Information Of Programmes

FACULTY OF LETTERS & SCIENCE / MAT311 - MATHEMATICS

Code: MAT311

Course Title: DIFFERENTIAL GEOMETRY I

Theoretical+Practice: 2+2

ECTS: 6

Year/Semester of Study

3 / Fall Semester

Level of Course

1st Cycle Degree Programme

Type of Course

Compulsory

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 differential geometry 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	Conceive the manifold structure of Euclidean space.	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-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data. PO-5 Develop suitable material for a subject on a mathematical area, to use the knowledge and experience gains with different methods	Examination Oral Examination Performance Project
PO: Programme Outcomes MME:Method of measurement & Evaluation

Course Contents
Affine and Euclidean spaces, Topological and Hausdorff Spaces, Differentiability, Differomorphism, Topological Manifolds, Differentiable Manifolds, Tangent Space, Vector Field, Derivatives of according to tangent vector and vector field, Integral Curve, Derivative to curve direction and Lie derivative, Dual Spaces, Cotangent Space and 1-form, Gradient, divergence, rotation,
Weekly Course Content
Week	Subject	Learning Activities and Teaching Methods
1	Affine and Euclidean spaces,	Lecture Method, Graphing
2	Topological and Hausdorff Spaces	Lecture Method
3	Topological Manifolds	Lecture Method, Brainstorming
4	Differentiability, Differomorphism	Lecture Method
5	Differentiable Manifolds	Lecture Method
6	Tangent Space	Lecture Method
7	Vector Field	Lecture Method
8	mid-term exam
9	Derivatives of according to tangent vector and vector field	Lecture Method
10	Integral Curve	Lecture Method
11	Derivative to curve direction and Lie derivative	Lecture Method
12	Dual Spaces	Lecture Method
13	Cotangent space and 1-form	Lecture Method
14	Gradient, divergence, rotation	Lecture Method
15	Introduction to spatial curve theory	Lecture Method
16	final exam
Recommend Course Book / Supplementary Book/Reading
1	Gray, A. Modern Differential Geometry, CRC Press LLC, 1998.
2	Hacısalihoğlu, H.Hilmi. Diferensiyel Geometri, Ankara Üniversitesi Fen Fakültesi, Matematik Bölümü.,2000.
3	Sabuncuoğlu, Arif. Diferensiyel Geometri, Nobel Yayınları, Ankara, 2001.
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	4	4
c) Performance Project			0
d) Prepare a workshop/Presentation/Report			0
e) Term paper/Project			0
Oral Examination	5	5	25
Quiz	5	5	25
Laboratory exam	2	5	10
Own study for mid-term exam	3	4	12
mid-term exam	2	1	2
Own study for final exam	5	6	30
final exam	2	1	2
			0
			0
Total work load;			166