PAÜ .:. Eğitim Öğretim Bilgi Sistemi

COURSE INFORMATION

Course Code	Course Title	L+P Hour	Semester	ECTS
MAT 513	DIFFERENTIABLE MANIFOLDS -I	3 + 0	2nd Semester	7,5

COURSE DESCRIPTION

Course Level	Master's Degree
Course Type	Elective
Course Objective	Manifolds on the development of the basic geometric and topological concepts.
Course Content	Differential manifolds and functions, induced topology on a manifold, varieties, Grassmann manifolds, Manifold structure on a topological space, properties of an induced topology, partitions of unity, tengent vectors, derived linear functions, immersions, submanifolds and some topological properties, reguler submanifolds, submersions and fibres, quotient manifolds, transformations groups, tangent bundle, vector fields, orientable manifolds.
Prerequisites	No the prerequisite of lesson.
Corequisite	No the corequisite of lesson.

COURSE LEARNING OUTCOMES

1	Learns differentiable manifolds and functions, knows reduced topology on a manifold, varieties, Grasman manifolds.
2	Learns manifold structure on a topological space, properties of the reduced topology, unit breakdown of unit.
3	Learns tangent vectors, derivatived linear functions, immersions, submanifold and some topological properties.
4	Knows regular submanifolds, submersiyonlar and fibers, section manifolds, transformation groups.
5	Knows tangent bundle, vector fields, directional manifolds.

COURSE'S CONTRIBUTION TO PROGRAM

	PO 01	PO 02	PO 03	PO 04	PO 05	PO 06	PO 07	PO 08
LO 001	5		4	4				5
LO 002	4		5	4				4
LO 003	5		4	5				5
LO 004	5		4	4				5
LO 005	4		5	5				4
Sub Total	23		22	22				23
Contribution	5	0	4	4	0	0	0	5

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION

Activities	Quantity	Duration (Hour)	Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)	14	3	42
Hours for off-the-classroom study (Pre-study, practice)	14	7	98
Assignments	1	5	5
Mid-terms	1	15	15
Final examination	1	35	35
Total Work Load ECTS Credit of the Course			195 7,5

COURSE DETAILS

Select Year

	Course Term	No	Instructors
Details	2025-2026 Fall	1	CANSEL AYCAN ÖZDEMİR

Course Details

Course Code	Course Title	L+P Hour	Course Code	Language Of Instruction	Course Semester	Mode of Delivery
MAT 513	DIFFERENTIABLE MANIFOLDS -I	3 + 0	1	Turkish	2025-2026 Fall	Face to Face

Course Coordinator	E-Mail	Phone Number	Course Location	Attendance
Prof. Dr. CANSEL AYCAN ÖZDEMİR	c_aycan@pau.edu.tr		FEN B0318	%70

Goals		Manifolds on the development of the basic geometric and topological concepts.
Content		Differential manifolds and functions, induced topology on a manifold, varieties, Grassmann manifolds, Manifold structure on a topological space, properties of an induced topology, partitions of unity, tengent vectors, derived linear functions, immersions, submanifolds and some topological properties, reguler submanifolds, submersions and fibres, quotient manifolds, transformations groups, tangent bundle, vector fields, orientable manifolds.

Topics

Weeks	Topics
1	inner product spaces,Multilinear algebra
2	rigid motions(rotational, translational)
3	topological manifolds
4	differentiable manifolds
5	product and quotient manifolds
6	tangent vectors and tangent space
7	lie algebra and lie bracket
8	middterm exam
9	differential relative to the direction
10	cotangent space, covector, 1-forms
11	Riemannian metric and Riemannian manifolds
12	tensors and tensor algebra
13	covariant, contravariant and mixed tensors
14	final exam

Materials

Materials are not specified.

Resources

Resources	Resources Language
yüksek diferensiyel geometriye giriş, H.H. Hacısalihoğlu	Türkçe

Course Assessment

Assesment Methods	Percentage (%)	Assesment Methods Title
Final Exam	50	Final Exam
Midterm Exam	50	Midterm Exam

L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes

Prospective Student