| Course Name | Advanced Linear Algebra and Optimization |
| Code | Semester | Theory (hour/week) | Application/Lab (hour/week) | Local Credits | ECTS |
|---|---|---|---|---|---|
| MATH 602 | Fall/Spring | 3 | 0 | 3 | 7.5 |
| Prerequisites | None | |||||
| Course Language | English | |||||
| Course Type | Elective | |||||
| Course Level | Third Cycle | |||||
| Mode of Delivery | - | |||||
| Teaching Methods and Techniques of the Course | ||||||
| Course Coordinator | - | |||||
| Course Lecturer(s) | ||||||
| Assistant(s) | ||||||
| Course Objectives | In this graduate course we introduce advanced mathematical optimization problem forms, models, and applications by introducing the relevant linear algebra concepts. |
| Learning Outcomes | The students who succeeded in this course;
|
| Course Description | This course provides essential materials for analyzing advanced mathematical optimization problem forms, models, and applications by introducing the relevant linear algebra concepts. |
| Related Sustainable Development Goals | |
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| Core Courses | |
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Managment Skills Courses | ||
| Transferable Skill Courses |
| Week | Subjects | Required Materials |
| 1 | Scalars, Vectors and Matrices, Hyper planes and HalfSpaces. | Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi. |
| 2 | Vector and Matrix PNorms (P=1,2,(), Solving Linear Equations and Nonlinear Equations. | Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi. |
| 3 | Matrix Inverses, NDimensional Functions: Regular and Contour Plots. | Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi. |
| 4 | Regular and Partial Derivatives, Gradient Vector and Hessian Matrix. | Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi. |
| 5 | Quadratic Forms, Convex and Concave Functions, Convex Regions. | Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi. |
| 6 | Optimality Conditions for Unconstrained Problems. | Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi. |
| 7 | KarushKuhnTucker (KKT or KT) Conditions and their Geometry. | Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi. |
| 8 | Solutions of an LP problem: Simplex Method | Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi. |
| 9 | Unconstrained Problems. | Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi. |
| 10 | Nonlinear optimization problems | Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi. |
| 11 | Nonlinear optimization problems | Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi. |
| 12 | Nonlinear optimization problems | Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi. |
| 13 | Lagrange multipliers | Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi. |
| 14 | Project Presentations | Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi. |
| 15 | Project Presentations | Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi. |
| 16 | Review of the Semester |
| Course Notes/Textbooks | Handouts prepared by the lecturer and some extracts above and exercises will be given. |
| Suggested Readings/Materials | Convex Optimization by Stephen Boyd and Lieven Vandenberghe , 2004. |
| Semester Activities | Number | Weigthing |
| Participation | ||
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | ||
| Portfolio | ||
| Homework / Assignments | ||
| Presentation / Jury | 1 | 10 |
| Project | 1 | 20 |
| Seminar / Workshop | ||
| Oral Exam | ||
| Midterm | 1 | 30 |
| Final Exam | 1 | 40 |
| Total |
| Weighting of Semester Activities on the Final Grade | 60 | |
| Weighting of End-of-Semester Activities on the Final Grade | 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 | 16 | 5 | 80 |
| Field Work | |||
| Quizzes / Studio Critiques | |||
| Portfolio | |||
| Homework / Assignments | |||
| Presentation / Jury | 1 | 20 | |
| Project | 1 | 25 | |
| Seminar / Workshop | |||
| Oral Exam | |||
| Midterms | 1 | 32 | |
| Final Exams | 1 | 40 | |
| Total | 245 |
| # | Program Competencies/Outcomes | * Contribution Level | ||||
1 | 2 | 3 | 4 | 5 | ||
| 1 | To be able to have adequate knowledge in Mathematics, Life Sciences and Bioengineering; to be able to use theoretical and applied information in these areas to model and solve Bioengineering problems. | |||||
| 2 | To be able to use scientific methods to complete and apply information from uncertain, limited or incomplete data; to be able to combine and use information from related disciplines. | |||||
| 3 | To be able to design and apply theoretical, experimental and model-based research; to be able to solve complex problems in such processes. | |||||
| 4 | Being able to utilize Natural Sciences and Bioengineering principles to design systems, devices and processes. | |||||
| 5 | To be able to follow and apply new developments and technologies in the field of Bioengineering. | |||||
| 6 | To be able to work effectively in multi-disciplinary teams within the discipline of Bioengineering; to be able to exhibit individual work. | |||||
| 7 | To be able to have the knowledge about the social, environmental, health, security and law implications of Bioengineering applications, to be able to have the knowledge to manage projects and business applications, and to be able to be aware of their limitations in professional life. | |||||
| 8 | To be able to have the social, scientific and ethical values in the stages of collection, interpretation, dissemination and application of data related to the field of Bioengineering. | |||||
| 9 | To be able to prepare an original thesis/term project in accordance with the criteria related to the field of Bioengineering. | |||||
| 10 | To be able to follow information about Bioengineering in a foreign language and to be able to participate in discussions in academic environments. | |||||
| 11 | To be able to improve the acquired knowledge, skills and qualifications for social and universal purposes regarding the studied area. | |||||
| 12 | To be able to recognize regional and global issues/problems, and to be able to develop solutions based on research and scientific evidence related to Bioengineering. | |||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
