Yozgat Bozok 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
MAT555	YARI-RİEMANN GEOMETRİ I	Elective	1	1	6

Level of Course Unit

Second Cycle

Objectives of the Course

To comprehend semi-Riemann geometry

Name of Lecturer(s)

Doç.Dr.Murat BABAARSLAN

Learning Outcomes

1	To learn sem--Riemann geometry
2	To apply semi-Riemann geometry

Mode of Delivery

Formal Education

Prerequisites and co-requisities

Recommended Optional Programme Components

Course Contents

Manifold theory: differentiable manifolds, tangent vectors, derivative transformation, curves, vector fields, 1-forms, Tensors: basic tensor algebra, tensor fields, tensor derivative, symmetrical bilinear forms, scalar multiplication, Semi-Riemannian manifolds: isometries, Levi-Civita connection, parallel translation, geodesics, exponential transformation, curvatures, Semi-Riemann product manifolds, local isometries, Semi-Riemannian submanifolds: tangents and normals, reduced connection, geodesics in submanifolds, total geodesic submanifolds, semi-Riemann hypersurfaces

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Manifold theory: differentiable manifolds
2	tangent vectors, derivative transformation
3	curves, vector fields, 1-forms
4	Tensors: basic tensor algebra
5	tensor fields, tensor derivative
6	symmetrical bilinear forms, scalar multiplication
7	Semi-Riemannian manifolds: isometries
8	Levi-Civita connection, parallel translation
9	geodesics, exponential transformation
10	curvatures, Semi-Riemann product manifolds
11	local isometries, Semi-Riemannian submanifolds
12	tangents and normals, reduced connection
13	geodesics in submanifolds, total geodesic submanifolds
14	semi-Riemann hypersurfaces

Recommended or Required Reading

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
Midterm Examination	1	100
SUM		100
End Of Term (or Year) Learning Activities	Quantity	Weight
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)

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	70	70
Final Examination	1	80	80
Makeup Examination	1	20	20
TOTAL WORKLOAD (hours)			170

Contribution of Learning Outcomes to Programme Outcomes

LO1

LO2

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