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COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
MAT 605THE GEOMETRY OF DISCRETE GROUPS3 + 01st Semester7,5

COURSE DESCRIPTION
Course Level Master's 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
PO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08
LO 0014 5 4 4 
LO 0025 45 4 4
LO 0035  5 4  
LO 004 4 4 5  
LO 0055  5  4 
LO 0065 5  5  
LO 0074  5 4 5
Sub Total284142442289
Contribution41231311

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
 Select Year   


 Course TermNoInstructors
Details 2018-2019 Spring1MUSTAFA AŞCI


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Course Details
Course Code Course Title L+P Hour Course Code Language Of Instruction Course Semester
MAT 605 THE GEOMETRY OF DISCRETE GROUPS 3 + 0 1 Turkish 2018-2019 Spring
Course Coordinator  E-Mail  Phone Number  Course Location Attendance
Prof. Dr. MUSTAFA AŞCI masci@pau.edu.tr FEN A0203 %
Goals To form a relation among discrete groups, topology and complex analysis, and to construct a combinatorial structure by constructing a non-Euclidean geometric structure.
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.
Topics
Materials
Materials are not specified.
Resources
Course Assessment
Assesment MethodsPercentage (%)Assesment Methods Title
Final Exam50Final Exam
Midterm Exam50Midterm Exam
L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes