COURSE UNIT TITLE

: INRODUCTION TO REPRESENTATION THEORY

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 4062 INRODUCTION TO REPRESENTATION THEORY ELECTIVE 4 0 0 7

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR ENGIN MERMUT

Offered to

Mathematics (Evening)
Mathematics

Course Objective

The goal of this course is to give an undergraduate-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 of the Course Unit

1   will be able to describe a linear representation of a group.
2   will be able to describe the characters of a group.
3   will be able to determine whether the given representation is irreducible or not.
4   will be able to identify the irreducible characters of a finite group.
5   will be able to calculate the character tables of finite groups.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Groups and Homomorphisms. Vector Spaces and Linear Transformations. § 1., 2., Representations and Characters of Groups G. James and M. Liebeck
2 Group Representations. § 3., Representations and Characters of Groups G. James and M. Liebeck
3 FG-modules. FG-submodules and Reducibility. § 4., 5., Representations and Characters of Groups G. James and M. Liebeck
4 Group Algebras. FG-homomorphisms. § 6.,7., Representations and Characters of Groups G. James and M. Liebeck
5 Maschke's Theorem. § 8., Representations and Characters of Groups G. James and M. Liebeck
6 Schur's Lemma. § 9., Representations and Characters of Groups G. James and M. Liebeck
7 Irreducible Modules and the Group Algebra. § 10., 11., Representations and Characters of Groups G. James and M. Liebeck
8 More on the Group Algebra. § 11., Representations and Characters of Groups G. James and M. Liebeck
9 Conjugacy Classes. Characters. § 12., Representations and Characters of Groups G. James and M. Liebeck
10 Inner Products of Characters. § 14., Representations and Characters of Groups G. James and M. Liebeck
11 The Number of Irreducible Characters. § 15., Representations and Characters of Groups G. James and M. Liebeck
12 Character Tables and Orthogonality Relations. § 16., Representations and Characters of Groups G. James and M. Liebeck
13 Normal Subgroups and Lifted Characters. § 17., Representations and Characters of Groups G. James and M. Liebeck
14 Some Elementary Character Tables. Tensor Products. § 18., 19., Representations and Characters of Groups G. James and M. Liebeck

Recomended or Required Reading

Textbook(s): G. James, M. Liebeck; Representations and Characters of Groups. Cambridge University Press.
Supplementary Book(s): J. P. Serre; Linear Representations of Finite Groups. Graduate texts in mathematics. NY: Springer-Verlag.

Planned Learning Activities and Teaching Methods

Lecture notes, presentation, problem solving, discussion.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 ASG ASSIGNMENT
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE MTE * 0.40 + ASG * 0.20 + FIN * 0.40
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + ASG * 0.20 + RST * 0.40


*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

1 Midterm Exam
Homework
Final Exam

Assessment Criteria

%40 (Midterm examination) + %20 (Homework) +%40 (Final examination)

Language of Instruction

English

Course Policies and Rules

You can be successful in this course by studying from your textbooks and lecture notes on the topics to be covered every week, coming to class by solving the given problems, establishing the concepts by discussing the parts you do not understand with your questions, learning the methods, and actively participating in the course.

Contact Details for the Lecturer(s)

Engin Mermut
e-mail: engin.mermut@deu.edu.tr
Phone: (232) 301 85 82

Office Hours

To be announced later.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 4 52
Preparations before/after weekly lectures 12 3 36
Preparation for midterm exam 1 20 20
Preparation for final exam 1 30 30
Preparing assignments 5 6 30
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 172

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.143343
LO.243343
LO.343343
LO.443343
LO.543343

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

Copyright 2015 DEÜ. BİD

HOME / ABOUT US / DEGREE PROGRAMMES / GENERAL INFORMATION FOR STUDENTS / INTERNATIONAL RELATIONS