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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 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.
   Learning outcomes Up

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

  1. describe a linear representation of a group.

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics

    Method of assessment

    1. Written exam
    2. Homework assignment
  2. describe the characters of a group.

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics

    Method of assessment

    1. Written exam
    2. Homework assignment
  3. determine whether the given representation is irreducible or not.

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics

    Method of assessment

    1. Written exam
    2. Homework assignment
  4. identify the irreducible characters of a finite group.

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics

    Method of assessment

    1. Written exam
    2. Homework assignment
  5. calculate the character tables of finite groups.

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics

    Method of assessment

    1. Written exam
    2. Homework assignment
   Contents Up
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: Mid-term
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 Up
Method of assessment Week number Weight (%)
Mid-terms: 8 30
Other in-term studies: 0
Project: 0
Homework: 3, 5, 7, 9, 11, 13 20
Quiz: 0
Final exam: 16 50
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face 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 mid-term exam: 15 2
Mid-term: 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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