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COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
MAT 605THE GEOMETRY OF DISCRETE GROUPS3 + 02nd Semester7,5

COURSE DESCRIPTION
Course Level Doctorate Degree
Course Type Elective
Course Objective To form a relation among discrete groups, topology and complex analysis, and to construct a combinatorial structure by constructing a non-Euclidean geometric structure.
Course Content Basic spaces, Riemann shpere and infinite boundary of upper half plane, Möbius group and transitivity properties of Möbius transforms, cross ratio, topological groups, topological transformations and clusters, PGL (2,R) group and its discrete subgroups and algebraic properties, Modular group.
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.
Mode of Delivery Face to Face

COURSE LEARNING OUTCOMES
1Knows the basic space, hyperbolic plane and Riemannian sphere.
2Defines the Möbius transformation.
3Understands topological group and properties.
4Learns discrete subgroups.
5Calculates hyperbolic distance and area.
6Knows PGL (2,R) and PSL (2,R) groups.
7Learns knowledge about modular group and basic regions.

COURSE'S CONTRIBUTION TO PROGRAM
Data not found.

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
ActivitiesQuantityDuration (Hour)Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)14342
Hours for off-the-classroom study (Pre-study, practice)14798
Assignments155
Mid-terms11515
Final examination13535
Total Work Load

ECTS Credit of the Course






195

7,5
COURSE DETAILS
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L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes