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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 |