GRADUATE SCHOOL
M.SC. in Computer Engineering (Without 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 | ||
| 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 | Accesses information in breadth and depth by conducting scientific research in Computer Engineering, evaluates, interprets and applies information. | X | ||||
| 2 | Is well-informed about contemporary techniques and methods used in Computer Engineering and their limitations. | X | ||||
| 3 | Uses scientific methods to complete and apply information from uncertain, limited or incomplete data, can combine and use information from different disciplines. | X | ||||
| 4 | Is informed about new and upcoming applications in the field and learns them whenever necessary. | X | ||||
| 5 | Defines and formulates problems related to Computer Engineering, develops methods to solve them and uses progressive methods in solutions. | X | ||||
| 6 | Develops novel and/or original methods, designs complex systems or processes and develops progressive/alternative solutions in designs. | X | ||||
| 7 | Designs and implements studies based on theory, experiments and modelling, analyses and resolves the complex problems that arise in this process. | X | ||||
| 8 | Can work effectively in interdisciplinary teams as well as teams of the same discipline, can lead such teams and can develop approaches for resolving complex situations, can work independently and takes responsibility. | X | ||||
| 9 | Engages in written and oral communication at least in Level B2 of the European Language Portfolio Global Scale. | X | ||||
| 10 | Communicates the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form. | X | ||||
| 11 | Is knowledgeable about the social, environmental, health, security and law implications of Computer Engineering applications, knows their project management and business applications, and is aware of their limitations in Computer Engineering applications. | X | ||||
| 12 | Highly regards scientific and ethical values in data collection, interpretation, communication and in every professional activity. | X | ||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest