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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 6055 REPRESENTATION THEORY ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

ASSISTANT PROFESSOR MURAT ALTUNBULAK

Offered to

Mathematics (English) Mathematics (English)

Course Objective

The aim of this course is to give basics of representation theory of both finite groups and classical groups.

Learning Outcomes of the Course Unit

1   will be able to describe representations 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 understand concepts of Lie groups and Lie algebras. 5   will be able to understand the representations of Lie groups and Lie algebras.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Representations of Finite Groups 2 Characters 3 Examples; Induced Representations; Group Algebras; Real Representations 4 Representations of Symmetric Groups: Young Diagrams and Frobenius Character Formula 5 Representations of Alternating Groups 6 Weyl's Construction 7 Lie Groups I 8 Lie Groups II 9 Lie Algebras and Lie Groups 10 Initial Classification of Lie Algebras 11 Lie Algebras in Dimension One, Two and Three 12 Representations of Special Linear Group of Order 2 13 Representations of Special Linear Group of Order 3 Part I 14 Representations of Special Linear Group of Order 3 Part II: Examples

Recomended or Required Reading

Textbook: Representation Theory: A First Course, W. Fulton, J. Harris. Springer-Verlag New York Inc. 1996. References: Linear Representations of Finite Groups, Jean-Pierre Serre. Springer-Verlag New York Inc. 1977.

Planned Learning Activities and Teaching Methods

Lecture Notes Problem Solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 ASG ASSIGNMENT 2 MTE MIDTERM EXAM 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE ASG * 0.30 + MTE * 0.30 + FIN * 0.40 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) ASG * 0.30 + MTE * 0.30 + 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

Attending at least 70 percent of lectures is mandatory.

Contact Details for the Lecturer(s)

Office: B-220 (Math. Dept.) Phone: (30)1 85 92

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 14 3 42 Preparations before/after weekly lectures 14 5 70 Preparation for midterm exam 1 20 20 Preparation for final exam 1 30 30 Preparing assignments 4 9 36 Midterm 1 3 3 Final 1 3 3 TOTAL WORKLOAD (hours) 204

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 LO.1 4 4 4 3 4 3 4 3 4 3 LO.2 4 4 4 3 4 3 4 3 4 3 LO.3 4 4 4 3 4 3 4 3 4 3 LO.4 4 4 3 3 4 3 3 3 4 3 LO.5 4 4 3 3 4 3 3 3 4 3