ECONOMICS AND FINANCE | |||||
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) | Build up a body of knowledge in mathematics and statistics, to use them, to understand how the mechanism of economy –both at micro and macro levels – works. | 3 |
2) | Understand the common as well as distinctive characters of the markets, industries, market regulations and policies. | 2 |
3) | Develop an awareness of different approaches to the economic events and why and how those approaches have been formed through the Economic History and understand the differences among those approaches by noticing at what extent they could explain the economic events. | 1 |
4) | Analyze the interventions of politics to the economics and vice versa. | 3 |
5) | Apply the economic analysis to everyday economic problems and evaluate the policy proposals for those problems by comparing opposite approaches. | 2 |
6) | Understand current and new economic events and how the new approaches to the economics are formed and evaluating. | 2 |
7) | Develop the communicative skills in order to explain the specific economic issues/events written, spoken and graphical form. | 3 |
8) | Know how to formulate the economics problems and issues and define the solutions in a well-formed written form, which includes the hypothesis, literature, methodology and results / empirical evidence. | 2 |
9) | Demonstrate the quantitative and qualitative capabilities and provide evidence for the hypotheses and economic arguments. | 2 |
10) | Understand the information and changes related to the economy by using a foreign language and communicate with colleagues. | 3 |