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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 5053 MATRIX GROUPS ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

Offered to

Mathematics Mathematics

Course Objective

This course aims to introduce basic theory of topological matrix groups and gives a brief introduction to Lie groups.

Learning Outcomes of the Course Unit

1   will be able to know basic theory and proporties of some important matrix groups 2   will be able to consider matrix groups as manifolds 3   will be able to classify compact matrix groups 4   will be able to gain an appreciation of the interplay between different areas of mathematics in the setting of matrix groups 5   will be able to familiar with the basic facts about representation theory of compact matrix groups

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 General linear groups 2 Orthogonal groups 3 Homomorphisms 4 Exponential and Logarithm 5 SO(3) and Sp(1) 6 The Topology of matrix groups 7 Maximal tori 8 Midterm 9 Covering by maximal tori 10 Conjugacy of maximal tori 11 Spin(k) 12 Normalizers, Weyl groups 13 Lie groups 14 Maximal tori

Recomended or Required Reading

Textbook: 1. M. L. Curtis, Matrix Groups, Springer, 2nd ed., 1984, ISBN-13: 978-0387960746 Supplementary Book: 2. Khristopher Tapp, Matrix Groups for undergraduates, AMS, 2005, ISBN-13: 978-0821837856

Planned Learning Activities and Teaching Methods

Lecture notes, Presentation, 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)

bedia.akyar@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 3 39 Tutorials 0 Preparing presentations 0 Preparations before/after weekly lectures 13 3 39 Preparation for midterm exam 1 20 20 Preparation for final exam 1 30 30 Preparation for quiz etc. 0 Preparing assignments 4 5 20 Preparing Group Assignments 4 5 20 Quiz etc. 0 Final 1 3 3 Midterm 1 3 3 TOTAL WORKLOAD (hours) 174

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