• HOME
• ABOUT US
  • Name Address
  • General Description
  • Governance
  • Academic Calendar
  • Degree Programmes
  • List of Programmes in English
  • General Admission and Registration Procedures
  • Credit Mobility and Recognition of Prior Learning
  • ECTS Credit Allocation
  • Academic Guidance
  • Contacts
• Degree Programmes
  • Third Cycle Programmes (Doctorate Degree)
  • Second Cycle Programmes (Master's Degree)
  • First Cycle Programmes (Bachelor's Degree)
  • Short Cycle Programmes (Associate's Degree)
• GENERAL INFORMATION FOR STUDENTS
  • Cost of Living
  • Accommodation
  • Meals
  • Medical Facilities
  • Facilities for Disabled Students
  • Insurance
  • Financial Supports
  • Student Affairs Office
  • Practical Information for International Students
  • Language Courses
  • Work Placement Possibilities
  • Sports, Social and Cultural Facilities
  • Student Associations and Clubs
  • About İzmir - Turkey
• INTERNATIONAL RELATIONS
  • International Relations Office
  • Registration Procedures
  • Agreements
  • Coordinators
  • Documents
  • List of Programmes in English
  • ECTS / DS Labels

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. More on the Group Algebra § 10., 11., Representations and Characters of Groups G. James and M. Liebeck 8 Midterm Exam 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. Problem Solving.

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

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

engin.mermut@deu.edu.tr Phone: (232) 301 85 82

Office Hours

To be announced.

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/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 PO.12 PO.13 LO.1 4 3 3 4 3 LO.2 4 3 3 4 3 LO.3 4 3 3 4 3 LO.4 4 3 3 4 3 LO.5 4 3 3 4 3