Syllabus ( MATH 563 )
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Basic information
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Course title: |
Graph Theory |
Course code: |
MATH 563 |
Lecturer: |
Prof. Dr. Sibel ÖZKAN
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ECTS credits: |
7.5 |
GTU credits: |
3 (3+0+0) |
Year, Semester: |
1/2, Fall and Spring |
Level of course: |
Second Cycle (Master's) |
Type of course: |
Area Elective
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Language of instruction: |
English
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Mode of delivery: |
Face to face
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Pre- and co-requisites: |
None |
Professional practice: |
No |
Purpose of the course: |
Combinatorial graphs serve as models for many problems in science, business, and industry. The aim of the course is to introduce students to the fundamentals of these structures. In this course, background for advanced theoretical studies will be given and the applications such as scheduling, network design, and optimization will be introduced. Topics include graphs and digraphs, trees, matchings, factorizations, connectivity, networks, graph colorings, and planar graphs. |
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Learning outcomes
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Upon successful completion of this course, students will be able to:
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Grasp and use the fundamental theory of graphs
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
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Work effectively in multi-disciplinary research teams
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Develop mathematical, communicative, problem-solving, brainstorming skills.
Method of assessment
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Written exam
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Model various real world applications as problems on graphs
Contribution to Program Outcomes
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Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
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Work effectively in multi-disciplinary research teams
Method of assessment
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Written exam
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Homework assignment
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Master the techniques of research used in theoretical part of graph theory
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
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Acquire scientific knowledge and work independently
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Work effectively in multi-disciplinary research teams
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Design and conduct research projects independently
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Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
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Develop mathematical, communicative, problem-solving, brainstorming skills.
Method of assessment
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Written exam
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Term paper
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Contents
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Week 1: |
Introduction and History: Graphs as a model for real world problems
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Week 2: |
Basics and Terminology |
Week 3: |
Subgraphs and Graph Isomorphisms |
Week 4: |
Paths and Trees |
Week 5: |
Cycles |
Week 6: |
Planar Graphs |
Week 7: |
Independence and Vertex Coloring |
Week 8: |
Edge Coloring |
Week 9: |
Mathcings |
Week 10: |
Graph Factorizations |
Week 11: |
Cycle Decompositions |
Week 12: |
Amalgamation method |
Week 13: |
Vertex Domination and its applications in military |
Week 14: |
Connectivity. Network Flows.
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Week 15*: |
- |
Week 16*: |
Final Exam. |
Textbooks and materials: |
Introduction to Graph Theory, Douglas West, Prentice Hall
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Recommended readings: |
1. Modern Graph Theory - Bela Bollobas, Springer-Verlag 2. Reinhard Diestel, Graph Theory, Springer-Verlag |
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* Between 15th and 16th weeks is there a free week for students to prepare for final exam.
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Assessment
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Method of assessment |
Week number |
Weight (%) |
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Mid-terms: |
8 |
25 |
Other in-term studies: |
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0 |
Project: |
14 |
25 |
Homework: |
3,5,7,9,11,13 |
20 |
Quiz: |
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0 |
Final exam: |
16 |
30 |
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Total weight: |
(%) |
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Workload
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Activity |
Duration (Hours per week) |
Total number of weeks |
Total hours in term |
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Courses (Face-to-face teaching): |
3 |
14 |
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Own studies outside class: |
2 |
14 |
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Practice, Recitation: |
0 |
0 |
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Homework: |
2 |
6 |
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Term project: |
4 |
14 |
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Term project presentation: |
2 |
1 |
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Quiz: |
0 |
0 |
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Own study for mid-term exam: |
10 |
2 |
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Mid-term: |
1 |
1 |
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Personal studies for final exam: |
10 |
2 |
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Final exam: |
2 |
1 |
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Total workload: |
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Total ECTS credits: |
* |
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* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)
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