Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | MAT529 | ADVANCED GEOMETRY I | Elective | 1 | 2 | 6 |
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Level of Course Unit |
Second Cycle |
Objectives of the Course |
The aim of this course is to give basic concepts and theorems of ADVANCED GEOMETRY I. |
Name of Lecturer(s) |
Doç.Dr.Murat BABAARSLAN |
Learning Outcomes |
1 | Knows the concept of differentiable manifolds | 2 | Dominate the concepts of tangent vectors and tangent space | 3 | Knows Lie operator | 4 | Knows 1-form | 5 | Knows differentiation of a transformation |
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Mode of Delivery |
Formal Education |
Prerequisites and co-requisities |
None |
Recommended Optional Programme Components |
None |
Course Contents |
Differentiable manifolds, tangent vectors and tangent spaces, directional derivative and covariant derivative, the Lie operator, cotangent vectors and cotangent spaces, 1-forms, a transformation of a differential |
Weekly Detailed Course Contents |
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1 | Differentiable manifolds | | | 2 | Differentiable manifolds | | | 3 | Tangent vectors and tangent spaces | | | 4 | Tangent vectors and tangent spaces | | | 5 | Directional derivative and covariant derivative | | | 6 | Directional derivative and covariant derivative | | | 7 | The Lie operator | | | 8 | Mid-Term Exam | | | 9 | The Lie operator | | | 10 | Cotangent vectors and cotangent spaces | | | 11 | Cotangent vectors and cotangent spaces | | | 12 | 1-forms | | | 13 | 1-forms | | | 14 | Transformation of a differential | | | 15 | Transformation of a differential | | | 16 | Final Exam | | |
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Recommended or Required Reading |
Prof. Dr. H. H. Hacısalihoğlu, Diferensiyel Geometri, İnönü Üniversitesi Fen Ed. Fak. Yayınları Mat. No 2 1983.
B. O'Neill, Semi Riemannian Geometry-With Applications to Relativity, New York, Academic Press Inc. (1983).
M. Berger and B. Gostiaux, Differential geometry: Manifolds, Curves and Surfaces, Springer-Verlag New York 1987.
M. Do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall (1976).
Yüksek Boyutlu Uzaylarda Dönüşümler ve Geometriler, Prof. Dr. H. Hilmi Hacısalihoğlu, İnönü Üniv., 1980 |
Planned Learning Activities and Teaching Methods |
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Assessment Methods and Criteria | |
Midterm Examination | 1 | 100 | SUM | 100 | |
Final Examination | 1 | 100 | SUM | 100 | Term (or Year) Learning Activities | 40 | End Of Term (or Year) Learning Activities | 60 | SUM | 100 |
| Language of Instruction | | Work Placement(s) | None |
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Workload Calculation |
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Midterm Examination | 1 | 80 | 80 |
Final Examination | 1 | 70 | 70 |
Makeup Examination | 1 | 40 | 40 |
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Contribution of Learning Outcomes to Programme Outcomes |
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* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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Yozgat Bozok University, Yozgat / TURKEY • Tel (pbx): +90 354 217 86 01 • e-mail: uo@bozok.edu.tr |