FACULTY OF ARTS AND SCIENCES
Department of Mathematics
MATH 305 | Course Introduction and Application Information
Course Name |
Optimization I
|
Code
|
Semester
|
Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
|
ECTS
|
MATH 305
|
Fall
|
3
|
0
|
3
|
7
|
Prerequisites |
None
|
|||||
Course Language |
English
|
|||||
Course Type |
Required
|
|||||
Course Level |
First Cycle
|
|||||
Mode of Delivery | - | |||||
Teaching Methods and Techniques of the Course | Problem SolvingPractical demonstrationLecture / Presentation | |||||
Course Coordinator | - | |||||
Course Lecturer(s) | ||||||
Assistant(s) |
Course Objectives | The objective of this course is to provide a deep understanding of mathematical aspects of linear programming (LP). |
Learning Outcomes |
The students who succeeded in this course;
|
Course Description | This course aims to cover basic theory and applications of linear optimization. |
|
Core Courses |
X
|
Major Area Courses | ||
Supportive Courses | ||
Media and Management Skills Courses | ||
Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
Week | Subjects | Related Preparation |
1 | The concept of Optimization. Modeling and formulation of Optimization problems | Wayne L. Winston, ‘’Operations Research: Applications and Algorithms’’, Cengage Learning; 4th Edition 2003. ISBN-13 : 978-0534380588 Chapter 1 |
2 | Linear programming (LP) Solutions of an LP problem: Geometric method | Wayne L. Winston, ‘’Operations Research: Applications and Algorithms’’, Cengage Learning; 4th Edition 2003. ISBN-13 : 978-0534380588 Chapter 2, Chapter 3 |
3 | Solutions of an LP problem: Analytic Method | Wayne L. Winston, ‘’Operations Research: Applications and Algorithms’’, Cengage Learning; 4th Edition 2003. ISBN-13 : 978-0534380588 Chapter 3 |
4 | Solutions of an LP problem: simplex method in canonic form | Lecture Notes |
5 | Simplex table, simplex method in table form | Lecture Notes |
6 | Two phase simplex method | Lecture Notes |
7 | Big M simplex method | Lecture Notes |
8 | Revised simplex method | Lecture Notes |
9 | Interior point method for LP | Lecture Notes |
10 | Interpretation of duality, shadow prices, theory of existence | Lecture Notes |
11 | Complementary slackness | Lecture Notes |
12 | Bigger model changes, reoptimization, parametric programing | Lecture Notes |
13 | Solution of LP problems using Phyton and Gurobi | Lecture Notes |
14 | Project presentations | |
15 | Semester review | |
16 | Final exam |
Course Notes/Textbooks | Lecture Notes
|
Suggested Readings/Materials | Wayne L. Winston, ‘’Operations Research: Applications and Algorithms’’, Cengage Learning; 4th Edition 2003. ISBN-13 : 978-0534380588 Pablo Pedregal, “Introduction to Optimization” Springer-Verlag New York, 1st Edition, 2004. ISBN-13: 978-0387403984 R.K.Sundaram, ''A first Course in Optimization Theory'' Cambridge Press, First Edition, 1996. ISBN-13: 978-0521497701 Edwin K.P. Chong and Stanislaw H. Zak, “An Introduction to Optimization” Wiley, 2nd Edition, 2001. ISBN-13: 978-0471391265
|
EVALUATION SYSTEM
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 |
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
|
4
|
56
|
Field Work |
0
|
||
Quizzes / Studio Critiques |
0
|
||
Portfolio |
0
|
||
Homework / Assignments |
0
|
||
Presentation / Jury |
1
|
18
|
18
|
Project |
1
|
18
|
18
|
Seminar / Workshop |
0
|
||
Oral Exam |
0
|
||
Midterms |
1
|
30
|
30
|
Final Exam |
1
|
40
|
40
|
Total |
210
|
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. |
X | ||||
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. |
X | ||||
5 | To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals. |
X | ||||
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. |
|||||
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. |
|||||
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. |
|||||
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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