Course Code:
MATH 423
Course Type:
Area Elective
P:
3
Lab:
0
Laboratuvar Saati:
0
Credits:
3
ECTS:
7
Course Language:
English
Course Objectives:
To introduce basic facts about representation theory of groups and to find a representation of a group as a group of matrices in order to have a concrete description of this group.
Course Content:

Generalities and basic definitions. Sums, quotients, tensor products, characters and decompositions of representations. Group algebra. Generalities on algebras and modules, semi-simple modules. Invertible and nilpotent elements. Idempotents. The Jacobson radical. Semi-simple and local algebras. Projective modules. Primitive decompositions and points. Blocks of an algebra. Duality. Symmetric algebras.

Course Methodology:
1: Lecture, 2: Problem Solving
Course Evaluation Methods:
A: Written examination, B: Homework

## Vertical Tabs

### Course Learning Outcomes

 Learning Outcomes Teaching Methods Assessment Methods 1) Visualizes groups as matrices 1,2 A 2) Uses group algebra to construct the regular representation of a group 1,2 A 3) Uses FG-modules to obtain information about representations of a group G over a field F 1,2 A 4) Computes the character table of a group 1,2 A 5) Applies tensor products to find all the irreducible characters of a direct product of groups 1,2 A 6) Uses blocks of an algebra to get information about its modules 1,2 A

### Course Flow

 Week Topics Study Materials 1 Generalities and basic definitions Textbook 2 Sums, quotients, tensor products, characters Textbook 3 Decompositions of representations Textbook 4 Group algebra Textbook 5 Generalities on algebras and modules, semi-simple modules Textbook 6 Invertible and nilpotent elements Textbook 7 Idempotents Textbook 8 The Jacobson radical Textbook 9 Semi-simple and local algebras Textbook 10 Projective modules Textbook 11 Primitive decompositions and points Textbook 12 Blocks of an algebra Textbook 13 Duality Textbook 14 Symmetric algebras Textbook

### Recommended Sources

 Textbook Representations and characters of groups. Gordon James, Martin Liebeck. Additional Resources Representations of finite groups and associative algebras. C.W. Curtis, I. Reiner.

### Material Sharing

 Documents Assignments Exams

### Assessment

 IN-TERM STUDIES NUMBER PERCENTAGE Mid-terms 2 100 Quizzes Assignments Total 100 CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE 40 CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE 60 Total 100

 COURSE CATEGORY Expertise/ Field Courses

### Course’s Contribution to Program

 No Program Learning Outcomes Contribution 1 2 3 4 5 1 The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry) x 2 Acquiring fundamental knowledge on fundamental research fields in mathematics x 3 Ability form and interpret the relations between research topics in mathematics x 4 Ability to define, formulate and solve mathematical problems X 5 Consciousness of professional ethics and responsibilty x 6 Ability to communicate actively x 7 Ability of self-development in fields of interest x 8 Ability to learn, choose and use necessary information technologies x 9 Lifelong education x

### ECTS

 Activities Quantity Duration (Hour) Total Workload (Hour) Course Duration (14x Total course hours) 14 3 42 Hours for off-the-classroom study (Pre-study, practice) 14 6 84 Mid-terms (Including self study) 2 15 30 Quizzes - - - Assignments - - - Final examination (Including self study) 1 20 20 Total Work Load 176 Total Work Load / 25 (h) 7.04 ECTS Credit of the Course 7