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| MAT3024 | Introduction to Motion Geometry | 4+0+0 | ECTS:6 | | Year / Semester | Spring 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: | | Introducing all properties of Dual numbers and D-Modul, we understand the plane geometry induced by them. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | recognize dual numbers, ring of dual numbers and D-modul. | 3,4,5,6 | 1,3, | | LO - 2 : | recognize the matrix representations of dual numbers. | 3,4,5,6 | 1,3, | | LO - 3 : | understand the types of absolute values of dual numbers. | 3,4,5,6 | 1,3 | | LO - 4 : | learn the actions of several subgroups of dual numbers on the plane. | 3,4,5,6 | 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), LO : Learning Outcome | | |
| Groups, Rings, Dual numbers, Ring of dual numbers, D-Modul, The matrix representation of a dual number, 1st absolute value of a dual number, Conjugate dual numbers, Group action on a set, System of equivalent vectors and G-orbit, G-invariant function, 2nd absolute value of a dual number, The group D1, The group GD1, Relation betveen The groups D1 and GD1, The problem of D1-equivalence, The problem of GD1-equivalence, The group D2, The group GD2, Relation betveen The groups D2 and GD2, The group D3, The group GD3, Relation betveen The groups D3 and GD3. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Groups, Rings | | | Week 2 | Dual numbers, Ring of dual numbers | | | Week 3 | D-Modul, The matrix representation of a dual number | | | Week 4 | 1st absolute value of a dual number, Conjugate dual numbers | | | Week 5 | Group action on a set, System of equivalent vectors and G-orbit | | | Week 6 | G-invariant function | | | Week 7 | 2nd absolute value of a dual number, The group D1 | | | Week 8 | The group GD1, Relation between The groups D1 and GD1 | | | Week 9 | Mid-term exam | | | Week 10 | The problem of D1-equivalence, The problem of GD1-equivalence | | | Week 11 | The group D2, The group GD2 | | | Week 12 | Relation betveen The groups D2 and GD2 | | | Week 13 | The group D3, The group GD3 | | | Week 14 | Relation betveen The groups D3 and GD3 | | | Week 15 | Applications | | | Week 16 | Final exam | | | |
| 1 | Prof.Dr. H.Hilmi Hacısalihoğlu, Hareket Geometrisi ve Kuaterniyonlar Teorisi, 1983. | | | |
| 1 | Müller, H.R., Kinematik Dersleri, Ankara Üniversitesi Yayınları, 1963. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 21/04/2025 | 2 | 30 | | Quiz | 5,12 | 21.03.2025
16.05.2025 | 30, 30 | 20 | | End-of-term exam | 16 | 13/06/2025 | 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 | 2 | 2 | 4 | | Dönem sonu sınavı için hazırlık | 15 | 1 | 15 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 180 |
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