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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 | 1 - 2 - 7 - 8 | 1, | | PO - 2 : | learn groups associated with Euclidean space | 1 - 2 - 7 - 8 | 1, | | PO - 3 : | have some information about problems of equivalent of points | 1 - 2 - 7 - 8 | 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), 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, Bezier curves and their equivalence problems |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Geometry , group, transformation and concept of invariant | | | Week 2 | The Euclidean Space. | | | Week 3 | Gram matrice and its determinant | | | Week 4 | Isometries and Orthogonal Transformations. | | | Week 5 | Euclidean groups | | | Week 6 | Actions of groups on sets, orbit and invariant function | | | Week 7 | Finding invariant functions for two points for the Euclidean groups | | | Week 8 | Equivalence problem of points for the orthogonal group | | | Week 9 | Mid-term exam | | | Week 10 | Equivalence problem of points for the special orthogonal group | | | Week 11 | Invariants of a System of Points for the special Euclidean group | | | Week 12 | Invariants of a System of Points for Euclidean group | | | Week 13 | Bezier curve and its fundamental properties | | | Week 14 | Exam | | | Week 15 | Equivalence problem of Bezier curves | | | Week 16 | Some applications of invariant theory in the Euclidean geometry | | | |
| 1 | Wail, H. 1946; The Classical Groups. Their Invariants and Representation, Princeton Univ. Press, Princeton | | | 2 | Khadjiev, D. 1988; An Aplication of Invariant Theory to Differential Geometry of Curves, Fan Publ. Tashkent (Russien) | | | |
| 1 | Springer, T. A. 1977; Invariant Theory, Springer-Verlag, New York | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | | 2 | 30 | | Quiz | 14 | | 1 | 20 | | 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 | | Arasınav için hazırlık | 11.5 | 1 | 11.5 | | Arasınav | 2 | 1 | 2 | | Kısa sınav | 1 | 1 | 1 | | Dönem sonu sınavı için hazırlık | 18 | 1 | 18 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 188.5 |
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