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| Course Description |
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| Course Name |
: |
Graph Theory |
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| Course Code |
: |
MT 416 |
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| Course Type |
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Optional |
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| Level of Course |
: |
First Cycle |
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| Year of Study |
: |
4 |
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| Course Semester |
: |
Spring (16 Weeks) |
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| ECTS |
: |
5 |
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| Name of Lecturer(s) |
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Asst.Prof.Dr. DİLEK KAHYALAR
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| Learning Outcomes of the Course |
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Knows preliminaries about graph theory.
Knows isomorphic graphs and their applications.
Knows paths and cycles.
Knows diagrams and their characteristics.
Knows the relation between graphs and their matrix.
Knows Euler and Hamilton graphs and their applications.
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| Mode of Delivery |
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Face-to-Face |
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| Prerequisites and Co-Prerequisites |
: |
None |
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| Recommended Optional Programme Components |
: |
None |
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| Aim(s) of Course |
: |
To inform the students about the Graphs theory which was based on the problem mentioned by the Swiss mathematician Euler in his article “The problem of seven bridges”. |
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| Course Contents |
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The definitions of graphs, isomorphic graphs. Paths and Cycles, examples of special graphs. Adjacency and incidence matrices of graphs. The definitions of digraphs. Eulerian and Hamiltonian graphs and digraphs. The shortest and longest path algorithms. Connectivity, Menger’s theorem. Trees, spanning trees. Planarity, planar graphs, Eular’s formula, testing for planarity.
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| Language of Instruction |
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Turkish |
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| Work Place |
: |
Classrooms Faculty of Science Annex |
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Course Outline /Schedule (Weekly) Planned Learning Activities |
| Week | Subject | Student's Preliminary Work | Learning Activities and Teaching Methods |
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1 |
Definitions and Examples |
Review of the relevant pages from sources |
Lecture and discussion |
|
2 |
Isomorphic Graphs |
Review of the relevant pages from sources |
Lecture and discussion |
|
3 |
Matrix of Graphs |
Review of the relevant pages from sources |
Lecture and discussion |
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4 |
Paths |
Review of the relevant pages from sources |
Lecture and discussion |
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5 |
Cycles |
Review of the relevant pages from sources |
Lecture and discussion |
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6 |
Family of graph |
Review of the relevant pages from sources |
Lecture and discussion |
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7 |
Digraphs |
Review of the relevant pages from sources |
Lecture and discussion |
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8 |
Mid-term exam |
Review of the topics discussed in the lecture notes and sources again |
Written Exam |
|
9 |
Eulerian Graphs |
Review of the relevant pages from sources |
Lecture and discussion |
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10 |
Hamilton Graphs |
Review of the relevant pages from sources |
Lecture and discussion |
|
11 |
Path Algorithms |
Review of the relevant pages from sources |
Lecture and discussion |
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12 |
Connectivity |
Review of the relevant pages from sources |
Lecture and discussion |
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13 |
Hamiltonian Digraphs |
Review of the relevant pages from sources |
Lecture and discussion |
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14 |
Matrices of Digraphs |
Review of the relevant pages from sources |
Lecture and discussion |
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15 |
Matrices of Digraphs |
Review of the relevant pages from sources |
Lecture and discussion |
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16/17 |
Final exam |
Review of the topics discussed in the lecture notes and sources |
Written exam |
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Required Course Resources |
| Resource Type | Resource Name |
| Recommended Course Material(s) |
 Graphs, An Introductory Approach, Robin J. Wilson, John J. Watkins
Graph Theory, Addision Wesley
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| Required Course Material(s) | |
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Assessment Methods and Assessment Criteria |
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Semester/Year Assessments |
Number |
Contribution Percentage |
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Mid-term Exams (Written, Oral, etc.) |
1 |
100 |
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Homeworks/Projects/Others |
0 |
0 |
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Total |
100 |
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Rate of Semester/Year Assessments to Success |
40 |
| |
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Final Assessments
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100 |
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Rate of Final Assessments to Success
|
60 |
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Total |
100 |
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| Contribution of the Course to Key Learning Outcomes |
| # | Key Learning Outcome | Contribution* |
|
1 |
Is able to prove Mathematical facts encountered in secondary school. |
4 |
|
2 |
Recognizes the importance of basic notions in Algebra, Analysis and Topology |
4 |
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3 |
Develops maturity of mathematical reasoning and writes and develops mathematical proofs. |
5 |
|
4 |
Is able to express basic theories of mathematics properly and correctly both written and verbally |
4 |
|
5 |
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. |
4 |
|
6 |
Expresses clearly the relationship between objects while constructing a model |
3 |
|
7 |
Draws mathematical models such as formulas, graphs and tables and explains them |
1 |
|
8 |
Is able to mathematically reorganize, analyze and model problems encountered. |
5 |
|
9 |
Knows at least one computer programming language |
4 |
|
10 |
Uses effective scientific methods and appropriate technologies to solve problems |
0 |
|
11 |
Knows programming techniques and is able to write a computer program |
0 |
|
12 |
Is able to do mathematics both individually and in a group. |
0 |
|
13 |
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians |
0 |
|
14 |
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields |
0 |
| * Contribution levels are between 0 (not) and 5 (maximum). |
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| Student Workload - ECTS |
| Works | Number | Time (Hour) | Total Workload (Hour) |
| Course Related Works |
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Class Time (Exam weeks are excluded) |
14 |
3 |
42 |
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Out of Class Study (Preliminary Work, Practice) |
14 |
3 |
42 |
| Assesment Related Works |
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Homeworks, Projects, Others |
0 |
0 |
0 |
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Mid-term Exams (Written, Oral, etc.) |
1 |
15 |
15 |
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Final Exam |
1 |
20 |
20 |
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Total Workload: | 119 |
| Total Workload / 25 (h): | 4.76 |
| ECTS Credit: | 5 |
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