Information Of Programmes

FACULTY OF LETTERS & SCIENCE / MAT413 - MATHEMATICS

Code: MAT413

Course Title: GEOMETRIES AND TOPOLOGY

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 some geometries and topology 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 relation between Euclidean geometry and topology.	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
Affine space and Affine frame, Euclidean space and Euclidean frame, Solid motions in Euclid plane, Solid motions in Euclid space, Line, Plane, Curve, Open and neighborhood, Topological transformations, Topological structure of curves, Homeomorphic structures to lines, Homeomorphic structures to specific curves, Homeomorphic structures to planes, Stereographic projection
Weekly Course Content
Week	Subject	Learning Activities and Teaching Methods
1	Affine space and Affine frame	Speech, Problem Solving
2	Euclidean space and Euclidean frame	Speech, Problem Solving
3	Solid motions in Euclid plane	Speech, Problem Solving
4	Solid motions in Euclid space	Speech, Problem Solving
5	Line	Speech, Problem Solving
6	Plane	Speech, Problem Solving
7	Curve	Speech, Problem Solving
8	mid-term exam
9	Open and neighborhood	Speech, Problem Solving
10	Topological transformations	Speech, Problem Solving
11	Topological structure of curves	Speech, Problem Solving
12	Homeomorphic structures to lines	Speech, Problem Solving
13	Homeomorphic structures to specific curves	Speech, Problem Solving
14	Homeomorphic structures to planes	Speech, Problem Solving
15	Stereographic projection	Speech, Problem Solving
16	final exam
Recommend Course Book / Supplementary Book/Reading
1	Sabuncuoğlu, Arif. Diferensiyel Geometri, Nobel Yayınları, Ankara, 2001.
2	Şahin, B., Manifoldların Diferensiyel Geometrisi, Nobel yayın dağıtım, 2012.
3	Gray, A. Modern Differential Geometry, CRC Press LLC, 1998.
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