|
|
| MAT4017 | Introduction to Hyperbolic Geometry | 4+0+0 | ECTS:6 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 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 teach basic definitions and concepts related to hyperbolic geometry. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | learn basic concepts of hyperbolic geometry. | 6,7 | 1, | | LO - 2 : | will meet different metrics from the Euclidean metric. | 6,7 | 1 | | LO - 3 : | will compare different models of hyperbolic geometry. | 6,7 | 1 | | 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 | | |
| Introduction to hyperbolic metric and hyperbolic field concepts. Review the basic concepts and relationships of hyperbolic trigonometry. |
| |
| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Hyperbolic geometry | | | Week 2 | Synonyms of hyperbolic plane | | | Week 3 | Hyperbolic metric | | | Week 4 | Properties of hyperbolic metric | | | Week 5 | Hyperbolic metric in the upper half plane | | | Week 6 | Hyperbolic metric on the unit disc | | | Week 7 | Topology with hyperbolic metric | | | Week 8 | Hyperbolic disk and representation | | | Week 9 | Midterm exam | | | Week 10 | Hyperbolic area | | | Week 11 | Gauss-Bonnet theorem | | | Week 12 | Hyperbolic poligons | | | Week 13 | Hyperbolic trigonometry | | | Week 14 | Relations in hyperbolic triangle | | | Week 15 | Some important theorems in hyperbolic geometry | | | Week 16 | Final exam | | | |
| 1 | J.W. Anderson Hyperbolic Geometry , Springer,2005. | | | |
| 1 | A.F. Beardon, The Geometry of Discrete Groups, Springer, 1983. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 10/11/2024 | 2 | 50 | | End-of-term exam | 16 | 06/01/2025 | 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 | 4 | 14 | 56 | | Sınıf dışı çalışma | 7 | 14 | 98 | | Arasınav için hazırlık | 2 | 2 | 4 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 6 | 2 | 12 | | Dönem sonu sınavı | 8 | 1 | 8 | | Total work load | | | 180 |
|