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| MAT5601 | Hyperbolic Geometry | 3+0+0 | ECTS:7.5 | | Year / Semester | Spring Semester | | Level of Course | Second Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Prof. Dr. Ali Hikmet DEĞER | | Co-Lecturer | | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | to introduce Non-Euclidean Geometry. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | meet a Geometry different from Euclidean geometry | 2,3 | 1,3, | | PO - 2 : | learn area, length concepts in the Non-Euclidean geometry | 2,3 | 1,3, | | PO - 3 : | use the models of upper half plane and unit disk in hyperbolic geometry | 2,3 | 1,3, | | 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), PO : Learning Outcome | | |
| General Mobius groups, length and distance in the upper half plane, other models of the hyperbolic plane, groups acting on the upper half plane. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Basic spaces, a model of the hyperbolic plane, Riemann sphere | | | Week 2 | Boundary at infinity | | | Week 3 | Group of Möbiüs transformation | | | Week 4 | Transivity properties of Möbiüs transformation | | | Week 5 | Classification of Mobiüs transformation | | | Week 6 | Matrix representation | | | Week 7 | Reflections | | | Week 8 | Conformality of Möbiüs transformation | | | Week 9 | Mid-term exam | | | Week 10 | Preserving the upper half plane | | | Week 11 | Transivity properties | | | Week 12 | Geometry of the action of Möbiüs transformation | | | Week 13 | Paths and elements of arc-length | | | Week 14 | Path metric spaces | | | Week 15 | Formulae for Hyperbolic distance, isometries | | | Week 16 | End-of-term exam | | | |
| 1 | James, A.W. 2005; Hyperbolic Geometry, Second Edition, Springer-Verlag | | | |
| 1 | Gareth, A.J. David, S. 1987; Complex Functions, CUP | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 24.11.2024 | 2 | 50 | | End-of-term exam | 16 | 24.02.2025 | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 8 | 14 | 112 | | Arasınav için hazırlık | 3 | 8 | 24 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 5 | 8 | 40 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 3 | 1 | 3 | | Total work load | | | 225 |
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