Information Package / Course Catalogue - Adnan Menderes University

General Information Unit Staff Academic Information Programme Outcomes Course Structure Diagram Contact Information

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Graph Theory and Applications in Mathematics Education

Course Code	: MTE534
Course Type	: Area Elective
Couse Group	: Second Cycle (Master's Degree)
Education Language	: Turkish
Work Placement	: N/A

Theory	: 3
Prt.	: 0
Credit	: 3
Lab	: 0
ECTS	: 8

Objectives of the Course

To give students the opportunity to construct the basics and concepts of graph theory and develop their perspectives.

Course Content

History of graph theory and some usage areas, definition of graph, types of graphs and matrix representations of graphs, connectivity and isomorphic graphs, operations in graphs, Euler and Hamilton graphs, planar and non-planar graphs, coloring in graphs and type of graph. The place of graph theory in mathematics education and examination of studies in the literature.

Name of Lecturer(s)

Learning Outcomes

1.	Learns the history of graph theory.
2.	Understands and explains the basic concepts of graph theory.
3.	Can explain Euler and Hamilton diagrams by giving examples from daily life.
4.	Understands what coloring is.
5.	Solves problems that require the application of graph theory.

Recommended or Required Reading

1.	J. Trudeau, Introduction to Graph Theory, Dover Publication, 1993.
2.	J. Clark, D. A. Holton, A First Look At Graph Theory, World Scientific, 1991.
3.	Tutte, W. T., & Tutte, W. T. (2001). Graph theory (Vol. 21). Cambridge university press.

Weekly Detailed Course Contents

Week 1 - Theoretical

History of graph theory and some applications.

Week 2 - Theoretical

Basic concepts in graph theory

Week 3 - Theoretical

Graph types and Matrix representation

Week 4 - Theoretical

Connectivity and isomorphic graphs

Week 5 - Theoretical

Graph operations and the concept of distance in graphs

Week 6 - Theoretical

Eulerian and Hamiltonian graphs

Week 7 - Theoretical

Application of graphs to daily life problems

Week 8 - Theoretical

Shortest path problem. (Midterm Exam)

Week 9 - Theoretical

Planar graphs and Euler's formula

Week 10 - Theoretical

Kind of a graph and non-planar graphs

Week 11 - Theoretical

Coloring problem

Week 12 - Theoretical

The place of graph theory in mathematics education

Week 13 - Theoretical

Relationship of graph theory with other disciplines (Engineering, software, number theory)

Week 14 - Theoretical

Examination of graph theory studies in mathematics education national and international literature

Assessment Methods and Criteria

Type of Assessment	Count	Percent
Midterm Examination	1	%30
Final Examination	1	%70

Workload Calculation

Activities	Count	Preparation	Time	Total Work Load (hours)
Lecture - Theory	14	2	3	70
Individual Work	14	0	3	42
Midterm Examination	1	36	2	38
Final Examination	1	48	2	50
TOTAL WORKLOAD (hours)				200

Contribution of Learning Outcomes to Programme Outcomes

	PÇ-1	PÇ-2	PÇ-3	PÇ-4	PÇ-5	PÇ-6	PÇ-7	PÇ-8	PÇ-9	PÇ-10	PÇ-11	PÇ-12	PÇ-13
OÇ-1	4	4	5	4	5	4	4	4	4			3	4
OÇ-2	4		5	5		4	4	4	4			4
OÇ-3	4	4		4		4	4	4			4
OÇ-4	4	4		4		4	4			4	4		4
OÇ-5	4	4	5	4	4	4			4			4

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