Syllabus ( MATH 523 )

Basic information


Course title: 
Representation Theory of Finite Groups 
Course code: 
MATH 523 
Lecturer: 
Assist. Prof. Roghayeh HAFEZIEH

ECTS credits: 
7.5 
GTU credits: 
3 (3+0+0) 
Year, Semester: 
1/2, Fall and Spring 
Level of course: 
Second Cycle (Master's) 
Type of course: 
Area Elective

Language of instruction: 
English

Mode of delivery: 
Face to face

Pre and corequisites: 
None 
Professional practice: 
No 
Purpose of the course: 
The goal of this course is to give a graduatelevel introduction to representation theory. Representation theory is concerned with the ways of writing a group as a group of matrices and it provides one of the keys to a proper understanding of finite groups. 



Learning outcomes


Upon successful completion of this course, students will be able to:

describe a linear representation of a group.
Contribution to Program Outcomes

Define and manipulate advanced concepts of Mathematics
Method of assessment

Written exam

Homework assignment

describe the characters of a group.
Contribution to Program Outcomes

Define and manipulate advanced concepts of Mathematics
Method of assessment

Written exam

Homework assignment

determine whether the given representation is irreducible or not.
Contribution to Program Outcomes

Define and manipulate advanced concepts of Mathematics
Method of assessment

Written exam

Homework assignment

identify the irreducible characters of a finite group.
Contribution to Program Outcomes

Define and manipulate advanced concepts of Mathematics
Method of assessment

Written exam

Homework assignment

calculate the character tables of finite groups.
Contribution to Program Outcomes

Define and manipulate advanced concepts of Mathematics
Method of assessment

Written exam

Homework assignment


Contents


Week 1: 
Rudiments of Group Theory

Week 2: 
Groups and their actions on sets

Week 3: 
General Linear Groups

Week 4: 
Modules Over Rings and Algebras

Week 5: 
Simple Modules , Schur’s Lemma

Week 6: 
Actions of Groups on Vector Spaces

Week 7: 
Representations

Week 8: 
Midterm

Week 9: 
Group Algebras, Modules

Week 10: 
Complete Reducibility

Week 11: 
Wedderburn’s Theorem

Week 12: 
Characters

Week 13: 
Orthogonality Relation

Week 14: 
The Character Table

Week 15*: 
Induction

Week 16*: 
Final exam 
Textbooks and materials: 
Groups and Representations, Alperin J. and Bell R. 
Recommended readings: 
Representations of finite groups, Andrew Baker 

* Between 15th and 16th weeks is there a free week for students to prepare for final exam.




Assessment



Method of assessment 
Week number 
Weight (%) 

Midterms: 
8 
30 
Other interm studies: 

0 
Project: 

0 
Homework: 
3, 5, 7, 9, 11, 13 
20 
Quiz: 

0 
Final exam: 
16 
50 

Total weight: 
(%) 



Workload



Activity 
Duration (Hours per week) 
Total number of weeks 
Total hours in term 

Courses (Facetoface teaching): 
3 
14 

Own studies outside class: 
4 
14 

Practice, Recitation: 
0 
0 

Homework: 
3 
6 

Term project: 
0 
0 

Term project presentation: 
0 
0 

Quiz: 
0 
0 

Own study for midterm exam: 
15 
2 

Midterm: 
3 
1 

Personal studies for final exam: 
15 
2 

Final exam: 
3 
1 



Total workload: 



Total ECTS credits: 
* 

* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)



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