• Basic information
• Learning outcomes
• Contents
• Assessment
• Workload

Learning outcomes

Upon successful completion of this course, students will be able to:

1. Grasp and use the relations between graphs theory and other disciplines.

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics in a specialized way
   2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
   3. Work effectively in multi-disciplinary research teams
   4. Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
   5. Effectively express his/her research ideas and findings both orally and in writing
   6. 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

   1. Written exam
   2. Homework assignment
   3. Seminar/presentation
2. Model and solve problems using graph theory

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics in a specialized way
   2. Understand relevant research methodologies and techniques and their appropriate application within his/her research field,
   3. Acquire scientific knowledge and work independently,
   4. Develop mathematical, communicative, problem-solving, brainstorming skills.
   5. Support his/her ideas with various arguments and present them clearly to a range of audience, formally and informally through a variety of techniques
   6. 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

   1. Written exam
   2. Homework assignment
   3. Seminar/presentation
3. Understand and to be able to use the necessary techniques to pursue research in graph theory.

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics in a specialized way
   2. Understand relevant research methodologies and techniques and their appropriate application within his/her research field,
   3. Acquire scientific knowledge and work independently,
   4. Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
   5. Effectively express his/her research ideas and findings both orally and in writing
   6. 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

   1. Written exam
   2. Homework assignment
   3. Seminar/presentation

Contents
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. Presentations and Project evaluations.
Week 14:	Hypergraph equivalents of basic theorems. Presentations and Project evaluations.
Week 15*:	-
Week 16*:	Final Exam.
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
	* Between 15th and 16th weeks is there a free week for students to prepare for final exam.

Assessment
Method of assessment	Week number	Weight (%)
Mid-terms:		0
Other in-term studies:		0
Project:	13, 14	25
Homework:	4, 6, 8, 10, 12	45
Quiz:		0
Final exam:	16	30
	Total weight:	(%)

Workload
Activity	Duration (Hours per week)	Total number of weeks	Total hours in term
Courses (Face-to-face teaching):	3	14
Own studies outside class:	3	14
Practice, Recitation:	0	0
Homework:	3	5
Term project:	4	12
Term project presentation:	2	1
Quiz:	0	0
Own study for mid-term exam:	0	0
Mid-term:	0	0
Personal studies for final exam:	10	4
Final exam:	2	1
		Total workload:
		Total ECTS credits:	*
	* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)