RC/LA Course Type Language of Instruction ECTS
YMB0003 Theory of Groups 3/0/0 DE Turkish 7
Course Goals
At the end of this course, the students  will be able to understand the basic results of  Groups,Sylow Subgroups,Abelian Groups,Category and Fuctor,Free Groups,Permutation Groups,Transitive and Primitive Groups,Regular Normal Subgroups and develop their knowledges about about this subjects
Prerequisite(s) none
Corequisite(s) none
Special Requisite(s) none
Instructor(s) Assoc. Prof. Neşe YELKENKAYA
Course Assistant(s) No
Schedule Look at the program
Office Hour(s) Prof. Dr. Erhan GÜZEL - 3-A-07, Monday 10:00-11:00,
Teaching Methods and Techniques Lecture, discussion.
Principle Sources B. Baumslag , B. Chandler, Group Theory, Schaum’s Outline Series, McGraw-Hill Book Company, 1968

G. Birkhoff,S. Maclane, A Survey of modern Algebra, macmillian, New York,1965

J.F. Fraleigh, A First Course ,n Abstract Algebra, Addison-Wesley, London, 1970

I. N. Goldstein, Abstract Algebra, Prentice Hall, new York, 1973

S, Lange, Algebra ,Addison-Wesley, Reading-Massachusetts, 1965
Other Sources -
Course Schedules
Week Contents Learning Methods
1. Week Definition of Group Oral and written presentation
2. Week Subgroups,Cyclic Groups Oral and written presentation
3. Week Symmetric Groups, Index Oral and written presentation
4. Week Normal Subgroup Oral and written presentation
5. Week Quotient Group Oral and written presentation
6. Week Group Homomorphisms,Kernel and Izomorphism Theorems Oral and written presentation
7. Week Sylow Subgroups Oral and written presentation
8. Week Midterm Written.
9. Week Abelian Groups Oral and written presentation
10. Week Categories and Functors Oral and written presentation
11. Week Free Groups Oral and written presentation
12. Week Permutation Groups Oral and written presentation
13. Week Transitive and Primitive Groups Oral and written presentation
14. Week Regular Normal Subgroups Oral and written presentation
15. Week Research Problems Oral and written presentation
16. Week Final Exam Week Written.
17. Week Final Exam Week Written.
Assessments
Evaluation tools Quantity Weight(%)
Homework / Term Projects / Presentations 2 40
Final Exam 1 60


Program Outcomes
PO-1Have scientific research in mathematics and computer science in the level of theoretical and practical knowledge.
PO-2On the basis of undergraduate level qualifications, develop and deepen the same or a different areas of information at the level of expertise, and analyze and interpret by using statistical methods
PO-3Develop new strategic approaches for the solution of complex problems encountered in applications related to the field and unforeseen and take responsibility for the solution.
PO-4Evaluate critically skills acquired in the field of information in the level of expertise and assess the learning guides.
PO-5Transfer current developments in the field and their work to the groups inside and outside the area supporting with quantitative and qualitative datas as written, verbal and visual by a systematic way.
PO-6Use information and communication technologies with computer software in advanced level.
PO-7Develop efficient algorithms by modeling problems faced in the field and solve such problems by using actual programming languages.
PO-8Respect to social, scientific, cultural and ethical values at the stages of data collection related to the field, interpretation, and implementation.
PO-9To solve problems related to the field, establish functional interacts by using strategic decision making processes.
PO-10Establish and discuss in written, oral and visual communication in an advanced level by using at least one foreign language.
Learning Outcomes
LO-1Know theoretical properties of Groups
LO-2 Know the structure of Sylow Subgroups
LO-3Have some knowledge about the relation between Group Theory and Category and Fuctor,Free Groups
LO-4Know some information about Free Groups,Permutation Groups,Transitive and Primitive Groups
LO-5Know theoretical properties of Regular Normal Subgroups
Course Assessment Matrix:
Program Outcomes - Learning Outcomes Matrix
 PO 1PO 2PO 3PO 4PO 5PO 6PO 7PO 8PO 9PO 10
LO 1
LO 2
LO 3
LO 4
LO 5