FACULTY OF ARTS AND SCIENCES

Department of Mathematics

MATH 455 | Course Introduction and Application Information

Course Name
Graph Theory
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 455
Fall/Spring
3
0
3
7

Prerequisites
None
Course Language
English
Course Type
Elective
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course -
Course Coordinator -
Course Lecturer(s)
Assistant(s)
Course Objectives Graph theory is very useful and useful in optimization and computation. The main objective of this course is to take a fresh approach to graph theory.
Learning Outcomes The students who succeeded in this course;
  • will be able to model with graphs.
  • will be able to determine whether or not a graph possesses certain properties.
  • will be able to design efficient algorithms for solving graph problems.
  • will be able to specialize in basic algorithm techniques in computer science.
  • will be able to solve the applications of biology in graph theory.
Course Description Graphs notations, Varieties of graphs, Walks and distance, paths, cycles, and trees, colorability, chromatic numbers, five color theorem, four color conjecture,

 



Course Category

Core Courses
Major Area Courses
X
Supportive Courses
Media and Management Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 Graphs and digraphs "Discrete and Combinatorial Mathematics: An Applied Introductiın" by R. P. Grimaldi, , Pearson, 5th Edition, 2003. ISBN-13: 978-0201726343
2 Common families of graphs "Discrete and Combinatorial Mathematics: An Applied Introductiın" by R. P. Grimaldi, , Pearson, 5th Edition, 2003. ISBN-13: 978-0201726343
3 Graph modeling applications "Discrete and Combinatorial Mathematics: An Applied Introductiın" by R. P. Grimaldi, , Pearson, 5th Edition, 2003. ISBN-13: 978-0201726343
4 Walks and distance, paths, cycles and trees "Discrete and Combinatorial Mathematics: An Applied Introductiın" by R. P. Grimaldi, , Pearson, 5th Edition, 2003. ISBN-13: 978-0201726343
5 Subgraphs, some graphs operations "Discrete and Combinatorial Mathematics: An Applied Introductiın" by R. P. Grimaldi, , Pearson, 5th Edition, 2003. ISBN-13: 978-0201726343
6 Midterm
7 Graph Isomorphism, representations "Discrete and Combinatorial Mathematics: An Applied Introductiın" by R. P. Grimaldi, , Pearson, 5th Edition, 2003. ISBN-13: 978-0201726343
8 Trees: Rooted trees, binary trees "Discrete and Combinatorial Mathematics: An Applied Introductiın" by R. P. Grimaldi, , Pearson, 5th Edition, 2003. ISBN-13: 978-0201726343
9 Catalan recursion, traversing a binary trees, spanning trees "Discrete and Combinatorial Mathematics: An Applied Introductiın" by R. P. Grimaldi, , Pearson, 5th Edition, 2003. ISBN-13: 978-0201726343
10 Vertex/edge connectivity, constructing reliable networks "Discrete and Combinatorial Mathematics: An Applied Introductiın" by R. P. Grimaldi, , Pearson, 5th Edition, 2003. ISBN-13: 978-0201726343
11 Max-Min duality and Menger’s theorems, Eulerian trails and tours "Discrete and Combinatorial Mathematics: An Applied Introductiın" by R. P. Grimaldi, , Pearson, 5th Edition, 2003. ISBN-13: 978-0201726343
12 Hamiltonian paths and cycles, traveling Salesman problem "Discrete and Combinatorial Mathematics: An Applied Introductiın" by R. P. Grimaldi, , Pearson, 5th Edition, 2003. ISBN-13: 978-0201726343
13 Vertex and edge coloring "Discrete and Combinatorial Mathematics: An Applied Introductiın" by R. P. Grimaldi, , Pearson, 5th Edition, 2003. ISBN-13: 978-0201726343
14 Map coloring, Mathematica applications "Discrete and Combinatorial Mathematics: An Applied Introductiın" by R. P. Grimaldi, , Pearson, 5th Edition, 2003. ISBN-13: 978-0201726343
15 Semester Review
16 Final Exam

 

Course Notes/Textbooks

"Discrete and Combinatorial Mathematics: An Applied Introduction" by R. P. Grimaldi , Pearson, 5th Edition, 2003. ISBN-13: 978-0201726343

Suggested Readings/Materials

"Graph Theory: Modeling, Applications, and Algorithms" by Geir Agnarsson and Raymond Greenlaw, Pearson, 1st Edition, 2007. ISBN-13: 978-0131423848

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
1
10
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm
2
50
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
3
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Theoretical Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: '.16.' x total hours)
16
0
Study Hours Out of Class
14
4
56
Field Work
0
Quizzes / Studio Critiques
0
Portfolio
0
Homework / Assignments
1
15
15
Presentation / Jury
0
Project
0
Seminar / Workshop
0
Oral Exam
0
Midterms
2
28
56
Final Exam
1
35
35
    Total
210

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics.

X
2

To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics.

X
3

To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials.

X
4

To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning.

5

To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals.

X
6

To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project.

7

To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge.

8

To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field.

9

To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security.

10

To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking.

11

To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language.

12

To be able to speak a second foreign language at a medium level of fluency efficiently.

13

To be able to relate the knowledge accumulated throughout the human history to their field of expertise.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 


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