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MATH 602 | Course Introduction and Application Information
| 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 | - | |||||
| National Occupation Classification | - | |||||
| 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. |
|
|
Core Courses | |
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Management Skills Courses | ||
| Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
| Week | Subjects | Related Preparation | Learning Outcome |
| 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 | Midterm | - | |
| 9 | Solutions of an LP problem: Simplex Method | Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi. | |
| 10 | Unconstrained 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 | Final Exam |
| 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. |
EVALUATION SYSTEM
| 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 Exams | ||
| Midterm |
1
|
30
|
| Final Exam |
1
|
40
|
| Total |
| Weighting of Semester Activities on the Final Grade |
3
|
60
|
| Weighting of End-of-Semester Activities on the Final Grade |
1
|
40
|
| Total |
ECTS / WORKLOAD TABLE
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Theoretical Course Hours (Including exam week: 16 x total hours) |
16
|
3
|
48
|
| Laboratory / Application Hours (Including exam week: '.16.' x total hours) |
16
|
0
|
|
| Study Hours Out of Class |
16
|
5
|
80
|
| Field Work |
0
|
||
| Quizzes / Studio Critiques |
0
|
||
| Portfolio |
0
|
||
| Homework / Assignments |
0
|
||
| Presentation / Jury |
1
|
10
|
10
|
| Project |
1
|
15
|
15
|
| Seminar / Workshop |
0
|
||
| Oral Exam |
0
|
||
| Midterms |
1
|
32
|
32
|
| Final Exam |
1
|
40
|
40
|
| Total |
225
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
|
#
|
PC Sub | Program Competencies/Outcomes |
* Contribution Level
|
||||
|
1
|
2
|
3
|
4
|
5
|
|||
| 1 |
To have an appropriate knowledge of methodological and practical elements of the basic sciences and to be able to apply this knowledge in order to describe engineering-related problems in the context of industrial systems. |
-
|
-
|
-
|
-
|
-
|
|
| 2 |
To be able to identify, formulate and solve Industrial Engineering-related problems by using state-of-the-art methods, techniques and equipment. |
-
|
-
|
-
|
-
|
-
|
|
| 3 |
To be able to use techniques and tools for analyzing and designing industrial systems with a commitment to quality. |
-
|
-
|
-
|
-
|
-
|
|
| 4 |
To be able to conduct basic research and write and publish articles in related conferences and journals. |
-
|
-
|
-
|
-
|
-
|
|
| 5 |
To be able to carry out tests to measure the performance of industrial systems, analyze and interpret the subsequent results. |
-
|
-
|
-
|
-
|
-
|
|
| 6 |
To be able to manage decision-making processes in industrial systems. |
-
|
-
|
-
|
-
|
-
|
|
| 7 |
To have an aptitude for life-long learning; to be aware of new and upcoming applications in the field and to be able to learn them whenever necessary. |
-
|
-
|
-
|
-
|
-
|
|
| 8 |
To have the scientific and ethical values within the society in the collection, interpretation, dissemination, containment and use of the necessary technologies related to Industrial Engineering. |
-
|
-
|
-
|
-
|
-
|
|
| 9 |
To be able to design and implement studies based on theory, experiments and modeling; to be able to analyze and resolve the complex problems that arise in this process; to be able to prepare an original thesis that comply with Industrial Engineering criteria. |
-
|
-
|
-
|
-
|
-
|
|
| 10 |
To be able to follow information about Industrial Engineering in a foreign language; to be able to present the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form. |
-
|
-
|
-
|
-
|
-
|
|
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
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