Syllabus ( MATH 665 )
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Basic information
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Course title: |
Advanced Topics in Graph Theory |
Course code: |
MATH 665 |
Lecturer: |
Prof. Dr. Sibel ÖZKAN
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ECTS credits: |
7.5 |
GTU credits: |
0 (3+0+0) |
Year, Semester: |
2018, Fall |
Level of course: |
Third Cycle (Doctoral) |
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: |
Graph Theory |
Professional practice: |
No |
Purpose of the course: |
In this course, based on basic knowledge on graph theory, more advanced topics such as network flows, Ramsey theory, Random graphs, graphs related with groups, and hypergraphs will be covered. |
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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 relations between graphs theory and other disciplines.
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics in a specialized way
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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
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Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
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Effectively express his/her research ideas and findings both orally and in writing
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Be aware of issues relating to the rights of other researchers and of research subjects e.g. confidentiality, attribution, copyright, ethics, malpractice, ownership of data
Method of assessment
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Written exam
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Homework assignment
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Seminar/presentation
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Model and solve problems using graph theory
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics in a specialized way
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Understand relevant research methodologies and techniques and their appropriate application within his/her research field,
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Acquire scientific knowledge and work independently,
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Develop mathematical, communicative, problem-solving, brainstorming skills.
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Support his/her ideas with various arguments and present them clearly to a range of audience, formally and informally through a variety of techniques
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Be aware of issues relating to the rights of other researchers and of research subjects e.g. confidentiality, attribution, copyright, ethics, malpractice, ownership of data
Method of assessment
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Written exam
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Homework assignment
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Seminar/presentation
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Understand and to be able to use the necessary techniques to pursue research in graph theory.
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics in a specialized way
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Understand relevant research methodologies and techniques and their appropriate application within his/her research field,
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Acquire scientific knowledge and work independently,
-
Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
-
Effectively express his/her research ideas and findings both orally and in writing
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Be aware of issues relating to the rights of other researchers and of research subjects e.g. confidentiality, attribution, copyright, ethics, malpractice, ownership of data
Method of assessment
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Written exam
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Homework assignment
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Seminar/presentation
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Contents
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Week 1: |
Basic concepts in directed and undirected graphs. |
Week 2: |
Introduction to network flows. |
Week 3: |
Max flow - Min cut Theorem |
Week 4: |
Connectivity and Menger's Theorem |
Week 5: |
Fundamental Ramsey Theorems |
Week 6: |
Ramsey Numbers |
Week 7: |
Induced Ramsey Theorems |
Week 8: |
Introduction to Random Graphs |
Week 9: |
Basic random graph models |
Week 10: |
Simple properties of almost all graphs |
Week 11: |
Arc-transitive graphs |
Week 12: |
Edge-transitive graphs |
Week 13: |
Hypergraphs, hypergraph equivalents of basic concepts |
Week 14: |
Hypergraph equivalents of basic theorems |
Week 15*: |
Presentations and Project evaluations |
Week 16*: |
Presentations and Project evaluations |
Textbooks and materials: |
R. Diestel, Graph Theory (Graduate Texts in Mathematics), Springer-Verlag B. Bollobas, Modern Graph Theory (Graduate Texts in Mathematics), Springer - Verlag |
Recommended readings: |
C. Godsil, G. Royle, Algebraic Graph Theory (Graduate Texts in Mathematics), Springer-Verlag C. Berge, Hypergraphs, North-Holland Mathematical Library B. Bollobas, Random Graphs, Cambridge Studies in Advanced Mathematics
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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: |
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0 |
Other in-term studies: |
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0 |
Project: |
14, 15 |
25 |
Homework: |
4, 6, 8, 10, 12 |
45 |
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: |
3 |
14 |
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Practice, Recitation: |
0 |
0 |
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Homework: |
3 |
5 |
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Term project: |
3 |
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: |
0 |
0 |
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Mid-term: |
0 |
0 |
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Personal studies for final exam: |
10 |
4 |
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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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