MAT4057 Graph TheoryBahçeşehir UniversityDegree Programs MATHEMATICSGeneral Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
MATHEMATICS
Bachelor TR-NQF-HE: Level 6 QF-EHEA: First Cycle EQF-LLL: Level 6

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT4057 Graph Theory Fall 3 0 3 6
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: English
Type of course: Departmental Elective
Course Level: Bachelor’s Degree (First Cycle)
Mode of Delivery: Face to face
Course Coordinator : Instructor MOHAMED KHALIFA
Recommended Optional Program Components: None
Course Objectives: Definition of Disconnected structures and their applications. The aim gives the application of graph theory in computer sciences, operation research, social sciences and biomathematics. In this concept connectivity, graph coloring, trees, Euler and Hamilton paths, Cycles, Mathcing, Covering, Shortest path and network structures will be given.

Learning Outcomes

The students who have succeeded in this course;
The students who succeeded in this course;
o will be able to define and analyze problems and to find solutions based on scientific methods.
o will be able to understand basic concepts of graph theory
o will be able to apply the graph coloring methods to the daily life problems
o will be able to use the dynamic graphs for helath sciences

Course Content

Graphs, some special graphs, connectivity, blocks, trees, linear paths, planarity, Kuratowsky theorem, coloring, cromatic numbers, five color theorem, four color theorem, petri nets.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Graph
2) Specific Graphs
3) Graph modelling and applications.
4) Walk, Distance, Path, Cycle and Trees
5) Subgraph and graph operations
6) Graph Isomoprhism
7) Trees: Binary Trees
8) Catalan Numbers. Travelling Binary Trees. Spanning Trees.
9) Edge and Vertex Connectivity.
10) Network Reliability.
11) MaxMin Duality and Menger’s Theorem. Eular Path
12) Hamilton Paths and Cycles. Travelling Sales Man Problem
13) Binary operations and Graphs.
14) Graph coloring and applications in mathematica. Petri nets.

Sources

Course Notes / Textbooks: R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004.
References:

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Quizzes 2 % 5
Homework Assignments 7 % 5
Midterms 2 % 50
Final 1 % 40
Total % 100
PERCENTAGE OF SEMESTER WORK % 60
PERCENTAGE OF FINAL WORK % 40
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Homework Assignments 7 4 28
Quizzes 2 5 10
Midterms 2 10 20
Final 1 25 25
Total Workload 125

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) To have a grasp of basic mathematics, applied mathematics and theories and applications in Mathematics 5
2) To be able to understand and assess mathematical proofs and construct appropriate proofs of their own and also define and analyze problems and to find solutions based on scientific methods, 5
3) To be able to apply mathematics in real life with interdisciplinary approach and to discover their potentials, 4
4) To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, 4
5) To be able to tell theoretical and technical information easily to both experts in detail and non-experts in basic and comprehensible way, 4
6) To be familiar with computer programs used in the fields of mathematics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level, 3
7) To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement, 3
8) To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense,
9) By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere, 5
10) To be able to continue lifelong learning by renewing the knowledge, the abilities and the competencies which have been developed during the program, and being conscious about lifelong learning, 3
11) To be able to adapt and transfer the knowledge gained in the areas of mathematics ; such as algebra, analysis, number theory, mathematical logic, geometry and topology to the level of secondary school, 3
12) To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. 4