Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 1 / Fall Semester | ||||
| Level of Course | 3rd Cycle Degree Programme | ||||
| Type of Course | Optional | ||||
| Department | MATHEMATICS (DOCTORATE DEGREE) | ||||
| Pre-requisities and Co-requisites | None | ||||
| Mode of Delivery | Face to Face | ||||
| Teaching Period | 14 Weeks | ||||
| Name of Lecturer | ESMA DEMİR ÇETİN (esma.demir@nevsehir.edu.tr) | ||||
| Name of Lecturer(s) | ESMA DEMİR ÇETİN, ÇAĞLA RAMİS, | ||||
| Language of Instruction | Turkish | ||||
| Work Placement(s) | None | ||||
| Objectives of the Course | |||||
| Given the basic concepts of Semi Riemann Manifolds that students need for doctoral education. Also show the ways to solve problems that students will experience. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Understand the effect of the metric structure on the manifold. |
PO-1 Students can design an original issue and explore new, different and / or comprehend complex issues. PO-3 Students will be dominated by current issues in mathematics. |
Examination Performance Project |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| Relation of the concept of manifold to Riemannian and semi-Riemannian metrics and their properties. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Introduction to manifolds | Speech, Problem Solving |
| 2 | Isometries | Speech, Problem Solving |
| 3 | The Levi-Civita connection | Speech, Problem Solving |
| 4 | Parallel translation | Speech, Problem Solving |
| 5 | Geodesics | Speech, Problem Solving |
| 6 | The exponiental map | Speech, Problem Solving |
| 7 | Curvatures | Speech, Problem Solving |
| 8 | mid-term exam | |
| 9 | Sectional curvature | Speech, Problem Solving |
| 10 | Semi-Riemannian surfaces | Speech, Problem Solving |
| 11 | Frame fields | Speech, Problem Solving |
| 12 | Some differential operators | Speech, Problem Solving |
| 13 | Ricci and scalar curvature | Speech, Problem Solving |
| 14 | Semi-Riemannian product manifolds | Speech, Problem Solving |
| 15 | Local isometries | Speech, Problem Solving |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | B. O’Neill, Semi Riemann Geometry with Applications to Relativity, Academic Press, 1983 | |
| Required Course instruments and materials | ||
| 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 | 16 | 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 | 1 | 14 | 14 |
| c) Performance Project | 0 | ||
| d) Prepare a workshop/Presentation/Report | 0 | ||
| e) Term paper/Project | 1 | 14 | 14 |
| Oral Examination | 0 | ||
| Quiz | 0 | ||
| Laboratory exam | 0 | ||
| Own study for mid-term exam | 3 | 14 | 42 |
| mid-term exam | 1 | 14 | 14 |
| Own study for final exam | 3 | 14 | 42 |
| final exam | 1 | 14 | 14 |
| 0 | |||
| 0 | |||
| Total work load; | 182 | ||