Akademik Dersler - Tanıtım


Code - Course Title	MAT523 - Introduction to Riemann Geometry
Course Type	Elective Courses
Language of Instruction	Türkçe
Laboratory + Practice	3+0
ECTS	7.5
Course Instructor(s)	PROFESÖR DOKTOR ŞENAY BULUT
Mode of Delivery	The mode of delivery of this course is only Face to face
Prerequisites	There is no prerequisite or co-requisite for this course.
Courses Recomended	Diferantiable Manifolds. Analysis.
Required or Recommended Resources	Semi-Riemannian Geometry, O'Neill
Recommended Reading List	Semi-Riemannian Geometry, O'Neill
Assessment methods and criteria	Written exam
Work Placement	N/A
Sustainability Development Goals

Weeks	Topics
Week - 1	Differentiable manifolds
Week - 2	Tangent vectors and vector fields
Week - 3	Dual spaces and 1-forms
Week - 4	Tensors on manifolds
Week - 5	The metric tensor
Week - 6	Some examples of Riemannian manifolds
Week - 7	Isometric manifolds
Week - 8	Afin connection and Covariant derivative
Week - 9	Parallel translation
Week - 10	The Levi Civita connection
Week - 11	The Riemann curvature tensor
Week - 12	Sectional curvature
Week - 13	TheRicci and Scalar curvatures of a Riemannian manifold
Week - 14	Some differential operators on Riemannian manifolds

Assessment Method and Passing Requirements
	Quamtity	Percentage (%)
2.Midterm Exam	1	30
Homework	1	20
Final Exam	1	50
Toplam (%)		100