FACULTY OF ARTS AND SCIENCES

Department of Mathematics

IE 354 | Course Introduction and Application Information

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
  IE 252 To succeed (To get a grade of at least DD)
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;
  • define combinatorial problems and their properties
  • solve combinational problems using basic counting techniques
  • identify famous combinatorial optimization problems
  • use the mathematical techniques and heuristics related to famous combinatorial optimization problems
  • apply algorithms involving combinatorial applications in graph theory, trees and searching, and networks
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.

 



Course Category

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 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
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.

 

EVALUATION SYSTEM

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 Exams
Midterm
2
70
Final Exam
Total

Weighting of Semester Activities on the Final Grade
100
Weighting of End-of-Semester Activities on the Final Grade
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
14
2
28
Field Work
0
Quizzes / Studio Critiques
0
Portfolio
0
Homework / Assignments
1
34
34
Presentation / Jury
0
Project
0
Seminar / Workshop
0
Oral Exam
0
Midterms
2
30
60
Final Exam
0
    Total
170

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics.

2

To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics.

3

To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials.

X
4

To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning.

5

To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals.

6

To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project.

7

To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge.

8

To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field.

X
9

To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security.

X
10

To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking.

X
11

To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language.

12

To be able to speak a second foreign language at a medium level of fluency efficiently.

13

To be able to relate the knowledge accumulated throughout the human history to their field of expertise.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 


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