Information Of Programmes

FACULTY OF LETTERS & SCIENCE / MAT414 - MATHEMATICS

Code: MAT414

Course Title: SEMI-RIEMANNIAN GEOMETRY

Theoretical+Practice: 4+0

ECTS: 6

Year/Semester of Study

4 / Spring Semester

Level of Course

1st Cycle Degree Programme

Type of Course

Optional

Department

MATHEMATICS

Pre-requisities and Co-requisites

None

Mode of Delivery

Face to Face

Teaching Period

14 Weeks

Name of Lecturer

ESMA DEMİR ÇETİN (esma.demir@nevsehir.edu.tr)

Name of Lecturer(s)

ESMA DEMİR ÇETİN, ÇAĞLA RAMİS,

Language of Instruction

Turkish

Work Placement(s)

None

Objectives of the Course

Giving basic information about Riemannian and semi Riemannian geometries that the student will need during undergraduate and graduate education. And to figure out how to go about solving problems.

Learning Outcomes		PO	MME
The students who succeeded in this course:
LO-1	Learn the application areas of Riemannian geometry.	PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts. PO-5 Develop suitable material for a subject on a mathematical area, to use the knowledge and experience gains with different methods	Examination Performance Project
PO: Programme Outcomes MME:Method of measurement & Evaluation

Course Contents
Differentiability, Differentiable manifold, The metric on manifold, Examples of metric, Tangent vector and tangent vector space, F* derivative transformation, Immersion, Minkowski space, Metric of Minkowski space, Vector types in Minkowski space, Length and angle in Minkowski space, Specific curves and surfaces in Minkowski space, Drawing curves in Euclidean space, Drawing curves in Minkowski space
Weekly Course Content
Week	Subject	Learning Activities and Teaching Methods
1	Differentiability	Speech, Problem Solving
2	Differentiable manifold	Speech, Problem Solving
3	The metric on manifold	Speech, Problem Solving
4	Examples of metric	Speech, Problem Solving
5	Tangent vector and tangent vector space	Speech, Problem Solving
6	F* derivative transformation	Speech, Problem Solving
7	Immersion	Speech, Problem Solving
8	mid-term exam
9	Minkowski space	Speech, Problem Solving
10	Metric of Minkowski space	Speech, Problem Solving
11	Vector types in Minkowski space	Speech, Problem Solving
12	Length and angle in Minkowski space	Speech, Problem Solving
13	Specific curves and surfaces in Minkowski space	Speech, Problem Solving
14	Drawing curves in Euclidean space	Speech, Problem Solving
15	Drawing curves in Minkowski space	Speech, Problem Solving
16	final exam
Recommend Course Book / Supplementary Book/Reading
1	Hacısalihoğlu, H.Hilmi. Diferensiyel Geometri 2, Ankara Üniversitesi Fen Fakültesi, Matematik Bölümü.,2000
2	Şahin, B., Manifoldların Diferensiyel Geometrisi, Nobel yayın dağıtım, 2012.
3	M. do Carmo, Riemannian geometry, Birkhauser, 1992.
4	Lopez, R., Differential Geometry of Curves and Surfaces in Minkowski Space, Universidad de Granada, 2008
Required Course instruments and materials

Assessment Methods
Type of Assessment	Week	Hours	Weight(%)
mid-term exam	8	2	40
Other assessment methods
1.Oral Examination
2.Quiz
3.Laboratory exam
4.Presentation
5.Report
6.Workshop
7.Performance Project
8.Term Paper
9.Project
final exam	16	2	60

Student Work Load
Type of Work	Weekly Hours	Number of Weeks	Work Load
Weekly Course Hours (Theoretical+Practice)	4	14	56
Outside Class
a) Reading			0
b) Search in internet/Library	1	14	14
c) Performance Project			0
d) Prepare a workshop/Presentation/Report			0
e) Term paper/Project	1	5	5
Oral Examination			0
Quiz			0
Laboratory exam			0
Own study for mid-term exam	3	14	42
mid-term exam	1	14	14
Own study for final exam	3	14	42
final exam	1	14	14
			0
			0
Total work load;			187