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
FMA646	RIEMANNIAN SURFACES II	Compulsory	1	1	6

Level of Course Unit

Second Cycle

Objectives of the Course

Objectives of Course is learning Riemannian Spaces.

Name of Lecturer(s)

Yrd. Doç. dr Seher ASLANCI

Learning Outcomes

1	Knows the definition of Manifolds
2	Learns the Characteristics of Riemannian Manifolds
3	Knows the Torsion -Free Riemannian Spaces

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

Differential Manifolds, Connection, Affine Connection, Covariant Derivative, Curvature and Torsion, Torsion -Free Spaces, Riemannian Manifolds, Riemannian Spaces with Constant Curvature.

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Differential Manifolds
2	Lineer Connection on Manifold
3	Absolute Differential
4	Manifold with Affine Connection
5	Covariant Derivative
6	Curvature and Torsion
7	Torsion -Free Spaces
8	Midterm Exam
9	Equal-Affine Connection
10	Metric Spaces
11	Weyl Spaces
12	Riemannian Manifolds
13	Riemannian Connections
14	Curvature tensors on Riemannian Spaces
15	Riemannian Spaces with Constant Curvature
16	Final Exam

Recommended or Required Reading

1.Salimov, A. Ve Magden, A.,( 2008) Diferensiyel Geometri. Aktif Yayınevi. Erzurum 2.Kühnel, W.( 2005) Differential Geometry. American Mathematical Society, 380, USA

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
Attending Lectures	14	3	42
Problem Solving	14	1	14
Self Study	14	6	84
Individual Study for Homework Problems	7	3	21
Individual Study for Mid term Examination	1	10	10
Individual Study for Final Examination	1	20	20
TOTAL WORKLOAD (hours)			195

Contribution of Learning Outcomes to Programme Outcomes

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

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