The aim of this course is give a background to understand the articles related the areas of General Linear Group,Special linear Group,Projective Linear Groups,Unitayr Group, Symlectic Group and their Representations and character Tables. and to do research on this subject.
Prerequisite(s)
Advanced Algebra,Group Theory
Corequisite(s)
None
Special Requisite(s)
None
Instructor(s)
Professor Erhan GÜZEL
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
L. Dornhoff, Group Representation Theory (Part A),Marcel Dekker,Inc., New York, 1971
B. Huppert, Endliche Gruppen I, springer-Verlag,Berlin-Vew York,1967
N. Biggs, Finite Groups of Automorphisms, London Mathematical Society Lecture Note Series 6,(1971)
Other Sources
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Course Schedules
Week
Contents
Learning Methods
1. Week
General Linear Group
Oral and written presentation.
2. Week
Specific Linear Group
Oral and written presentation.
3. Week
Projective general linear, Unitary group, Symplectic Group and representations and character tables of these groups.
Oral and written presentation.
4. Week
Projective Specific Linear
Oral and written presentation.
5. Week
Unit Group
Oral and written presentation.
6. Week
Symplectic Group
Oral and written presentation.
7. Week
Representation Theory preliminary information
Oral and written presentation.
8. Week
Splitting Fields and absolute irreducible modules
Oral, written presentation and homework.
9. Week
Characters
Oral and written presentation.
10. Week
Multiplicity, Generalized Characters
Oral and written presentation.
11. Week
Character Tables
Oral and written presentation.
12. Week
Induced Characters
Oral and written presentation.
13. Week
Representation of General and Specific linear groups
Oral and written presentation.
14. Week
Representation of Unit and Symplectic linear groups
Oral and written presentation.
15. Week
Character tables For Classic Groups
Oral and written presentation.
16. Week
Final Exam Week
Final Exam
17. Week
Final Exam Week
Final Exam
Assessments
Evaluation tools
Quantity
Weight(%)
Program Outcomes
PO-1
Have ability to develop new mathematical ideas and methods by using high-level mental processes such as creative and critical thinking, problem solving and decision-making.
PO-2
Follow the current developments in the field of mathematics, and make the critical analysis, synthesis and evaluation of new and complex ideas.
PO-3
Understand the interdisciplinary interaction related to Mathematics and play a role in an effective manner in environments that require with the resolution of problems encountered in this process.
PO-4
Defend original views on the discussion of the issues in the field of mathematics with experts and communicate to show competence in oral and written.
PO-5
Do research with high-level national and international scientific working groups, and acquire the responsibility to contribute to the literature by publishing original works in respected scientific journals.
PO-6
Use computer software to solve problems effectively by following the developments in information and communication technologies.
PO-7
Contribute to the solution of social, scientific, cultural and ethical problems encountered issues related to the field and support the development of these values.
PO-8
To solve problems related to the field, establish functional interacts by using strategic decision making processes.
PO-9
Establish and discuss in written, oral and visual communication at an advanced level by using at least one foreign language.
Learning Outcomes
LO-1
Have some knowledge about the structure theory for classical groups
LO-2
Have some knowledge about the structure theory for the character tables of General Linear Group and Special linear Group
LO-3
Have some knowledge about the structure theory for the character tables of Projective Linear Groups
LO-4
Have some knowledge about the structure theory for the representation of General Linear Group and Special linear Group
LO-5
Have some knowledge about the structure theory for the representation of Projective Linear Groups
LO-6
Have some knowledge about the structure theory for the character tables and representations of Projective Linear GroupsUnitayr Group and Symlectic Group
