Course Name | Combinatorial Optimization |
Code | Semester | Theory (hour/week) | Application/Lab (hour/week) | Local Credits | ECTS |
---|---|---|---|---|---|
IE 354 | Fall/Spring | 3 | 0 | 3 | 6 |
Prerequisites |
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Course Language | English | ||||||||
Course Type | Elective | ||||||||
Course Level | First Cycle | ||||||||
Mode of Delivery | - | ||||||||
Teaching Methods and Techniques of the Course | |||||||||
Course Coordinator | - | ||||||||
Course Lecturer(s) | - | ||||||||
Assistant(s) | - |
Course Objectives | To introduce the concepts of combinatorics, counting rules, recurrence relations and other topics related with combinatorial optimization. To present the application of these concepts to operational research problems. |
Learning Outcomes | The students who succeeded in this course;
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Course Description | The course covers a broad range of topics in combinatorial modeling and the systematic analysis. The topics include basic counting rules, generating functions, recurrence relations, some famous combinatorial optimization problems and related mathematical techniques. |
Related Sustainable Development Goals | |
| Core Courses | |
Major Area Courses | ||
Supportive Courses | ||
Media and Managment Skills Courses | ||
Transferable Skill Courses |
Week | Subjects | Required Materials |
1 | What is Combinatorics? | |
2 | Introduction to Counting | Reading the slides supplied by the instructor Inroduction to Basic Counting Rules |
3 | Basic counting rules I | Reading the slides supplied by the instructor Basic Counting Rules |
4 | Basic counting rules II | Reading the slides supplied by the instructor Basic Counting Rules |
5 | Basic counting rules III | Reading the slides supplied by the instructor Basic Counting Rules |
6 | Recurrence relations I | Reading the slides supplied by the instructor Recurrence relations |
7 | Recurrence relations II | Reading the slides supplied by the instructor Recurrence relations |
8 | Midterm Exam | |
9 | Graph Theory I Famous Problems in Combinatorial Optimization I | Reading the slides supplied by the instructor Graph Theory |
10 | Graph Theory II Famous Problems in Combinatorial Optimization II | Reading the slides supplied by the instructor Graph Theory |
11 | Graph Theory III Famous Problems in Combinatorial Optimization III | Reading the slides supplied by the instructor Graph Theory |
12 | Graph Theory IV Famous Problems in Combinatorial Optimization IV | Reading the slides supplied by the instructor Graph Theory |
13 | Computational Complexity, Analysis of algorithms | Reading the slides supplied by the instructor Computational Complexity |
14 | Optimization Methods Famous Problems in Combinatorial Optimization V | Reading the slides supplied by the instructor Optimization Methods |
15 | Midterm Exam | |
16 | Review of the Semester |
Course Notes/Textbooks | Lovasz, Laszlo. Matching Theory. Ahuja, R., T. Magnanti, and J. Orlin. Network Flows. Schrijver, A. Theory of Linear and Integer Programming. Chvatal, V. Linear Programming. Bertsimas, D., and J. Tsitsiklis. Linear Optimization. Cook, W. J., W. H. Cunningham, W. R. Pulleyblank, and A. Schrijver. Combinatorial Optimization. Papadimitriou, C. H., and K. Steiglitz. Combinatorial Optimization. |
Suggested Readings/Materials | Introductory Combinatorics, R.A. Brualdi, Prentice Hall, NJ, 1999 Applied Combinatorics, F.S. Roberts, Prentice Hall, NJ, 1984 Applied Combinatorics, A. Tucker, John Wiley & Sons, NY, 1984 A Friendly Introduction to Graph Theory, F. Buckley and M. Lewinter, Prentice Hall, NJ, 2002 Discrete and Combinatorial Mathematics: An Applied Introduction, Fifth Edition. Ralph P. Grimaldi, Addison Wesley, 2003. Combinatorial Optimization: Algorithms and Complexity, Christos H. Papadimitriou and Kenneth Steiglitz, Dover Publications, 1998. Lecture handouts. |
Semester Activities | Number | Weigthing |
Participation | 1 | 10 |
Laboratory / Application | ||
Field Work | ||
Quizzes / Studio Critiques | ||
Portfolio | ||
Homework / Assignments | 1 | 20 |
Presentation / Jury | ||
Project | ||
Seminar / Workshop | ||
Oral Exam | ||
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 |
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 | 14 | 3 | 42 |
Field Work | |||
Quizzes / Studio Critiques | |||
Portfolio | |||
Homework / Assignments | 1 | 40 | |
Presentation / Jury | |||
Project | |||
Seminar / Workshop | |||
Oral Exam | |||
Midterms | 1 | 20 | |
Final Exams | 1 | 30 | |
Total | 180 |
# | Program Competencies/Outcomes | * Contribution Level | ||||
1 | 2 | 3 | 4 | 5 | ||
1 | To have knowledge in Mathematics, science, physics knowledge based on mathematics; mathematics with multiple variables, differential equations, statistics, optimization and linear algebra; to be able to use theoretical and applied knowledge in complex engineering problems | |||||
2 | To be able to identify, define, formulate, and solve complex mechatronics engineering problems; to be able to select and apply appropriate analysis and modeling methods for this purpose. | |||||
3 | To be able to design a complex electromechanical system, process, device or product with sensor, actuator, control, hardware, and software to meet specific requirements under realistic constraints and conditions; to be able to apply modern design methods for this purpose. | |||||
4 | To be able to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in Mechatronics Engineering applications; to be able to use information technologies effectively. | |||||
5 | To be able to design, conduct experiments, collect data, analyze and interpret results for investigating Mechatronics Engineering problems. | |||||
6 | To be able to work effectively in Mechatronics Engineering disciplinary and multidisciplinary teams; to be able to work individually. | |||||
7 | To be able to communicate effectively in Turkish, both in oral and written forms; to be able to author and comprehend written reports, to be able to prepare design and implementation reports, to present effectively, to be able to give and receive clear and comprehensible instructions. | |||||
8 | To have knowledge about global and social impact of engineering practices on health, environment, and safety; to have knowledge about contemporary issues as they pertain to engineering; to be aware of the legal ramifications of engineering solutions. | |||||
9 | To be aware of ethical behavior, professional and ethical responsibility; information on standards used in engineering applications. | |||||
10 | To have knowledge about industrial practices such as project management, risk management and change management; to have awareness of entrepreneurship and innovation; to have knowledge about sustainable development. | |||||
11 | Using a foreign language, he collects information about Mechatronics Engineering and communicates with his colleagues. ("European Language Portfolio Global Scale", Level B1) | |||||
12 | To be able to use the second foreign language at intermediate level. | |||||
13 | To recognize the need for lifelong learning; to be able to access information; to be able to follow developments in science and technology; to be able to relate the knowledge accumulated throughout the human history to Mechatronics Engineering. |
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest