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Syllabus ( MATH 563 )


   Basic information
Course title: Graph Theory
Course code: MATH 563
Lecturer: Prof. Dr. Sibel ÖZKAN
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
Language of instruction: English
Mode of delivery: Face to face
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.
   Learning outcomes Up

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

  1. Grasp and use the fundamental theory of graphs

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Work effectively in multi-disciplinary research teams
    3. Develop mathematical, communicative, problem-solving, brainstorming skills.

    Method of assessment

    1. Written exam
  2. Model various real world applications as problems on graphs

    Contribution to Program Outcomes

    1. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    2. Work effectively in multi-disciplinary research teams

    Method of assessment

    1. Written exam
    2. Homework assignment
  3. Master the techniques of research used in theoretical part of graph theory

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Acquire scientific knowledge and work independently
    3. Work effectively in multi-disciplinary research teams
    4. Design and conduct research projects independently
    5. Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
    6. Develop mathematical, communicative, problem-solving, brainstorming skills.

    Method of assessment

    1. Written exam
    2. Term paper
   Contents Up
Week 1: Introduction and History: Graphs as a model for real world problems
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
Week 15*: Network Flows
Week 16*: Final Exam
Textbooks and materials:
Recommended readings: 1. Introduction to Graph Theory, Douglas West, Prentice Hall
2. Modern Graph Theory - Bela Bollobas, Springer-Verlag
3. Reinhard Diestel, Graph Theory, Springer-Verlag
  * Between 15th and 16th weeks is there a free week for students to prepare for final exam.
Assessment Up
Method of assessment Week number Weight (%)
Mid-terms: 8 25
Other in-term studies: 0
Project: 14 25
Homework: 3,5,7,9,11,13 20
Quiz: 0
Final exam: 16 30
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 3 14
Own studies outside class: 2 14
Practice, Recitation: 0 0
Homework: 2 6
Term project: 4 14
Term project presentation: 2 1
Quiz: 0 0
Own study for mid-term exam: 10 2
Mid-term: 1 1
Personal studies for final exam: 10 2
Final exam: 2 1
    Total workload:
    Total ECTS credits:
*
  * ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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