GRADUATE SCHOOL
M.SC. in Computer Engineering (With Thesis)
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
|
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| Course Language |
English
|
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| Course Type |
Elective
|
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| Course Level |
Third Cycle
|
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| Mode of Delivery | - | |||||
| Teaching Methods and Techniques of the Course | - | |||||
| 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 |
| 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
|
#
|
Program Competencies/Outcomes |
* Contribution Level
|
||||
|
1
|
2
|
3
|
4
|
5
|
||
| 1 | Accesses information in breadth and depth by conducting scientific research in Computer Engineering; evaluates, interprets and applies information. |
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| 2 | Is well-informed about contemporary techniques and methods used in Computer Engineering and their limitations. | |||||
| 3 | Uses scientific methods to complete and apply information from uncertain, limited or incomplete data; can combine and use information from different disciplines. |
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| 4 | Is informed about new and upcoming applications in the field and learns them whenever necessary. | |||||
| 5 | Defines and formulates problems related to Computer Engineering, develops methods to solve them and uses progressive methods in solutions. |
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| 6 | Develops novel and/or original methods, designs complex systems or processes and develops progressive/alternative solutions in designs | |||||
| 7 | Designs and implements studies based on theory, experiments and modelling; analyses and resolves the complex problems that arise in this process. |
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| 8 | Can work effectively in interdisciplinary teams as well as teams of the same discipline, can lead such teams and can develop approaches for resolving complex situations; can work independently and takes responsibility. |
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| 9 | Engages in written and oral communication at least in Level B2 of the European Language Portfolio Global Scale. |
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| 10 | Communicates the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form. |
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| 11 | Is knowledgeable about the social, environmental, health, security and law implications of Computer Engineering applications, knows their project management and business applications, and is aware of their limitations in Computer Engineering applications. |
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| 12 | Highly regards scientific and ethical values in data collection, interpretation, communication and in every professional activity. |
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*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest