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| MAT5070 | Advanced Linear Algebra | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Second 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 | Dr. Öğr. Üyesi Şerife YILMAZ | | Co-Lecturer | Assoc. Prof. Dr. Osman Kazancı | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The aim of the course is to give a general knowledge on main principles, problems and methods of the linear algebra. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | give an introduction to more advanced calculus and elementary linear algebra. | 1,3 | 1 | | PO - 2 : | establish the bijection between matrices and linear transformations, compute dimensions, kernel and range for linear transformations, and verify diagonalization. | 1,3 | 1 | | PO - 3 : | apply the results of bilinear forms in mathematical problems. | 1,3 | 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 | | |
| Vector spaces and linear transformations, linear and bilinear forms, symmetric and skew-symmetric bilinear forms, unitary spaces. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Lineer spaces | | | Week 2 | Linear operators | | | Week 3 | Matrices | | | Week 4 | Rank of a matrix | | | Week 5 | A system of linear equations | | | Week 6 | The method of Gauss | | | Week 7 | Permutations | | | Week 8 | Mid-term exam | | | Week 9 | Determinants | | | Week 10 | Minors | | | Week 11 | Inverse matrices | | | Week 12 | Euclidean spaces | | | Week 13 | Simmetric bilinear forms | | | Week 14 | Skew-simmetric bilinear forms | | | Week 15 | Unitar spaces | | | Week 16 | End-of-term exam | | | |
| 1 | Hacısalihoğlu, H. H., 1982; Lineer Cebir, Bizim Büro, Ankara | | | |
| 1 | Şahmurov, V., Uzgören, G., 1999; Lineer Cebir, Papatya Yayıncılık, Istanbul | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 8 | 05/04/2016 | 2 | 30 | | In-term studies (second mid-term exam) | 12 | 03/05/2016 | 1,5 | 20 | | End-of-term exam | 17 | 25/05/2016 | 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 | 20 | 1 | 20 | | Arasınav | 2 | 1 | 2 | | Kısa sınav | 1.5 | 1 | 1.5 | | Dönem sonu sınavı için hazırlık | 20 | 1 | 20 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 199.5 |
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