Nevşehir Hacı Bektaş Veli University Course Catalogue

Information Of Programmes

INSTITUTE OF SCIENCE / MAT534 - MATHEMATICS

Code: MAT534 Course Title: THE SEQUENCE SPACES AND SUMMABILITY II Theoretical+Practice: 3+0 ECTS: 6
Year/Semester of Study 1 / Spring Semester
Level of Course 2nd Cycle Degree Programme
Type of Course Optional
Department MATHEMATICS
Pre-requisities and Co-requisites None
Mode of Delivery Face to Face
Teaching Period 14 Weeks
Name of Lecturer ZARİFE ZARARSIZ (zarifezararsiz@nevsehir.edu.tr)
Name of Lecturer(s) ZARİFE ZARARSIZ,
Language of Instruction Turkish
Work Placement(s) None
Objectives of the Course
Study of dual spaces of some fundamental sequence spaces and introduction of matrix transformations between these sequence spaces, study of semi-conservative FK-spaces, study of distinguished subspaces of FK-spaces, giving characterizations for distinguished subspaces of matrix spaces.

Learning Outcomes PO MME
The students who succeeded in this course:
LO-1 Paranormed sequence space and the dual space of a sequence space are known. PO-1 Fundamental theorems of about some sub-theories of Analysis, Applied Mathematics, Geometry, and Algebra can apply to new problems.
PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other.
PO-3 Mathematics, natural sciences and their branches in these areas and related issues has sufficient infrastructure solutions for the problems of theoretical and practical uses of mathematics.
Examination
LO-2 The matrix transformations on a sequence space are known. PO-1 Fundamental theorems of about some sub-theories of Analysis, Applied Mathematics, Geometry, and Algebra can apply to new problems.
PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other.
PO-3 Mathematics, natural sciences and their branches in these areas and related issues has sufficient infrastructure solutions for the problems of theoretical and practical uses of mathematics.
Examination
LO-3 Some special sequence spaces are recognized. PO-1 Fundamental theorems of about some sub-theories of Analysis, Applied Mathematics, Geometry, and Algebra can apply to new problems.
PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other.
PO-3 Mathematics, natural sciences and their branches in these areas and related issues has sufficient infrastructure solutions for the problems of theoretical and practical uses of mathematics.
Examination
LO-4 Defines semi-conservative FK-spaces. PO-1 Fundamental theorems of about some sub-theories of Analysis, Applied Mathematics, Geometry, and Algebra can apply to new problems.
PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other.
PO-17 Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary.
Examination
LO-5 It refers to the study of distinguished subspaces of matrix fields and their associated characterizations. PO-1 Fundamental theorems of about some sub-theories of Analysis, Applied Mathematics, Geometry, and Algebra can apply to new problems.
PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other.
PO-3 Mathematics, natural sciences and their branches in these areas and related issues has sufficient infrastructure solutions for the problems of theoretical and practical uses of mathematics.
PO-17 Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary.
Examination
PO: Programme Outcomes
MME:Method of measurement & Evaluation

Course Contents
Size Theorems, Oscillatory Spaces and Two-Norm Convergence, Sequence Spaces and Monotonic Norms, Duals of Sequence Spaces, Stable Sets, Relations and Transformations Between FK-spaces, Functional Dual, Semi-Conservative Spaces and Matrix Fields, Elegant Subspaces of FK-spaces, Elegant Subspaces of Summability Fields
Weekly Course Content
Week Subject Learning Activities and Teaching Methods
1 Size Theorems Oral represantation, questioning - answering, problem solving
2 Oscillatory Spaces and Two Norm Convergence Oral represantation, questioning - answering, problem solving
3 Sequence Spaces and Monotonic Norms Oral represantation, questioning - answering, problem solving
4 Duals of Sequence Spaces Oral represantation, questioning - answering, problem solving
5 Stable Sets Oral represantation, questioning - answering, problem solving
6 Relations and Transformations Between FK-spaces Oral represantation, questioning - answering, problem solving
7 Functional Dual Oral represantation, questioning - answering, problem solving
8 mid-term exam
9 Semi-Conservative Spaces and Matrix Spaces Oral represantation, questioning - answering, problem solving
10 Distinguished Features of FK-spaces Subspaces Oral represantation, questioning - answering, problem solving
11 Distinguished Features of FK-spaces Subspaces Oral represantation, questioning - answering, problem solving
12 Selected Subspaces of Summability Spaces Oral represantation, questioning - answering, problem solving
13 Selected Subspaces of Summability Spaces Oral represantation, questioning - answering, problem solving
14 Selected Subspaces of Summability Spaces Oral represantation, questioning - answering, problem solving
15 Selected Subspaces of Summability Spaces Oral represantation, questioning - answering, problem solving
16 final exam
Recommend Course Book / Supplementary Book/Reading
1 Boos, J.,Classical and modern methods in summability, Wilansky, A., Summabilitythrough functional analysis
2 Summability Theory and Its Applications, Feyzi Başar, ISBN 9781032275369.
Required Course instruments and materials
Books and internet

Assessment Methods
Type of Assessment Week Hours Weight(%)
mid-term exam 8 2 40
Other assessment methods
1.Oral Examination
2.Quiz
3.Laboratory exam
4.Presentation
5.Report
6.Workshop
7.Performance Project
8.Term Paper
9.Project
final exam 15 2 60

Student Work Load
Type of Work Weekly Hours Number of Weeks Work Load
Weekly Course Hours (Theoretical+Practice) 3 14 42
Outside Class
       a) Reading 4 6 24
       b) Search in internet/Library 3 12 36
       c) Performance Project 0
       d) Prepare a workshop/Presentation/Report 0
       e) Term paper/Project 0
Oral Examination 0
Quiz 0
Laboratory exam 0
Own study for mid-term exam 5 7 35
mid-term exam 2 1 2
Own study for final exam 8 5 40
final exam 2 1 2
0
0
Total work load; 181