| ARTIFICIAL INTELLIGENCE ENGINEERING | |||||
| 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 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | En |
| Type of course: | Must Course |
| Course Level: | Bachelor |
| 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 |
| 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: | 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 |
| Attendance | 0 | % 0 |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | 0 | % 0 |
| Homework Assignments | % 0 | |
| Presentation | % 0 | |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | 2 | % 60 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 40 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| 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 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 14 | 7 | 98 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 0 | 0 | 0 |
| Quizzes | 0 | 0 | 0 |
| Preliminary Jury | 0 | 0 | 0 |
| Midterms | 2 | 2 | 4 |
| Paper Submission | 0 | 0 | 0 |
| Jury | 0 | 0 | 0 |
| 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) | Have sufficient background in mathematics, science and artificial intelligence engineering. | 5 |
| 2) | Use theoretical and applied knowledge in the fields of mathematics, science and artificial intelligence engineering together for engineering solutions. | 5 |
| 3) | Identify, define, formulate and solve engineering problems, select and apply appropriate analytical methods and modeling techniques for this purpose. | |
| 4) | Analyse a system, system component or process and design it under realistic constraints to meet desired requirements; apply modern design methods in this direction. | |
| 5) | Select and use modern techniques and tools necessary for engineering applications. | |
| 6) | Design and conduct experiments, collect data, and analyse and interpret results. | |
| 7) | Work effectively both as an individual and as a multi-disciplinary team member. | |
| 8) | Access information via conducting literature research, using databases and other resources | |
| 9) | Follow the developments in science and technology and constantly update themself with an awareness of the necessity of lifelong learning. | |
| 10) | Use information and communication technologies together with computer software with at least the European Computer License Advanced Level required by their field. | |
| 11) | Communicate effectively, both verbal and written; know a foreign language at least at the European Language Portfolio B1 General Level. | |
| 12) | Have an awareness of the universal and social impacts of engineering solutions and applications; know about entrepreneurship and innovation; and have an awareness of the problems of the age. | |
| 13) | Have a sense of professional and ethical responsibility. | |
| 14) | Have an awareness of project management, workplace practices, employee health, environment and work safety; know the legal consequences of engineering practices. |