| GASTRONOMY (TURKISH) | |||||
| 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) | - Possess advanced level theoretical and practical knowledge supported by textbooks with updated information, practice equipments and other resources. | |
| 2) | Use of advanced theoretical and practical knowledge within the field. -Interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the field. | |
| 3) | Inform people and institutions, transfer ideas and solution proposals to problems in written and orally on issues in the field. - Share the ideas and solution proposals to problems on issues in the field with professionals and non-professionals by the support of qualitative and quantitative data. -Organize and implement project and activities for social environment with a sense of social responsibility. -Monitor the developments in the field and communicate with peers by using a foreign language at least at a level of European Language Portfolio B1 General Level. -Use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge. | |
| 4) | Evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach. -Determine learning needs and direct the learning. -Develop positive attitude towards lifelong learning. | |
| 5) | Act in accordance with social, scientific, cultural and ethic values on the stages of gathering, implementation and release of the results of data related to the field. - Possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also, environmental protection, worker's health and security. | |
| 6) | Conduct studies at an advanced level in the field independently. - Take responsibility both as a team member and individually in order to solve unexpected complex problems faced within the implementations in the field. - Planning and managing activities towards the development of subordinates in the framework of a project |