Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 1 / Fall 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 | |||||
| It is aimed to find a limit for a non-convergent (divergent) sequence and to use infinite matrices, which is the most common method. It is aimed to teach the basic concepts of sequence spaces and summability. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | The Linear spaces 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 normed spaces are teach |
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 | The sequence spaces and matrix transformations on the sequence spaces 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. |
Examination |
| LO-4 | Defines convolutional and coregular matrices and FU-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 | Expresses the inclusion theorems for summability methods. |
PO- |
Examination |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| Linear, metric, normed, paranorm sequence spaces, Dual space of a sequence space, Conservative and Regular Matrices, Conull and Coregular Matrices, Characterization of some matrix classes, Dual summability methods, Toeplitz matrix examples, Summability Field and Perfect Parts of Triangular Matrices, FK Spaces, Coregular and Conull FK Spaces, Commutability, Consistency, Absolute Summability Fields. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Linear, metric, normed, paranormed sequence spaces | oral represantation, questioning - answering, problem solving |
| 2 | Linear, metric, normed, paranormed sequence spaces | oral represantation, questioning - answering, problem solving |
| 3 | Dual space of a sequence space | oral represantation, questioning - answering, problem solving |
| 4 | Conservative and Regular Matrices, Conull and Coregular Matrices | oral represantation, questioning - answering, problem solving |
| 5 | Conservative and Regular Matrices, Conull and Coregular Matrices | oral represantation, questioning - answering, problem solving |
| 6 | Characterization of some classes of matrices | oral represantation, questioning - answering, problem solving |
| 7 | Dual summability methods | oral represantation, questioning - answering, problem solving |
| 8 | mid-term exam | |
| 9 | Examples of Toeplitz matrices, Summability Field and Perfect Parts of Triangular Matrices | oral represantation, questioning - answering, problem solving |
| 10 | FK Spaces | oral represantation, questioning - answering, problem solving |
| 11 | Coregular and Conull FK Spaces | oral represantation, questioning - answering, problem solving |
| 12 | Interchangeability | oral represantation, questioning - answering, problem solving |
| 13 | Interchangeability, Consistency | oral represantation, questioning - answering, problem solving |
| 14 | Absolute Summability Fields | oral represantation, questioning - answering, problem solving |
| 15 | Absolute Summability Fields | oral represantation, questioning - answering, problem solving |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | Summability Theory and Its Applications by Feyzi Başar | |
| 2 | Boos, J.,Classical and modern methods in summability, Wilansky, A., Summabilitythrough functional analysis | |
| 3 | William Henry Ruckle, Sequence Spaces, Pitman Publishing, 1981. | |
| 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 | 14 | 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 | 0 | ||
| b) Search in internet/Library | 6 | 5 | 30 |
| c) Performance Project | 0 | ||
| d) Prepare a workshop/Presentation/Report | 8 | 5 | 40 |
| e) Term paper/Project | 2 | 7 | 14 |
| Oral Examination | 0 | ||
| Quiz | 0 | ||
| Laboratory exam | 0 | ||
| Own study for mid-term exam | 4 | 5 | 20 |
| mid-term exam | 2 | 1 | 2 |
| Own study for final exam | 6 | 5 | 30 |
| final exam | 2 | 1 | 2 |
| 0 | |||
| 0 | |||
| Total work load; | 180 | ||