Information Of Programmes

FACULTY OF LETTERS & SCIENCE / MAT415 - MATHEMATICS

Code: MAT415

Course Title: DIFFERENTIABLE MANIFOLDS

Theoretical+Practice: 4+0

ECTS: 6

Year/Semester of Study

4 / Fall 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 differentiable manifolds 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 mectric and differentiable subjects	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
Vector and vector space, Inner product and norm, Multi linearity, Tensor and tensor algebra, Tensor classes, Topological manifold, Examples of topological manifold, Differentiable structure, Differentiable manifold, Examples of differentiable manifold, Manifold structure of R^n, Manifold structure of projective space, Metric structures on manifolds
Weekly Course Content
Week	Subject	Learning Activities and Teaching Methods
1	Vector and vector space	Speech, Problem Solving
2	Inner product and norm	Speech, Problem Solving
3	Multi linearity	Speech, Problem Solving
4	Tensor and tensor algebra	Speech, Problem Solving
5	Tensor classes	Speech, Problem Solving
6	Topological manifold	Speech, Problem Solving
7	Examples of topological manifold	Speech, Problem Solving
8	mid-term exam
9	Differentiable structure	Speech, Problem Solving
10	Differentiable manifold	Speech, Problem Solving
11	Examples of differentiable manifold	Speech, Problem Solving
12	Manifold structure of R^n	Speech, Problem Solving
13	Manifold structure of projective space	Speech, Problem Solving
14	Metric	Speech, Problem Solving
15	Metric structures on manifolds	Speech, Problem Solving
16	final exam
Recommend Course Book / Supplementary Book/Reading
1	Hacısalihoğlu, H.Hilmi. Diferensiyel Geometri, Ankara Üniversitesi Fen Fakültesi, Matematik Bölümü.,2000.
2	Hacısalihoğlu, H.Hilmi. Ekmekci, N., Tensör Geometri, Ankara Üniversitesi Fen Fakültesi, Matematik Bölümü., 2004
3	Şahin, B., Manifoldların Diferensiyel Geometrisi, Nobel yayın dağıtım, 2012.
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