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MATH 659 | Course Introduction and Application Information
| Course Name |
Graph Theory
|
|
Code
|
Semester
|
Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
|
ECTS
|
|
MATH 659
|
Fall/Spring
|
3
|
0
|
3
|
7.5
|
| Prerequisites |
None
|
|||||
| Course Language |
English
|
|||||
| Course Type |
Elective
|
|||||
| Course Level |
Third Cycle
|
|||||
| Mode of Delivery | - | |||||
| Teaching Methods and Techniques of the Course | - | |||||
| National Occupation Classification | - | |||||
| Course Coordinator | - | |||||
| Course Lecturer(s) | ||||||
| Assistant(s) | - | |||||
| 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 succeeded in this course;
|
| Course Description | Graphs, some special graphs, connectivity, blocks, trees, linear paths, planarity, Kuratowsky theorem, coloring, cromatic numbers, five color theorem, four color theorem, petri nets. |
|
|
Core Courses | |
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Management Skills Courses | ||
| Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
| Week | Subjects | Related Preparation | Learning Outcome |
| 1 | Graph | R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004. | |
| 2 | Specific Graphs | R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004. | |
| 3 | Graph modelling and applications. | R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004. | |
| 4 | Walk, Distance, Path, Cycle and Trees | R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004. | |
| 5 | Subgraph and graph operations | R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004. | |
| 6 | Midterm | ||
| 7 | Graph Isomoprhism | R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004. | |
| 8 | Trees: Binary Trees | R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004. | |
| 9 | Catalan Numbers. Travelling Binary Trees. Spanning Trees. | R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004. | |
| 10 | Edge and Vertex Connectivity. Network Reliability. | R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004. | |
| 11 | MaxMin Duality and Menger’s Theorem. Eular Path | R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004. | |
| 12 | Hamilton Paths and Cycles. Travelling Sales Man Problem | R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004. | |
| 13 | Binary operations and Graphs. | R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004. | |
| 14 | Graph coloring and applications in mathematica. | R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004. | |
| 15 | Petri Nets | R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson, 2004. | |
| 16 | Review of the Semester |
| Course Notes/Textbooks | J.Gross & J.Yellen, Graph Theory and its Applications, CRC Press, 1998 |
| Suggested Readings/Materials | Graph Theory: Modeling, Applications, and Algorithms, by Geir Agnarsson and Raymond Greenlaw, Pearson Prentice Hall, 2007 |
EVALUATION SYSTEM
| Semester Activities | Number | Weigthing |
| Participation |
1
|
5
|
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | ||
| Portfolio | ||
| Homework / Assignments | ||
| Presentation / Jury |
2
|
20
|
| Project |
1
|
25
|
| Seminar / Workshop | ||
| Oral Exams | ||
| Midterm |
1
|
20
|
| Final Exam |
1
|
30
|
| Total |
| Weighting of Semester Activities on the Final Grade |
70
|
|
| Weighting of End-of-Semester Activities on the Final Grade |
30
|
|
| 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 |
10
|
8
|
80
|
| Field Work |
0
|
||
| Quizzes / Studio Critiques |
0
|
||
| Portfolio |
0
|
||
| Homework / Assignments |
0
|
||
| Presentation / Jury |
2
|
10
|
20
|
| Project |
1
|
7
|
7
|
| Seminar / Workshop |
0
|
||
| Oral Exam |
0
|
||
| Midterms |
1
|
30
|
30
|
| Final Exam |
1
|
40
|
40
|
| Total |
225
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
|
#
|
PC Sub | Program Competencies/Outcomes |
* Contribution Level
|
||||
|
1
|
2
|
3
|
4
|
5
|
|||
| 1 |
To have an appropriate knowledge of methodological and practical elements of the basic sciences and to be able to apply this knowledge in order to describe engineering-related problems in the context of industrial systems. |
-
|
-
|
-
|
-
|
-
|
|
| 2 |
To be able to identify, formulate and solve Industrial Engineering-related problems by using state-of-the-art methods, techniques and equipment. |
-
|
-
|
-
|
-
|
-
|
|
| 3 |
To be able to use techniques and tools for analyzing and designing industrial systems with a commitment to quality. |
-
|
-
|
-
|
-
|
-
|
|
| 4 |
To be able to conduct basic research and write and publish articles in related conferences and journals. |
-
|
-
|
-
|
-
|
-
|
|
| 5 |
To be able to carry out tests to measure the performance of industrial systems, analyze and interpret the subsequent results. |
-
|
-
|
-
|
-
|
-
|
|
| 6 |
To be able to manage decision-making processes in industrial systems. |
-
|
-
|
-
|
-
|
-
|
|
| 7 |
To have an aptitude for life-long learning; to be aware of new and upcoming applications in the field and to be able to learn them whenever necessary. |
-
|
-
|
-
|
-
|
-
|
|
| 8 |
To have the scientific and ethical values within the society in the collection, interpretation, dissemination, containment and use of the necessary technologies related to Industrial Engineering. |
-
|
-
|
-
|
-
|
-
|
|
| 9 |
To be able to design and implement studies based on theory, experiments and modeling; to be able to analyze and resolve the complex problems that arise in this process; to be able to prepare an original thesis that comply with Industrial Engineering criteria. |
-
|
-
|
-
|
-
|
-
|
|
| 10 |
To be able to follow information about Industrial Engineering in a foreign language; to be able to present the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form. |
-
|
-
|
-
|
-
|
-
|
|
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
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