GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION

THEORY OF MANIFOLDS I/5451305

Course Title:	THEORY OF MANIFOLDS I
Credits	3	ECTS	7.5
Course Semester	1	Type of The Course	Elective

COURSE INFORMATION

-- (CATALOG CONTENT)

-- (TEXTBOOK)

-- (SUPPLEMENTARY TEXTBOOK)

-- (PREREQUISITES AND CO-REQUISITES)

-- LANGUAGE OF INSTRUCTION

Turkish

-- COURSE OBJECTIVES

-- COURSE LEARNING OUTCOMES

They can define the basic definitions about differentiable manifolds
Deal with various examples of differentiable manifolds and smooth maps
They construct a topological structure on differentiable manifolds.
Have familiarity with tangent vectors, tensors and differential forms.
Do work practically with vector fields and differential forms.
Learns derivatived linear functions, immersions, submanifold and some topological properties.

-- MODE OF DELIVERY

The mode of delivery of this course is Face to face

--WEEKLY SCHEDULE
1. Week	Continuous functions, Topological spaces, Some special topological spaces
2. Week	Some classical theory of differentiable functions, differentiable manifolds
3. Week	Differentiable functions,The induced topology on a manifold
4. Week	Differentiable varieties, Grassmann manifolds
5. Week	Manifold structure on a topological space, properties of the induced topology, Topological restrictions on a manifold
6. Week	Partial differentiation on a manifold , Tangent vectors
7. Week	The inverse function Theorem, Leibniz’s Formula.
8. Week	Immersions,General properties of immersions,submanifolds,regular submanifolds
9. Week	Some topological properties of submanifolds, an imbedding theorem
10. Week	Submersions, The fibres of a submersion.
11. Week	Quotient manifolds
12. Week	Transformation Groups.
13. Week	Discontinuous transformation groups
14. Week	Fundamental domains,examples of quotient manifolds
15. Week
16. Week

-- TEACHING and LEARNING METHODS

-- ASSESSMENT CRITERIA

	Quantity	Total Weighting (%)
Midterm Exams	1	25
Assignment	2	25
Application	0	0
Projects	0	0
Practice	0	0
Quiz	0	0

Percent of In-term Studies		50
Percentage of Final Exam to Total Score		50

-- WORKLOAD

Activity	Total Number of Weeks	Duration (weekly hour)	Total Period Work Load
Weekly Theoretical Course Hours	14	3	42
Weekly Tutorial Hours			0
Reading Tasks			0
Searching in Internet and Library	6	15	90
Material Design and Implementation			0
Report Preparing			0
Preparing a Presentation			0
Presentation			0
Midterm Exam and Preperation for Midterm Exam	1	20	20
Final Exam and Preperation for Final Exam	1	30	30
Other (should be emphasized)			0
TOTAL WORKLOAD:			182
TOTAL WORKLOAD / 25:			7.28
Course Credit (ECTS):			7.5

-- COURSE'S CONTRIBUTION TO PROGRAM

NO	PROGRAM LEARNING OUTCOMES	1	2	3	4	5
1					X
2					X
3				X
4					X
5			X
6						X
7
8				X
9						X
10
11
12		X

-- NAME OF LECTURER(S)

(Assoc. Prof.Dr. Mustafa ÖZKAN)

-- WEB SITE(S) OF LECTURER(S)

(http://websitem.gazi.edu.tr/site/ozkanm)

-- EMAIL(S) OF LECTURER(S)

(ozkanm@gazi.edu.tr)

Gazi University

Information Package

Programme Information

Search

GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR