Nevşehir Hacı Bektaş Veli University Course Catalogue
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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 | Calculates the duals of some known sequence 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-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 |
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| 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 | ||