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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 5005 TOPOLOGICAL VECTOR SPACES - I 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 (English) Mathematics (English)

Course Objective

The aim of this course is to investigate the properties of the topological vector spaces.

Learning Outcomes of the Course Unit

1   Will be able to understand topological vector space. 2   Will be able to use finite dimensional vector space. 3   Will be able to understand convex sets. 4   Will be able to understand locally convex spaces. 5   Will be able to use different topologies on locally convex spaces.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Definitions and elementary properties 2 Definitions and elementary properties 3 Duality and Hahn-Banach Theorem 4 Duality and Hahn-Banach Theorem 5 Duality and Hahn-Banach Theorem 6 Barrelled spaces and the Banach-Steinhaus theorem 7 Barrelled spaces and the Banach-Steinhaus theorem 8 Midterm 9 Inductive and projective limits 10 Completeness and the closed graph theorem 11 Completeness and the closed graph theorem 12 Some further topics 13 Some further topics 14 Compact linear mappings

Recomended or Required Reading

Textbook(s): [1] F. Treves. Topological Vector Spaces, Distributions and Kernels. [2] A. P. Robertson and W. J. Robertson. Topological Vector Spaces.

Planned Learning Activities and Teaching Methods

Lecture notes, Presentation

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 FIN FINAL EXAM 3 FCG FINAL COURSE GRADE MTE * 0.40 + FIN * 0.60 4 RST RESIT 5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + RST * 0.60 *** 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)

Definitions and elementary propertiesahmet.ozcelik@deu.edu.tr Office: 0232 3018585

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 3 39 Preparations before/after weekly lectures 13 3 39 Preparation for midterm exam 1 15 15 Preparation for final exam 1 25 25 Preparing Individual Assignments 10 5 50 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 2 3 3 4 3 2 2 3 3 LO.2 4 2 3 3 4 3 2 2 3 3 LO.3 4 2 3 3 4 3 2 2 3 3 LO.4 4 2 3 3 4 3 2 2 3 3 LO.5 4 2 3 3 4 3 2 2 3 3