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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 6010 LIE GROUPS 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 course aims to give an introduction to the classical theories of Lie Groups and Lie Algebras.

Learning Outcomes of the Course Unit

1   will be able to understand concepts of Lie groups and matrix groups. 2   will be able to understand local and global structure of Lie groups. 3   will be able to understand concept of Lie algebras. 4   will be able to identify solvable and semisimple Lie algebras. 5   will be able to use the Killing form.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Lie groups. Matrix groups. 2 Local structure of Lie groups. 3 Examples of Lie groups. 4 Subgroups and homomorphisms 5 Global structure of Lie groups. 6 More examples. 7 Exponentiation and matrix groups. 8 Midterm Exam 9 Lie algebras and associative algebras. 10 Solvable and semisimple Lie algebras. 11 Nilpotent subalgebras and Cartan subalgebras. 12 The Killing form. 13 Simple Lie algebras and Dynkin diagrams. 14 Identification of simple Lie algebras.

Recomended or Required Reading

Textbook(s): An Introduction To Lie Groups And Lie Algebras, With Applications; J. G. Belinfante, B. Kolman, and H. A. Smith. SIAM Review, Vol. 8, No. 1 (Jan., 1966), 11-46. References: Lecture Notes on Lie Groups; A.A. Klyachko (Bilkent University)

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 * 0.30 +ASG * 0.20 +FIN * 0.50 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.30 + ASG * 0.20 + RST * 0.50 *** 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 13 3 39 Preparation for midterm exam 1 20 20 Preparation for final exam 1 30 30 Preparing assignments 4 8 32 Preparations before/after weekly lectures 13 5 65 Midterm 1 3 3 Final 1 3 3 TOTAL WORKLOAD (hours) 192

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