GRADUATE SCHOOL
M.SC. In Industrial Engineering (With Thesis)
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
|
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Course Language |
English
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Course Type |
Elective
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Course Level |
Third Cycle
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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. |
|
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 |
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. |
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 |
60
|
|
Weighting of End-of-Semester Activities on the Final Grade |
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
|
20
|
20
|
Project |
1
|
25
|
25
|
Seminar / Workshop |
0
|
||
Oral Exam |
0
|
||
Midterms |
1
|
32
|
32
|
Final Exam |
1
|
40
|
40
|
Total |
245
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
#
|
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. |
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2 | To be able to identify, formulate and solve Industrial Engineering-related problems by using state-of-the-art methods, techniques and equipment. |
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3 | To be able to use techniques and tools for analyzing and designing industrial systems with a commitment to quality. |
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4 | To be able to conduct basic research and write and publish articles in related conferences and journals. |
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5 | To be able to carry out tests to measure the performance of industrial systems, analyze and interpret the subsequent results. |
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6 | To be able to manage decision-making processes in industrial systems. |
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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. |
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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. |
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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. |
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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