Ordu University Lifelong Learning Programme

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type of Course Unit	Year of Study	Semester	Number of ECTS Credits
FMA629	ADVANCED DIFFERENTIAL GEOMETRY I	Compulsory	1	1	6

Level of Course Unit

Second Cycle

Objectives of the Course

The aim of the course is to teach some important information for those who want to do research on differential geometry.

Name of Lecturer(s)

Yrd. Doç. Dr. Süleyman ŞENYURT

Learning Outcomes

1	To have the ability and knowledge of the advanced level of related to the field and use it in real learning environments

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

• Differentiable manifolds • Tensor algebra • Tensor fields • Differential forms • Fiber bundles • Connections of vector bundles and Linear Connections • Affine Connections • Curvature and torsion tensors • Geodesics • Riemannian Connections • Submanifolds • II.Basic forms and reduced connection • Gauss, Codazzi and Ricci Curvature • Total umbilic submanifolds

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Differentiable manifolds
2	Tensor algebra
3	Tensor fields
4	Differential forms
5	Fiber bundles
6	Connections of vector bundles
7	Linear Connections
8	Midterm exam
9	Affine Connections
10	Curvature and torsion tensors
11	Geodesics, Riemannian Connections
12	Submanifolds
13	II.Basic forms and reduced connection
14	Gauss, Codazzi and Ricci Curvature
15	Total umbilic submanifolds
16	Final exam

Recommended or Required Reading

Brickell, F., Clark, R. S., (1970), Differentiable Manifolds, Windsor House, Condon S.W. 1. Hacısalihoğlu, H. H. 1980; Yüksek Boyutlu Uzaylarda Dönüşümler ve Geometriler, İnönü Üniversitesi Yayınları No 1, İstanbul.

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
SUM		0
End Of Term (or Year) Learning Activities	Quantity	Weight
SUM		0
Yarıyıl (Yıl) İçi Etkinlikleri		40
Yarıyıl (Yıl) Sonu Etkinlikleri		60
SUM		100

Language of Instruction

Turkish

Work Placement(s)

None

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	2	2
Final Examination	1	2	2
Makeup Examination	1	2	2
Attending Lectures	16	5	80
Problem Solving	10	5	50
Self Study	10	4	40
Individual Study for Mid term Examination	6	5	30
Individual Study for Final Examination	4	5	20
TOTAL WORKLOAD (hours)			226

Contribution of Learning Outcomes to Programme Outcomes

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7
LO1	4	3	5	5	3	4	5

* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High