MATH 602 | Course Introduction and Application Information - Applied Mathematics and Statistics – 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	Problem Solving Practical demonstration Lecture / Presentation
National Occupation Classification	-
Course Coordinator	-
Course Lecturer(s)	Doç. Dr. Cemal Murat ÖZKUT
Assistant(s)	Araş. Gör. Merve KAHRAMAN ARİMAN

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.
Related Sustainable Development Goals

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

Week	Subjects	Related Preparation
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

#

Program Competencies/Outcomes

* Contribution Level

1

2

3

4

5

1

To be able to demonstrate independent and critical thinking in Applied Mathematics and Statistics.

-

2

To be able to define problems in Applied Mathematics/Statistics and verify whether they are mathematically/statistically consistent.

-

X

3

To be able to analyse and solve real life problems using applied methods and interdisciplinary approach of Mathematics/Statistics.

-

X

4

To be able to independently conduct, conclude, and report on specialized research in Applied Mathematics and Statistics.

-

5

To be able to efficiently use national and international resources, for staying updated in the field, communicating with colleagues, and following the related literature.

-

6

To be able to develop proficiency in using computer software widely utilized in the fields of Applied Mathematics and Statistics.

-

7

To be able to evaluate solution processes efficiently using mathematical reasoning and modeling in order to contribute to the solutions of social and scientific problems.

-

8

To be able to synthesize theoretical frameworks with practical applications through mathematical and statistical methods.

-

9

To be able to develop strategies, policies and plans for problems and research areas in Applied Mathematics/Statistics in order to interpret the results and translate them into practice.

-

10

To be able to translate key topics, events, and phenomena in Applied Mathematics and Statistics into the context of other scientific disciplines.

-

X

-

11

To be able to engage in lifelong learning by continuously updating and improving knowledge and skills in Applied Mathematics and Statistics.

-

X

MATH 602 | Course Introduction and Application Information

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

EVALUATION SYSTEM

ECTS / WORKLOAD TABLE

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

IZMIR UNIVERSITY OF ECONOMICS GÜZELBAHÇE CAMPUS

GLOBAL CAREER

CONTRIBUTION TO SCIENCE

VALUING PEOPLE

BENEFIT TO SOCIETY