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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 5046 TOPOLOGICAL VECTOR SPACES - II 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 give an interest of Frechet spaces. We will study Inductive, Projective limits and Spaces LF.

Learning Outcomes of the Course Unit

1   will be able to understand vector spaces as topological spaces. 2   will be able to understand properties of convex sets. 3   will be able to separate convex sets. 4   will be able to use Hahn-Banach theorem and its consequences. 5   will be able to use the Lp-spaces and their properties.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Frechet Spaces 2 Frechet Spaces 3 Normable Spaces. Banach spaces. 4 Hilbert Spaces 5 Inductive and Projective Limits, Spaces LF 6 Inductive and Projective Limits, Spaces LF 7 Bounded Sets 8 Midterm 9 Approximation procedures in spaces of functions 10 Approximation procedures in spaces of functions 11 Partition of Unity 12 Partition of Unity 13 The Open mapping Theorem. 14 The Open mapping Theorem.

Recomended or Required Reading

Textbook: F. Treves. Topological Vector Spaces, Distributions and Kernels, Reference Books : C. Goffmann and G. Pedrick. A First Course in Functional Analysis.

Planned Learning Activities and Teaching Methods

Lecture notes All class members are expected to attend both the lecture and seminar hours and take part in the discussion sessions.

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)

ahmet.ozcelik@deu.edu.tr office: 0232 301 8585

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 Midterm 1 3 3 Final 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 3 2 2 2 4 3 3 3 LO.2 4 3 3 2 2 2 4 3 3 3 LO.3 4 3 3 2 2 2 4 3 3 3 LO.4 4 3 3 2 2 2 4 3 3 3 LO.5 4 3 3 2 2 2 4 3 3 3