TÜRKÇE
ENGLISH
Information
| Unit | INSTITUTE OF SOCIAL SCIENCES |
| ECONOMETRICS (MASTER) (WITH THESIS) | |
| Code | IEM717 |
| Name | Vector Spaces II |
| Term | 2018-2019 Academic Year |
| Term | Fall |
| 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 | Knows the properties of the determinant function |
| LO02 | gives some special examples of linear transformations and proves some important theorems about linear transformations |
| LO03 | knows about very simple triangular and diagonal forms of linear transformations |
| LO04 | Finds out minimal polynomial.By determininig the class of the annihilating polynomials of linear transformation . Calculates the Jordan form of the linear transformation |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | - | Explains contemporary concepts about Econometrics, Statistics, and Operation Research | |
| PLO02 | - | Explains relationships between acquired knowledge about Econometrics, Statistics, and Operation Research | |
| PLO03 | - | Explains how to apply acquired knowledge in the field to Economics, Business, and other social sciences | |
| PLO04 | - | Models problems with Mathematics, Statistics, and Econometrics | |
| PLO05 | - | Applies the most suitable method to estimate the model & interprets its results | |
| PLO06 | - | Acquires the ability to analyze, benchmark, evaluate and interpret at conceptual levels to develop solutions to problems | |
| PLO07 | - | Collects, edits, and analyzes data for the purpose of study | |
| PLO08 | - | Performs an individual work to solve a problem with Econometrics, Statistics, and Operation Research | |
| PLO09 | - | Effectively works, take responsibility, and the leadership as a member of a team | |
| PLO10 | - | Uses acquired knowledge in the field to determine the vision, aim, and goals for an organization/institution | |
| PLO11 | - | Awareness towards life-long learning and follow-up of the new information and knowledge in the field of study | |
| PLO12 | - | Develops the ability of using different resources in the form of academic rules, synthesis the information gathered, and effective presentation in an area which has not been studied | |
| PLO13 | - | Appropriately presents results of a study & reports findings in a master's thesis or report written in Turkish or in a foreign language | |
| PLO14 | - | Uses a package program of Econometrics, Statistics, and Operation Research or writes a new code | |
| PLO15 | - | Improves himself/herself constantly by defining educational requirements considering interests and talents in scientific, cultural, art and social fields besides career development | |
| PLO16 | - | Searches for new approaches and methods to solve problems being faced | |
| PLO17 | - | Recognizes and implements social, scientific, and professional ethic values | |
| PLO18 | - | Follows actuality, and interprets the data about economic and social events | |
| PLO19 | - | Develops solutions for organizations using Econometrics, Statistics, and Operation Research |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Applications of determinant function | Review of the relevant pages from sources | |
| 2 | Uniqueness of determinant and some properties of determinant | Review of the relevant pages from sources | |
| 3 | Eigenvalues and eigenvectors | Review of the relevant pages from sources | |
| 4 | Annihilating polynomials and invariant subalgebras | Review of the relevant pages from sources | |
| 5 | Diagonalizations and triangulation | Review of the relevant pages from sources | |
| 6 | Direct-sum decompositions | Review of the relevant pages from sources | |
| 7 | Invariant direct sums and The Primary Decomposition Theorem | Review of the relevant pages from sources | |
| 8 | Mid-Term Exam | Review of the relevant pages from sources | |
| 9 | Cyclic subspaces and annihilators | Review of the relevant pages from sources | |
| 10 | Cyclic Decompositions | Review of the relevant pages from sources | |
| 11 | Jordan Form | Review of the relevant pages from sources | |
| 12 | Inner products | Review of the relevant pages from sources | |
| 13 | Inner product spaces | Review of the relevant pages from sources | |
| 14 | Orthogonality and orthogonal complement | Review of the relevant pages from sources | |
| 15 | Orthogonality and orthogonal complement | Review of the relevant pages from sources | |
| 16 | Term Exams | Review of the relevant pages from sources | |
| 17 | Term Exams | Review of the relevant pages from sources |