MATH 602 | Course Introduction and Application Information - M.SC. in Computer Engineering (With Thesis)

Course Name

Advanced Linear Algebra and Optimization

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 602	Fall/Spring	3	0	3	7.5

Prerequisites	None
Course Language	English
Course Type	Elective
Course Level	Third Cycle
Mode of Delivery	-
Teaching Methods and Techniques of the Course	-
National Occupation Classification	-
Course Coordinator	-
Course Lecturer(s)	Prof. Dr. Gözde Yazgı TÜTÜNCÜ
Assistant(s)	Araş. Gör. Dr. Ayşe BELER Araş. Gör. Merve KAHRAMAN ARİMAN Araş. Gör. Sıla Selenay KOÇ

Course Objectives

In this graduate course we introduce advanced mathematical optimization problem forms, models, and applications by introducing the relevant linear algebra concepts.

Learning Outcomes

The students who succeeded in this course;

will be able to modeloptimization problems.
will be able to develop and apply optimization related theorems.
will be able to solve decision problems using Simplex Algorithm.
will be able to calculate local optimum solution of a given problem.
will be able to calculate global optimum solution of a given problem.
will be able to analyze advanced linear systems.

Course Description

This course provides essential materials for analyzing advanced mathematical optimization problem forms, models, and applications by introducing the relevant linear algebra concepts.

Course Category	Core Courses
	Major Area Courses
	Supportive Courses
	Media and Management Skills Courses
	Transferable Skill Courses

Week	Subjects	Related Preparation	Learning Outcome
1	Scalars, Vectors and Matrices, Hyper planes and HalfSpaces.	Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi.
2	Vector and Matrix PNorms (P=1,2,(), Solving Linear Equations and Nonlinear Equations.	Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi.
3	Matrix Inverses, NDimensional Functions: Regular and Contour Plots.	Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi.
4	Regular and Partial Derivatives, Gradient Vector and Hessian Matrix.	Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi.
5	Quadratic Forms, Convex and Concave Functions, Convex Regions.	Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi.
6	Optimality Conditions for Unconstrained Problems.	Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi.
7	KarushKuhnTucker (KKT or KT) Conditions and their Geometry.	Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi.
8	Midterm	-
9	Solutions of an LP problem: Simplex Method	Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi.
10	Unconstrained Problems.	Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi.
11	Nonlinear optimization problems	Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi.
12	Nonlinear optimization problems	Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi.
13	Lagrange multipliers	Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi.
14	Project Presentations	Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi.
15	Project Presentations	Rao, S.S. (1984). “Optimization Theory and Application”. Wiley Eastern Ltd., New Delhi.
16	Final Exam

Course Notes/Textbooks	Handouts prepared by the lecturer and some extracts above and exercises will be given.
Suggested Readings/Materials	Convex Optimization by Stephen Boyd and Lieven Vandenberghe , 2004.

Semester Activities	Number	Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury	1	10
Project	1	20
Seminar / Workshop
Oral Exams
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
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	16	5	80
Field Work			0
Quizzes / Studio Critiques			0
Portfolio			0
Homework / Assignments			0
Presentation / Jury	1	10	10
Project	1	15	15
Seminar / Workshop			0
Oral Exam			0
Midterms	1	32	32
Final Exam	1	40	40
		Total	225

#	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.		-	-	-	-	-
2	Is well-informed about contemporary techniques and methods used in Computer Engineering and their limitations.		-	-	-	-	-
3	Uses scientific methods to complete and apply information from uncertain, limited or incomplete data; can combine and use information from different disciplines.		-	-	-	-	-
4	Is informed about new and upcoming applications in the field and learns them whenever necessary.		-	-	-	-	-
5	Defines and formulates problems related to Computer Engineering, develops methods to solve them and uses progressive methods in solutions.		-	-	-	-	-
6	Develops novel and/or original methods, designs complex systems or processes and develops progressive/alternative solutions in designs		-	-	-	-	-
7	Designs and implements studies based on theory, experiments and modelling; analyses and resolves the complex problems that arise in this process.		-	-	-	-	-
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.		-	-	-	-	-
9	Engages in written and oral communication at least in Level B2 of the European Language Portfolio Global Scale.		-	-	-	-	-
10	Communicates the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form.		-	-	-	-	-
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.		-	-	-	-	-
12	Highly regards scientific and ethical values in data collection, interpretation, communication and in every professional activity.		-	-	-	-	-

MATH 602 | Course Introduction and Application Information

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

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