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
MAT529	ADVANCED GEOMETRY I	Elective	1	1	6

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

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

Week	Theoretical	Practice	Laboratory
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

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

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)

None

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	80	80
Final Examination	1	70	70
Makeup Examination	1	40	40
TOTAL WORKLOAD (hours)			190

Contribution of Learning Outcomes to Programme Outcomes

LO1

LO2

LO3

LO4

LO5

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