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| MAT4013 | Transformations and Geometries | 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. Ömer PEKŞEN | | Co-Lecturer | | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | undertandig what the geometry is and classifying geometries by the transformation groups. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | learn what geometry is all about | 1 - 3 - 5 - 7 | 1, | | LO - 2 : | undertand how to distinguish the different geometries | 1 - 3 - 5 - 7 | 1, | | LO - 3 : | be familiar with Euclidean, Similarity, Affine and Projective Geometries | 1 - 3 - 5 - 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 | | |
| Euclidean geometry, transformations from the plane to itself, transformation grups, geometric invariants, translations, rotations, reflections, similarity geometry, similarity transformations, similarity group, Affine geometry, affine transformations, affine group, decomposition of a general affine transformation, projective transformations, Projektive group, projektive geometry |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Euclidean geometry, transformations from the plane to itself, | | | Week 2 | transformation grups, geometric invariants, | | | Week 3 | translations, rotations, | | | Week 4 | reflections | | | Week 5 | similarity geometry, similarity transformations, | | | Week 6 | similarity group, | | | Week 7 | Affine geometry, | | | Week 8 | affine transformations, | | | Week 9 | midterm exam | | | Week 10 | affine group, | | | Week 11 | decomposition of a general affine transformation, | | | Week 12 | projective transformations | | | Week 13 | projektive group | | | Week 14 | Projektive Geometry | | | Week 15 | Projektive Geometry | | | Week 16 | final exam | | | |
| 1 | Hacısalihoğlu, H.H. 1984. Dönüşümler ve Geometriler, M.E.B. Bilim ve Kültür eserleri Dizisi, Yayın No: 337 | | | |
| 1 | Kaya, R., Hacısalihoğlu, H.H. (Editör: Olgun Ş.) 1991. Geometri, Anadolu Üniversitesi Yayın No: 404 | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 16/11/2024 | 2 | 30 | | Quiz | 5
13 | 22/10-17/12/2024 | 2 | 20 | | 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 | 6.5 | 14 | 91 | | Arasınav için hazırlık | 10 | 1 | 10 | | Arasınav | 2 | 1 | 2 | | Kısa sınav | 1 | 2 | 2 | | Dönem sonu sınavı için hazırlık | 15 | 1 | 15 | | Dönem sonu sınavı | 2 | 2 | 4 | | Total work load | | | 180 |
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