Syllabus ( MATH 523 )
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Basic information
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Course title: |
Representation Theory of Finite Groups |
Course code: |
MATH 523 |
Lecturer: |
Assoc. Prof. Dr. Roghayeh HAFEZIEH
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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
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Language of instruction: |
English
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Mode of delivery: |
Face to face
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Pre- and co-requisites: |
None |
Professional practice: |
No |
Purpose of the course: |
The goal of this course is to give a graduate-level 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. |
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Learning outcomes
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Upon successful completion of this course, students will be able to:
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describe a linear representation of a group.
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
Method of assessment
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Written exam
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Homework assignment
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describe the characters of a group.
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
Method of assessment
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Written exam
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Homework assignment
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determine whether the given representation is irreducible or not.
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
Method of assessment
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Written exam
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Homework assignment
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identify the irreducible characters of a finite group.
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
Method of assessment
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Written exam
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Homework assignment
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calculate the character tables of finite groups.
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
Method of assessment
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Written exam
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Homework assignment
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Contents
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Week 1: |
Rudiments of Group Theory
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Week 2: |
Groups and their actions on sets
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Week 3: |
General Linear Groups
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Week 4: |
Modules Over Rings and Algebras
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Week 5: |
Simple Modules , Schur’s Lemma
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Week 6: |
Actions of Groups on Vector Spaces
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Week 7: |
Representations
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Week 8: |
Group Algebras. Midterm Exam.
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Week 9: |
Modules.
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Week 10: |
Complete Reducibility
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Week 11: |
Wedderburn’s Theorem
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Week 12: |
Characters
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Week 13: |
Orthogonality Relation
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Week 14: |
The Character Table. Induction.
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Week 15*: |
-
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Week 16*: |
Final exam |
Textbooks and materials: |
Groups and Representations, Alperin J. and Bell R. |
Recommended readings: |
Representations of finite groups, Andrew Baker |
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* Between 15th and 16th weeks is there a free week for students to prepare for final exam.
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Assessment
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Method of assessment |
Week number |
Weight (%) |
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Mid-terms: |
8 |
30 |
Other in-term studies: |
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0 |
Project: |
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0 |
Homework: |
3, 5, 7, 9, 11, 13 |
20 |
Quiz: |
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0 |
Final exam: |
16 |
50 |
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Total weight: |
(%) |
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Workload
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Activity |
Duration (Hours per week) |
Total number of weeks |
Total hours in term |
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Courses (Face-to-face teaching): |
3 |
14 |
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Own studies outside class: |
4 |
14 |
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Practice, Recitation: |
0 |
0 |
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Homework: |
3 |
6 |
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Term project: |
0 |
0 |
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Term project presentation: |
0 |
0 |
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Quiz: |
0 |
0 |
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Own study for mid-term exam: |
15 |
2 |
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Mid-term: |
3 |
1 |
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Personal studies for final exam: |
15 |
2 |
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Final exam: |
3 |
1 |
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Total workload: |
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Total ECTS credits: |
* |
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* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)
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