Akademik Dersler - Tanıtım


Code - Course Title	MAT637 - Fuchsian Groups
Course Type	Elective Courses
Language of Instruction	Türkçe
Laboratory + Practice	3+0
ECTS	7.5
Course Instructor(s)	PROFESÖR DOKTOR ALİ DENİZ
Mode of Delivery	The mode of delivery of this course is face to face.
Prerequisites	There is no pre-requisite for this course.
Courses Recomended	Abstract Algebra 1-2, Metric and Topological Spaces, Hyperbolic Geometry
Required or Recommended Resources	S. Katok, Fuchs Groups, Chicago Lectures in Math., 1992.
Recommended Reading List	A. F. Beardon, The Geometry of Discrete Groups, Springer 1983.
Assessment methods and criteria	Written Exam
Work Placement	N/A
Sustainability Development Goals

Weeks	Topics
Week - 1	Hyperbolic Geometry, Hyperbolic metric, geodesics
Week - 2	Isometries of hyperbolic plane
Week - 3	Hyperbolic Area and The Gauss Bonnet Formula
Week - 4	Definition of Fuchsian group and some examples
Week - 5	The group PSL(2,R)
Week - 6	Discrete groups
Week - 7	Algebraic properties of Fuchsian groups
Week - 8	Fundamental region of a Fuchsian group
Week - 9	Dirichlet region and the construction of Dirichlet region for a Fuchsian group
Week - 10	Isometric circles
Week - 11	Ford fundamental region
Week - 12	The geometry of Fuchsian groups
Week - 13	Geometrically finite Fuchsian groups
Week - 14	Co-compakt Fuchsian Groups

Assessment Method and Passing Requirements
	Quamtity	Percentage (%)
Toplam (%)		0