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Information
| Unit | INSTITUTE OF SOCIAL SCIENCES |
| ECONOMETRICS (MASTER) (WITH THESIS) | |
| Code | IEM716 |
| Name | Vector Spaces I |
| Term | 2022-2023 Academic Year |
| Term | Spring |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ERSİN KIRAL |
| Course Instructor |
The current term course schedule has not been prepared yet.
|
Course Goal / Objective
To give insight and skill about the concrete aspects of linear algebra,To provide basic concepts of matrices and the systems of homogeny and linear equations,To solve the systems using matrices,To teach vector spaces and abstract mathematical concepts,To teach abstract thought
Course Content
Linear systems relationship between matrices and linear systems,Row-matrice operators and solvind linear systems,vector spaces and subspaces,bases, dimensions and coordinates,Linear transformations and The algebra of linear transformations,linear functionals,dual spaces,annihilating polynomials,Lagrange interpolation,commutative rings and determinant function,permutations.
Course Precondition
Resources
Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Learns some concepts vectors and matrices and relationship between them |
| LO02 | Writes a basis of a vector space and find the coordinates |
| LO03 | Finds dual and double dual of the vector spac eand determines the annihilator |
| LO04 | By constructing the polynomial algebra says fundamental theorems about it |
| LO05 | Learns the determinant functions and permutations |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Linear equation systems,solving systems by using matrices | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 2 | Solving homogen and linear systems with Elementary row- operations | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 3 | Matrix multiplication,inverse matrices, Cramer system | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 4 | Vector spaces and subspaces | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 5 | Bases, dimensions and coordinates | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 6 | Linear Transformations and Tha algebra of Linear transformations | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 7 | İsomorphisms and representations of matrices | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 8 | Mid-Term Exam | Review of the relevant pages from sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Linear functionals,dual spaces,annihilating polynomials | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 10 | Double dual and the transpose of a Linear Transformation | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 11 | Lagrange interpolation | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 12 | Polynomial ideals and unique factorization | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 13 | Commutative rings and determinant function | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 14 | Permutations | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 15 | Solving problems | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | Review of the relevant pages from sources | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review of the relevant pages from sources | Ölçme Yöntemleri: Yazılı Sınav |