The aim of this course is to give a background to understand the articles related the areas of Group Algebra,Semisimple Group Algebra,Splitting Fields and Absolutely Irreducible Modules, Characters, Character Tables, Representations of Abelian Groups, Induced Characters, Permutation Groups and to do research on this subject.
Prerequisite(s)
Advanced Algebra,Group Theory
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
-L. Dornhoff, Group representation Theory,Part A , Marcel Dekker,Inc., New York,1971
-J.P.Serre, Représentations Linéaires des Groupes Finis, Hermann,Paris,1967
Other Sources
- I. M. Isaacs, Character Theory of Finite Groups, Academic Press, 1976.
Course Schedules
Week
Contents
Learning Methods
1. Week
Group Algebra.
Written and Oral presentation
2. Week
Theory of Semisimple Rings.
Written and Oral presentation
3. Week
Theory of Semisimple Rings.
Written and Oral presentation
4. Week
Semisimple Group Algebras.
Written and Oral presentation
5. Week
Splitting Fields and Absolutely Irreducible Modules
Written and Oral presentation
6. Week
Characters
Written and Oral presentation
7. Week
Multiplicities, Generalized Characters
Written and Oral presentation
8. Week
Character Tables
Written and Oral presentation
9. Week
Midterm
Written
10. Week
Representations of Abelian Groups
Written and Oral presentation
11. Week
Induced Characters
Written and Oral presentation
12. Week
Induced Characters
Written and Oral presentation
13. Week
Representations of Direct Products.
Written and Oral presentation
14. Week
Permutation Groups.
Written and Oral presentation
15. Week
Final Examinations.
Written
16. Week
Final Examinations.
Written
17. Week
Final Examinations.
Written
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
30
Homework / Term Projects / Presentations
3
20
Final Exam
1
50
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 semi-simple rings with unit.
LO-2
Know the basic concepts in ordinary representation theory.
LO-3
Have some knowledge about character theory.
LO-4
Know some important techniques for the application of characters to group theory.
LO-5
Determine the character table of some special groups.
