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| MATL7352 | Invariants of vectors in Lorentz space | 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 | Face to face | | 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 introduce some of the main ideas of four dimensional Lorentz space, to reinforce their elementary calculus and basic linear algebra knowledge giving a good opportunity to exhibit their interplay through application to geometry. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | have some information about Lorentz space | | | | PO - 2 : | learn groups associated with Lorentz space | | | | PO - 3 : | learn equivalence problems of vectors and system of its invariants | | | | 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 | | |
| Lorentz space. O(3,1),SO(3,1),M(3,1) and SM(3,1) Groups. G-equivalence of system of points and G-invariant functions. Equivalence problem for groups O(3,1) and SO(3,1). Equivalence problem for groups M(3,1) and SM(3,1). Complete system and minimal complete system of group O(3,1) . Complete system and minimal complete system of group SO(3,1). Complete system and minimal complete system of groups M(3,1) and SM(3,1). Second complete system and minimal complete system of groups O(3,1) and SO(3,1) . Second complete system and minimal complete system of groups M(3,1) and SM(3,1). Second type equivalence problem for groups O(3,1) and SO(3,1). Second type equivalence problem for groups M(3,1) and SM(3,1). Applcations of invariants of vectors |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Lorentz space | | | Week 2 | O(3,1),SO(3,1),M(3,1) and SM(3,1) Groups | | | Week 3 | G-equivalence of system of vectors and G-invariant functions | | | Week 4 | Equivalence problem of vectors for the groups O(3,1) and SO(3,1) | | | Week 5 | Equivalence problem of vectors for the groups M(3,1) and SM(3,1). | | | Week 6 | Complete system of vectors for the group O(3,1) | | | Week 7 | Complete system of vectors for the group SO(3,1). | | | Week 8 | Complete system of vectors for the groups M(3,1) and SM(3,1). | | | Week 9 | Midterm exam | | | Week 10 | Second complete system of vectors for the groups O(3,1) and SO(3,1) | | | Week 11 | Second complete system of vectors for the groups M(3,1) and SM(3,1). | | | Week 12 | Second type equivalence problem for groups O(3,1) and SO(3,1). | | | Week 13 | Second type equivalence problem for groups M(3,1) and SM(3,1). | | | Week 14 | Applications of invariants of vectors | | | Week 15 | General evaluation of semester | | | Week 16 | Final exam | | | |
| 1 | G.L.Naber, Minkowski Spacetime Geometry, Springer-Verlag, New York,1992. | | | |
| 1 | Hermann Weyl, The Classic Groups:Their Invariants , Princeton Univ. Press, Princeton, New Jersey, 1946. | | | 2 | G. Farin, Curves and surfaces for computer-aided geometric design,Academic Press, San Diego, CA,1997. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 22/11/2018 | 2 | 50 | | In-term studies (second mid-term exam) | 16 | 17/01/2019 | 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 | 10 | 14 | 140 | | Arasınav için hazırlık | 6 | 1 | 6 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 10 | 1 | 10 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 202 |
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