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MAT4017Introduction to Hyperbolic Geometry4+0+0ECTS:6
Year / SemesterFall Semester
Level of CourseFirst Cycle
Status Elective
DepartmentDEPARTMENT of MATHEMATICS
Prerequisites and co-requisitesNone
Mode of Delivery
Contact Hours14 weeks - 4 hours of lectures per week
LecturerDoç. Dr. Ali Hikmet DEĞER
Co-LecturerAssoc. Prof. Dr. Bahadır ÖZGÜR GÜLER
Language of instructionTurkish
Professional practise ( internship ) None
 
The aim of the course:
To teach basic definitions and concepts related to hyperbolic geometry.
 
Learning OutcomesCTPOTOA
Upon successful completion of the course, the students will be able to :
LO - 1 : learn basic concepts of hyperbolic geometry.1,2,3,4,5,6,7,81
LO - 2 : will meet different metrics from the Euclidean metric.1,2,3,4,5,6,7,81
LO - 3 : will compare different models of hyperbolic geometry.1,2,3,4,5,6,7,81
CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome

 
Contents of the Course
Introduction to hyperbolic metric and hyperbolic field concepts. Review the basic concepts and relationships of hyperbolic trigonometry.
 
Course Syllabus
 WeekSubjectRelated Notes / Files
 Week 1Hyperbolic geometry
 Week 2Synonyms of hyperbolic plane
 Week 3Hyperbolic metric
 Week 4Properties of hyperbolic metric
 Week 5Hyperbolic metric in the upper half plane
 Week 6Hyperbolic metric on the unit disc
 Week 7Topology with hyperbolic metric
 Week 8Hyperbolic disk and representation
 Week 9Midterm exam
 Week 10Hyperbolic area
 Week 11Gauss-Bonnet theorem
 Week 12Hyperbolic poligons
 Week 13Hyperbolic trigonometry
 Week 14Relations in hyperbolic triangle
 Week 15Some important theorems in hyperbolic geometry
 Week 16Final exam
 
Textbook / Material
1J.W. Anderson Hyperbolic Geometry , Springer,2005.
 
Recommended Reading
1A.F. Beardon, The Geometry of Discrete Groups, Springer, 1983.
 
Method of Assessment
Type of assessmentWeek NoDate

Duration (hours)Weight (%)
Mid-term exam 9 10/04/2019 2 50
End-of-term exam 16 06/06/2019 2 50
 
Student Work Load and its Distribution
Type of workDuration (hours pw)

No of weeks / Number of activity

Hours in total per term
Yüz yüze eğitim 4 14 56
Sınıf dışı çalışma 6 14 84
Arasınav için hazırlık 2 2 4
Arasınav 2 1 2
Dönem sonu sınavı için hazırlık 6 2 12
Dönem sonu sınavı 2 1 2
Total work load160