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| MAT7260 | Euclidean Geometry | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Third 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. İdris ÖREN | | Co-Lecturer | None | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | to investigate some fundamental features of Euclidean geometry, to examine the invariants of this geometry by using the invariant theory methods. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | have some information about Euclidean space | | | | PO - 2 : | learn groups associated with Euclidean space | | | | PO - 3 : | have some information about problems of equivalent of points | | | | 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 | | |
| The Euclidean Space, Isometries, Translations, Orthogonal Transformations, Everey Isometry is a Union of an Orthogonal Transformation and a Translation, Invariants of a Systemof Points, The Complete System of Invariants, Similarities, Invariants of Points with Respect to the Group of Similarities. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | The Euclidean Space. | | | Week 2 | The Euclidean Space. | | | Week 3 | Translations and Orthogonal Transformations. | | | Week 4 | Translations and Orthogonal Transformations. | | | Week 5 | Everey Isometry is a Union of an Orthogonal Transformation and a Translation. | | | Week 6 | Everey Isometry is a Union of an Orthogonal Transformation and a Translation. | | | Week 7 | Invariants of a System of Points. | | | Week 8 | Invariants of a System of Points. | | | Week 9 | The Complete System of Invariants. | | | Week 10 | The Complete System of Invariants. | | | Week 11 | Similarities. | | | Week 12 | Similarities. | | | Week 13 | Similarities. | | | Week 14 | Invariants of Points with Respect to the Group of Similarities. | | | Week 15 | Invariants of Points with Respect to the Group of Similarities. | | | Week 16 | Invariants of Points with Respect to the Group of Similarities. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | | 2 | 50 | | End-of-term exam | 16 | | 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 | | Laboratuar çalışması | 0 | 0 | 0 | | Arasınav için hazırlık | 25 | 1 | 25 | | Arasınav | 2 | 1 | 2 | | Uygulama | 0 | 0 | 0 | | Klinik Uygulama | 0 | 0 | 0 | | Ödev | 5 | 2 | 10 | | Proje | 0 | 0 | 0 | | Kısa sınav | 0 | 0 | 0 | | Dönem sonu sınavı için hazırlık | 25 | 1 | 25 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 0 | 0 | 0 | | Diğer 2 | 0 | 0 | 0 | | Total work load | | | 218 |
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