| Course Name | Linear Algebra I |
| Code | Semester | Theory (hour/week) | Application/Lab (hour/week) | Local Credits | ECTS |
|---|---|---|---|---|---|
| MATH 105 | Fall | 3 | 0 | 3 | 5 |
| Prerequisites | None | |||||
| Course Language | English | |||||
| Course Type | Required | |||||
| Course Level | First Cycle | |||||
| Mode of Delivery | face to face | |||||
| Teaching Methods and Techniques of the Course | Problem SolvingQ&ALecturing / Presentation | |||||
| Course Coordinator | ||||||
| Course Lecturer(s) | ||||||
| Assistant(s) | ||||||
| Course Objectives | This course aims to teach students to solve linear systems of equations using several methods, introduce linear independence and linear transformations, and find inverses and determinants of matrices. |
| Learning Outcomes | The students who succeeded in this course;
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| Course Description | This course introduces linear system of equations, vector and matrix equations, linear independence, linear transformation, determinants and applications in various fields. |
| Related Sustainable Development Goals | |
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| Core Courses | X |
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Managment Skills Courses | ||
| Transferable Skill Courses |
| Week | Subjects | Required Materials |
| 1 | Systems of linear equations. Row reduction and echelon forms | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed. (Pearson, 2015). Section 1.1, 1.2 |
| 2 | Row reduction and echelon forms, vector equations | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed. (Pearson, 2015). Section 1.2, 1.3 |
| 3 | The matrix equation, solution sets of linear systems | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed. (Pearson, 2015). Section 1.4, 1.5 |
| 4 | Applications of linear systems. Linear independence | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed. (Pearson, 2015). Section 1.6, 1.7 |
| 5 | Introduction to linear transformations The matrix of a linear transformation | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed. (Pearson, 2015). Section 1.8, 1.9 |
| 6 | Linear models in business, science, and engineering | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed. (Pearson, 2015). Section 1.10 |
| 7 | Midterm Exam | |
| 8 | Matrix Operations, The inverse of a matrix | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed. (Pearson, 2015). Section 2.1, 2.2 |
| 9 | Characterizations of invertible matrices | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed. (Pearson, 2015). Section 2.3 |
| 10 | Matrix factorizations | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed. (Pearson, 2015). Section 2.5 |
| 11 | The Leontief Input-Output Model | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed. (Pearson, 2015). Section 2.6 |
| 12 | Subspaces of R^n, dimension and rank | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed. (Pearson, 2015). Section 2.8, 2.9 |
| 13 | Introduction to determinants, Properties of determinants | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed. (Pearson, 2015). Section 3.1, 3.2. |
| 14 | Cramer’s rule, volume and linear transformations | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed. (Pearson, 2015). Section 3.3 |
| 15 | Semester review | |
| 16 | Final exam |
| Course Notes/Textbooks | David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed. (Pearson, 2015). ISBN-13:978-0321982384 |
| Suggested Readings/Materials | Howard Anton, Chris Rorres, ''Elementary Linear Algebra'' Publisher:Wiley, 9th Edition,2005. ISBN-13: 978-0471669593 Seymour Lipschutz, ''Linear Algebra'', Shaum’s Outline Series, 2nd Edition.2011, ISBN-13:9780070380073 |
| Semester Activities | Number | Weigthing |
| Participation | ||
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | 5 | 30 |
| Portfolio | ||
| Homework / Assignments | ||
| Presentation / Jury | ||
| Project | ||
| Seminar / Workshop | ||
| Oral Exam | ||
| Midterm | 1 | 30 |
| Final Exam | 1 | 40 |
| Total |
| Weighting of Semester Activities on the Final Grade | 6 | 60 |
| Weighting of End-of-Semester Activities on the Final Grade | 1 | 40 |
| Total |
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Course Hours (Including exam week: 16 x total hours) | 16 | 3 | 48 |
| Laboratory / Application Hours (Including exam week: 16 x total hours) | 16 | ||
| Study Hours Out of Class | 14 | 3 | 42 |
| Field Work | |||
| Quizzes / Studio Critiques | 5 | 6 | |
| Portfolio | |||
| Homework / Assignments | |||
| Presentation / Jury | |||
| Project | |||
| Seminar / Workshop | |||
| Oral Exam | |||
| Midterms | 1 | 12 | |
| Final Exams | 1 | 18 | |
| Total | 150 |
| # | Program Competencies/Outcomes | * Contribution Level | ||||
1 | 2 | 3 | 4 | 5 | ||
| 1 | To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics. | X | ||||
| 2 | To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics. | X | ||||
| 3 | To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials. | |||||
| 4 | To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning. | X | ||||
| 5 | To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals. | X | ||||
| 6 | To be able to take responsibility both as a team member or individual 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. | |||||
| 7 | To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge. | |||||
| 8 | To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field. | |||||
| 9 | To be able to 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. | |||||
| 10 | To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking. | |||||
| 11 | To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language. | |||||
| 12 | To be able to speak a second foreign language at a medium level of fluency efficiently. | |||||
| 13 | To be able to relate the knowledge accumulated throughout the human history to their field of expertise. | |||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
