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
Course Language	English
Course Type	Elective
Course Level	Second Cycle
Mode of Delivery	-
Teaching Methods and Techniques of the Course	-
National Occupation Classification	-
Course Coordinator	Öğr. Gör. Dr. Haluk Eliş
Course Lecturer(s)	Öğr. Gör. Dr. Haluk Eliş
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

#	Content	PC Sub	* Contribution Level
#	Content	PC Sub	1	2	3	4	5
1	Be able to resolve linear independence and find null spaces and factors of matrices.
2	Be able to determine existence of restricted solutions to linear equations and inequalities.
3	Be able to resolve definiteness of Hermitian and real symmetric matrices by Gaussian pivoting.

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

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	Learning Outcome
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, 3^rd edition, McGraw-Hill, 1976, ISBN: 0-07-054234-X

- Kenneth A. Ross, Elementary Analysis:The Theory of Calculus, 2^nd 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	Weighting	LO 1	LO 2	LO 3
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

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