Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
7MATH411MATHEMATICAL OPTIMIZATION3+036

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course Introducing Mathematical structures and algorithms used for cost minimization, profit maximization, resource management and application of those algorithms in modelling various problems
Course Content
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers BERKANT USTAOĞLU
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources A. Schrijver “Combinatorial Optimization” Springer
W.J. Cook, W.H. Cunningham, W.R. Pulleyblank, A. Schrijver “Combinatorial Optimization”, Wiley

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 20
Quizzes 0 % 0
Homeworks 4 % 10
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 20
Total
7
% 50

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 42 1 42
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 14 7 98
Exams and Exam Preparations 7 6 42
Total Work Load   Number of ECTS Credits 6 182

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 Solve problems algorithmically
2 To model and solve practical problems with the assistance of mathematical tools.
3 To analyze problems and devise appropriate modelling structures.
4 Ability to abstract.


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Concepts in optimization W.J. Cook, W.H. Cunningham, W.R. Pulleyblank, A. Schrijver “Combinatorial Optimization”, Wiley
2 Linear programs W.J. Cook, W.H. Cunningham, W.R. Pulleyblank, A. Schrijver “Combinatorial Optimization”, Wiley
3 Linear optimization, problems and modeling W.J. Cook, W.H. Cunningham, W.R. Pulleyblank, A. Schrijver “Combinatorial Optimization”, Wiley
4 Systems of linear inequalities W.J. Cook, W.H. Cunningham, W.R. Pulleyblank, A. Schrijver “Combinatorial Optimization”, Wiley
5 Convex sets, polyhedra and extreme points W.J. Cook, W.H. Cunningham, W.R. Pulleyblank, A. Schrijver “Combinatorial Optimization”, Wiley
6 Simplex method, feasible solution W.J. Cook, W.H. Cunningham, W.R. Pulleyblank, A. Schrijver “Combinatorial Optimization”, Wiley
7 Two-phase method, degeneracy and termination W.J. Cook, W.H. Cunningham, W.R. Pulleyblank, A. Schrijver “Combinatorial Optimization”, Wiley
8 Duality and complementary slackness W.J. Cook, W.H. Cunningham, W.R. Pulleyblank, A. Schrijver “Combinatorial Optimization”, Wiley
9 Sensitivity W.J. Cook, W.H. Cunningham, W.R. Pulleyblank, A. Schrijver “Combinatorial Optimization”, Wiley
10 Network flows W.J. Cook, W.H. Cunningham, W.R. Pulleyblank, A. Schrijver “Combinatorial Optimization”, Wiley
11 Min-cut max-flow theorem W.J. Cook, W.H. Cunningham, W.R. Pulleyblank, A. Schrijver “Combinatorial Optimization”, Wiley
12 Integer programming W.J. Cook, W.H. Cunningham, W.R. Pulleyblank, A. Schrijver “Combinatorial Optimization”, Wiley
13 Non-linear optimization W.J. Cook, W.H. Cunningham, W.R. Pulleyblank, A. Schrijver “Combinatorial Optimization”, Wiley
14 Karush-Kuhn-Tucker Theorem W.J. Cook, W.H. Cunningham, W.R. Pulleyblank, A. Schrijver “Combinatorial Optimization”, Wiley
15 Final 1st week W.J. Cook, W.H. Cunningham, W.R. Pulleyblank, A. Schrijver “Combinatorial Optimization”, Wiley
16 Final 2nd week W.J. Cook, W.H. Cunningham, W.R. Pulleyblank, A. Schrijver “Combinatorial Optimization”, Wiley


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 4 4 4 2 3 1 3 1
C2 4 4 4 4 3 4 3 4 4 4 2
C3 4 4 1 4 3 4 4 4
C4 4 4 1 2 2 3 3 4 4 2

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


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