LAW | |||||
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 | Fall | 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) | List the relations between concepts and institutions related to various legal disciplines and this concepts and institutions. | |
2) | Have the knowledge of legal methodology and methods of comment. | |
3) | Comment the modern legal gains with the historical knowledge. | |
4) | Have the knowledge of philosophical currents of thought which are the bases of legal rules. | |
5) | Have the knowledge of legal regulations, judicial decisions and the scientific evaluations related to them. | |
6) | Resolve the juridical disagreements in light of legal acts, juridical decisions and doctrine. | |
7) | Use at least one foreign language as scientific language. | |
8) | Have the knowledge of the political and juridical foundation of the state. | |
9) | Have the knowledge of the historical development of the rights of individuals and societies and of the basic documents which are accepted throughout this development. | |
10) | Have the ability to resolve the disagreements which can violate the social order in national or international level. | |
11) | Have the ability to prevent the juridical disagreements between individuals. | |
12) | Have the knowledge of international and comparative law systems. | |
13) | Have the knowledge of the construction and the conduct of the national and international commercial relations. | |
14) | Use Turkish in an efficient way both verbal and written. | |
15) | Have the professional and ethical responsibility. | |
16) | Have the knowledge on the European Union’s legislation and institutions. | |
17) | Have the knowledge on juridical regulations and applications related to economical and financial mechanisms. | |
18) | Have the knowledge of the operation of the national and the international judicial bodies. |