| EUROPEAN UNION RELATIONS | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT1041 | Linear Algebra | Spring | 3 | 0 | 3 | 6 |
| This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
| Language of instruction: | English |
| Type of course: | Non-Departmental Elective |
| Course Level: | Bachelor’s Degree (First Cycle) |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Instructor MAHMOUD JAFARI SHAH BELAGHI |
| Course Lecturer(s): |
Prof. Dr. SÜREYYA AKYÜZ Assoc. Prof. HALE GONCE KÖÇKEN Dr. Öğr. Üyesi DİLRÜBA ÖZMEN ERTEKİN Prof. Dr. NAFİZ ARICA |
| Recommended Optional Program Components: | None |
| Course Objectives: | To define matrix operations such as addition, multiplication, inversion and to prove some of related properties; To teach to solve a system of linear equations by using matrices; To give the definitions of a vector space, subspace, base and dimension and to prove some of related theorems; To introduce the notion of a linear map and the types of linear maps (such as injective, surjective and bijective); To teach the matrix representation of linear mappings and proving some of related properties; To construct the space of linear mappings and to give its structural properties; To define the transpose of a linear functional and to prove related properties. |
|
The students who have succeeded in this course; 1. Solve systems of linear equations using multiple methods, including Gaussian elimination and matrix inversion. 2. Carry out matrix operations, including inverses and determinants. 3. Demonstrate understanding of the concepts of vector space and subspace. 4. Demonstrate understanding of linear independence, span, and basis. 5. Determine eigenvalues and eigenvectors and solve eigenvalue problems. 6. Apply principles of matrix algebra to linear transformations. |
| Systems of linear equations, matrices; Vector spaces, subspaces, base and dimension, coordinate; Linear mappings, kernel and image subspaces; Matrix representations of linear mappings; Linear functional, transpose of a linear mapping. Eigenvalues and eigenvectors, diagonalization of matrices. |
| Week | Subject | Related Preparation |
| 1) | - Introduction to Systems of Linear Equations - Gaussian Elimination and Gauss-Jordan Elimination | |
| 2) | - Operations with Matrices - Properties of Matrix Operations | |
| 3) | - The Inverse of a Matrix | |
| 4) | - The Determinant of a Matrix - Evaluation of a Determinant Using Elementary Operations | |
| 5) | - Properties of Determinants | |
| 6) | - Vectors in R^n - Vector Spaces \ review. | |
| 7) | - Subspaces of Vector Spaces - Spanning Sets and Linear Independence | |
| 8) | - Basis and Dimension | |
| 9) | - Rank of a Matrix and Systems of Linear Equations | |
| 10) | - Introduction to Linear Transformations | |
| 11) | - The Kernel and Range of a Linear Transformation | |
| 12) | - Matrices for Linear Transformations - Transition Matrices and Similarity \ review. | |
| 13) | - Eigenvalues and Eigenvectors - Diagonalization | |
| 14) | - Symmetric Matrices and Orthogonal Diagonalization |
| Course Notes / Textbooks: | Elementary Linear Algebra, Howard Anton, Wiley Publishing Co. (2000) |
| References: | 1.Lang, S., "Linear Algebra", Addison-Wesley Publishing Company, (1968). 2.Hoffman, K. M., Kunze R. A., "Linear Algebra", Printice Hall, 2. edition, (1971). 3.Koç, C., "Basic Linear Algebra", Matematik Vakfı, (1995). 4. Lipschutz, S., "Linear Algebra, Schaum’s Outline Series", McGraw-Hill, Inc., (1974). 5.Kolman, B., Hill, D. R., "Introductory Algebra with Applications", Prentice Hall |
| Semester Requirements | Number of Activities | Level of Contribution |
| Midterms | 2 | % 60 |
| Final | 1 | % 40 |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 60 | |
| PERCENTAGE OF FINAL WORK | % 40 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Study Hours Out of Class | 14 | 7 | 98 |
| Midterms | 2 | 2 | 4 |
| Final | 1 | 2 | 2 |
| Total Workload | 146 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution | |
| 1) | To be able to examine, interpret data and assess ideas with the scientific methods in the area of EU studies. | 2 |
| 2) | To be able to inform authorities and institutions in the area of EU studies, to be able to transfer ideas and proposals supported by quantitative and qualitative data about the problems. | 2 |
| 3) | To be introduced to and to get involved in other disciplines that EU studies are strongly related with (political science, international relations, law, economics, sociology, etc.) and to be able to conduct multi-disciplinary research and analysis on European politics. | 3 |
| 4) | To be able to evaluate current news on European Union and Turkey-EU relations and identify, analyze current issues relating to the EU’s politics and policies. | 2 |
| 5) | To be able to use English in written and oral communication in general and in the field of EU studies in particular. | 1 |
| 6) | To have ethical, social and scientific values throughout the processes of collecting, interpreting, disseminating and implementing data related to EU studies. | 1 |
| 7) | To be able to assess the historical development, functioning of the institutions and decision-making system and common policies of the European Union throughout its economic and political integration in a supranational framework. | 2 |
| 8) | To be able to evaluate the current legal, financial and institutional changes that the EU is going through. | 2 |
| 9) | To explain the dynamics of enlargement processes of the EU by identifying the main actors and institutions involved and compare previous enlargement processes and accession process of Turkey. | 2 |
| 10) | To be able to analyze the influence of the EU on political, social and economic system of Turkey. | 2 |
| 11) | To acquire insight in EU project culture and to build up project preparation skills in line with EU format and develop the ability to work in groups and cooperate with peers. | 2 |
| 12) | To be able to recognize theories and concepts used by the discipline of international relations and relate them to the historical development of the EU as a unique post-War political project. | 3 |