Akademik Dersler - Tanıtım


Code - Course Title	MAT539 - Fractal Geometry
Course Type	Elective Courses
Language of Instruction	Türkçe
Laboratory + Practice	3+0
ECTS	7.5
Course Instructor(s)	DOÇENT DOKTOR DERYA ÇELİK, PROFESÖR DOKTOR BÜNYAMİN DEMİR
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	MAT 325 Metric and Topological Spaces I, II
Required or Recommended Resources	• Fractals everywhere, Barnsley, M., Academic Press, 1993.• Measure, topology, and fractal geometry, Edgar, G., Springer, 2000.
Recommended Reading List	• Fractal Geometry: Mathematical Foundations and Applications, Falconer, K., Jhon Wiley & Sons, 2003.
Assessment methods and criteria	Written exam
Work Placement	N/A
Sustainability Development Goals

Weeks	Topics
Week - 1	Classical fractals: Cantor set, Sierpinski gasket, Koch curve ...
Week - 2	Complete metric spaces, contraction maps, fixed point theorem and Hausdorff metric
Week - 3	Space of fractals and itereted function system
Week - 4	The notions of countable and graph-directed IFS and the notion of attractor
Week - 5	Collage theorem and its applications
Week - 6	IFS with Condentation
Week - 7	Space filling curves
Week - 8	Fractal dimension
Week - 9	Hausdorff measure and dimension
Week - 10	Iteration of complex functions
Week - 11	Mandelbrot set
Week - 12	Julia sets
Week - 13	Algorithms to obtain Julia sets
Week - 14	Fractal interpolation functions

Assessment Method and Passing Requirements
	Quamtity	Percentage (%)
1.Midterm Exam	1	40
Final Exam	1	60
Toplam (%)		100