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
FMA630	ADVANCED DIFFERENTIAL GEOMETRY II	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.
2
3
4
5

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

• Fibre spaces • principal fiber bundles • Vector bundles • Vector bundle morphisms • Cross-section of vector bundles • Connections of vector bundles • Linear connections of vector bundles and curvature of Linear Connections connections of Tangent bundle • Torsion and curvature of non-linear connections on tangent bundle • Fins spaces • Kartan connection in Fins spaces • Transformation of Fins connection

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Fibre spaces
2	Principal fiber bundles
3	Vector bundles
4	Vector bundle morphisms
5	Cross-section of vector bundles
6	Connections of vector bundles
7	Linear connections of vector bundles
8	Midterm exam
9	Curvature of Linear Connections
10	Connections of Tangent bundle
11	Torsion and curvature of non-linear connections on tangent bundle
12	Fins spaces
13	Kartan connection in Fins spaces
14	Transformation of Fins connection
15	Transformation of Fins connection
16	Final exam

Recommended or Required Reading

Nomizu, K., Sasaki T., (1994), Afin Diferential Geometry, Cambridge University Pres. 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
Problem Solving	14	4	56
Discussion	20	4	80
Brain Storming	20	2	40
TOTAL WORKLOAD (hours)			182

Contribution of Learning Outcomes to Programme Outcomes

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7
LO1	5	4	3	5	4	3	4
LO2
LO3
LO4
LO5

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