IE 354 | Course Introduction and Application Information - Department of Mathematics

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

-

National Occupation Classification

-

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

#	Content	PC Sub	* Contribution Level
#	Content	PC Sub	1	2	3	4	5
1	define combinatorial problems and their properties
2	solve combinational problems using basic counting techniques
3	identify famous combinatorial optimization problems
4	use the mathematical techniques and heuristics related to famous combinatorial optimization problems
5	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

Week	Subjects	Related Preparation	Learning Outcome
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.

Semester Activities	Number	Weighting	LO 1	LO 2	LO 3	LO 4	LO 5
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

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

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	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.		-	-	-	-	-