GRADUATE SCHOOL
M.SC. In Industrial Engineering (With Thesis)
IE 501 | Course Introduction and Application Information
| Course Name |
Mathematics for Operations Research
|
|
Code
|
Semester
|
Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
|
ECTS
|
|
IE 501
|
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 |
Second Cycle
|
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| Mode of Delivery | - | |||||
| Teaching Methods and Techniques of the Course | - | |||||
| Course Coordinator | ||||||
| Course Lecturer(s) | ||||||
| Assistant(s) | - | |||||
| Course Objectives | The objectives of this course are to enable the students to review basic theoretical concepts of linear algebra, optimization, real analysis and functional analysis, to be exposed of operational research applications of these mathematical concepts. This course introduces the key role of mathematics in optimization and linear systems. It explains effective procedures for performing mathematical tasks that arise in many fields, including operations research, engineering, systems sciences, statistics, and economics.\nWe emphasize the basic concepts and methodologies, and include dozens of examples and applications. |
| Learning Outcomes |
The students who succeeded in this course;
|
| Course Description | The course basically covers sets, functions, countability, compact sets, lim sup and lim inf, convergence in R, convergence in metric spaces, normed spaces, inner product spaces, convexity, and functions of several variables |
|
|
Core Courses | |
| Major Area Courses |
X
|
|
| Supportive Courses | ||
| Media and Management Skills Courses | ||
| Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
| Week | Subjects | Related Preparation |
| 1 | Proof, contrapositives, converses, sets | Course notes |
| 2 | Sets, functions, countability | Course notes |
| 3 | Properties of R | Course notes |
| 4 | Sequences in R, subsequences, limits of sequences | Course notes |
| 5 | Infimum and supremum of a set, lim inf and lim sup | Course notes |
| 6 | lim inf and lim sup, series | Course notes |
| 7 | Metric spaces, open and closed sets | Course notes |
| 8 | Compact sets, connected sets | Course notes |
| 9 | Convergence in metric spaces | Course notes |
| 10 | Continuous functions | Course notes |
| 11 | Properties of continuous functions | Course notes |
| 12 | Uniform continuity | Course notes |
| 13 | Vector spaces | Course notes |
| 14 | Normed spaces, inner product spaces | Course notes |
| 15 | Functions of several variables | Course notes |
| 16 | Course review |
| Course Notes/Textbooks | Course notes |
| Suggested Readings/Materials | - Erhan Çınlar and Robert J. Vanderbei, Mathematical Methods of Engineering Analysis, free e-book, 2000. - Walter Rudin, Principles of Mathematical Analysis, 3rd edition, McGraw-Hill, 1976, ISBN: 0-07-054234-X - Kenneth A. Ross, Elementary Analysis:The Theory of Calculus, 2nd edition, Springer, 2013, ISBN: 978-1-4614-6270-5 - Rangarajan K. Sundaram, A First Course in Optimization Theory, Cambridge University Press, 1996, ISBN:978-0-521-49770-1 |
EVALUATION SYSTEM
| Semester Activities | Number | Weigthing |
| Participation | ||
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | ||
| Portfolio | ||
| Homework / Assignments |
6
|
20
|
| Presentation / Jury | ||
| Project | ||
| Seminar / Workshop | ||
| Oral Exams | ||
| Midterm |
1
|
35
|
| Final Exam |
1
|
45
|
| Total |
| Weighting of Semester Activities on the Final Grade |
55
|
|
| Weighting of End-of-Semester Activities on the Final Grade |
45
|
|
| 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 |
15
|
6
|
90
|
| Field Work |
0
|
||
| Quizzes / Studio Critiques |
0
|
||
| Portfolio |
0
|
||
| Homework / Assignments |
6
|
10
|
60
|
| Presentation / Jury |
0
|
||
| Project |
0
|
||
| Seminar / Workshop |
0
|
||
| Oral Exam |
0
|
||
| Midterms |
1
|
10
|
10
|
| Final Exam |
1
|
17
|
17
|
| Total |
225
|
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. |
X | ||||
| 2 | To be able to identify, formulate and solve Industrial Engineering-related problems by using state-of-the-art methods, techniques and equipment. |
X | ||||
| 3 | To be able to use techniques and tools for analyzing and designing industrial systems with a commitment to quality. |
X | ||||
| 4 | To be able to conduct basic research and write and publish articles in related conferences and journals. |
X | ||||
| 5 | To be able to carry out tests to measure the performance of industrial systems, analyze and interpret the subsequent results. |
X | ||||
| 6 | To be able to manage decision-making processes in industrial systems. |
X | ||||
| 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. |
X | ||||
| 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. |
X | ||||
| 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. |
X | ||||
| 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. |
X | ||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest