| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT2051 | Linear Algebra II | Fall | 3 | 0 | 3 | 6 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | En |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Instructor MAHMOUD JAFARI SHAH BELAGHI |
| Course Objectives: | To introduce tensors and tensor algebra. To show students the tensors in relation with matrices, linear and multilinear mappings. |
|
The students who have succeeded in this course; At the end of this course students will be able to use tensors and tensor algebra. Students will be able 1) to use tensor arithmetic in the development of multilinear algebra. 2) Students will have formulated the mathematical properties of mixed,exterior tensors 3) to grasp the relations between tensors and matrices,linear and multilinear mappings. 4) to understand structural properties of tensor product space and tensor product. |
| Tensor product, Subspaces and factor spaces, Direct decompositions, Linear mappings, Tensor product of several vector spaces, Dual spaces, Finite dimensional vector spaces, Tensor product of vector spaces with additional structure, Tensor product of algebras,Tensor algebra, Tensors,Skew symmetric tensors,Skew symmetric mappings, Exterior algebra, mixed exterior algebra, The algebra ^(E,E*), Poincaré isomorphism, Homomorphisms, derivations and antiderivations, The operator i(a), Applications to linear transformations, Multilinear functions as tensors. |
| Week | Subject | Related Preparation | |
| 1) | Preliminaries | ||
| 2) | Preliminaries | ||
| 3) | Tensor product | ||
| 4) | Examples of tensor product | ||
| 5) | Subspaces and factor spaces, Direct decompositions,Linear mappings | ||
| 6) | Tensor product of several vector spaces, Dual spaces, Finite dimensional vector spaces | ||
| 7) | Examples | ||
| 8) | Tensor product of vector spaces with additional structure,Tensor product of algebras | ||
| 9) | Tensor algebra, Tensors | ||
| 10) | Skew symmetric tensors, The factor algebra × E/N(E) | ||
| 11) | Skew symmetric mappings, Exterior algebra | ||
| 12) | Mixed exterior algebra, The algebra ^(E,E*), The Poincaré isomorphism | ||
| 13) | Homomorphisms, derivations and antiderivations, The operator i(a) | ||
| 14) | Applications to linear transformations, Multilinear functions as tensors | ||
| Course Notes: | Multilinear algebra, Greub W. |
| References: | . |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | % 0 | |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | % 0 | |
| Homework Assignments | % 0 | |
| Presentation | % 0 | |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | 2 | % 45 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 55 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 45 | |
| PERCENTAGE OF FINAL WORK | % 55 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 7 | 10 | 70 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 1 | 3 | 3 |
| Quizzes | 4 | 1 | 4 |
| Preliminary Jury | 0 | ||
| Midterms | 2 | 2 | 4 |
| Paper Submission | 0 | ||
| Jury | 0 | ||
| Final | 1 | 2 | 2 |
| Total Workload | 125 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |