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 | NECDET BATIR (nbatir@nevsehir.edu.tr) | ||||
| Name of Lecturer(s) | NECDET BATIR, | ||||
| Language of Instruction | Turkish | ||||
| Work Placement(s) | None | ||||
| Objectives of the Course | |||||
| Teach to selecting topics of functional analysis. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | The spectral theory of finite dimensional spaces is known. |
PO-1 Fundamental theorems of about some sub-theories of Analysis, Applied Mathematics, Geometry, and Algebra can apply to new problems. PO-6 Following the developments in science and technology and gain self-renewing ability. PO-8 To perform the ethical responsibilities in working life. PO-13 Ability to use mathematical knowledge in technology. |
Examination |
| LO-2 | Further properties of resolvent and spectrum is know |
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-4 Ability to learn scientific, mathematical perception and the ability to use that information to related areas. PO-6 Following the developments in science and technology and gain self-renewing ability. |
Examination |
| LO-3 | Banach algebras is 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. PO-4 Ability to learn scientific, mathematical perception and the ability to use that information to related areas. |
Examination |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| Spectral theory in finite dimensional normed spaces, spectral properties of bounded linear operators, further properties of resolvent and spectrum, use of complex analysis in spectral theory, Banach algebras, further properties of Banach algebras | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Spectral theory in finite dimensional normed spaces, | Oral representation, questioning and answering |
| 2 | Spectral theory in finite dimensional normed spaces, | Oral representation, questioning and answering |
| 3 | Spectral properties of bounded linear operators | Oral representation, questioning and answering |
| 4 | Spectral properties of bounded linear operators | Oral representation, questioning and answering |
| 5 | Further properties of resolvent and spectrum | Oral representation, questioning and answering |
| 6 | Further properties of resolvent and spectrum | Oral representation, questioning and answering |
| 7 | Use of complex analysis in spectral theory | Oral representation, questioning and answering |
| 8 | mid-term exam | |
| 9 | Use of complex analysis in spectral theory | Oral representation, questioning and answering |
| 10 | Banach algebras | Oral representation, questioning and answering |
| 11 | Banach algebras | Oral representation, questioning and answering |
| 12 | Banach algebras | Oral representation, questioning and answering |
| 13 | Further properties of Banach algebras | Oral representation, questioning and answering |
| 14 | Further properties of Banach algebras | Oral representation, questioning and answering |
| 15 | Further properties of Banach algebras | Oral representation, questioning and answering |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | Introductory fnctioanl analysis with applications, E. Kreyzing | |
| Required Course instruments and materials | ||
| Related resources | ||
| 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 | 10 | 1 | 20 |
| 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 | 0 | ||
| b) Search in internet/Library | 3 | 15 | 45 |
| c) Performance Project | 0 | ||
| d) Prepare a workshop/Presentation/Report | 5 | 4 | 20 |
| 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 | 7 | 5 | 35 |
| final exam | 2 | 1 | 2 |
| 0 | |||
| 0 | |||
| Total work load; | 181 | ||