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Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| MATHEMATICS PR. | |
| Code | MT416 |
| Name | Graph Theory |
| Term | 2019-2020 Academic Year |
| Semester | 8. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Label | E Elective |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. DİLEK ERSALAN |
| Course Instructor |
Doç. Dr. DİLEK ERSALAN
(Bahar)
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
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.
Course Content
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, Mengers theorem. Trees, spanning trees. Planarity, planar graphs, Eulars formula, testing for planarity.
Course Precondition
Resources
Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Knows preliminaries about graph theory. |
| LO02 | Knows isomorphic graphs and their applications. |
| LO03 | Knows paths and cycles. |
| LO04 | Knows diagrams and their characteristics. |
| LO05 | Knows the relation between graphs and their matrix. |
| LO06 | Knows Euler and Hamilton graphs and their applications. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | - | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | 2 |
| PLO02 | - | Understands importance of basic consepts of Algebra, Analaysis and Topology. | 1 |
| PLO03 | - | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 4 |
| PLO04 | - | Demonstrate the ability to express the basic theories of mathematics both correctly. | 2 |
| PLO05 | - | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 5 |
| PLO06 | - | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | 3 |
| PLO07 | - | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 2 |
| PLO08 | - | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 4 |
| PLO09 | - | Comprehends at least one of the computer programming languages. | 1 |
| PLO10 | - | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 2 |
| PLO11 | - | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | 2 |
| PLO12 | - | In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities. | 2 |
| PLO13 | - | Understands the programming techniques and shows the ability to do programming. | 1 |
| PLO14 | - | Demonstrates the ability to study mathematics both independently and as a group. | 4 |
| PLO15 | - | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | |
| PLO16 | - | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | |
| PLO17 | - | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | |
| PLO18 | - | Gains the ability to use information technologies effectively for contemporary mathematical applications. | |
| PLO19 | - | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | |
| PLO20 | - | Gains the consciousness of prefesional ethics and responsibility. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Definitions and Examples | Review of the relevant pages from sources | |
| 2 | Isomorphic Graphs | Review of the relevant pages from sources | |
| 3 | Matrix of Graphs | Review of the relevant pages from sources | |
| 4 | Paths | Review of the relevant pages from sources | |
| 5 | Cycles | Review of the relevant pages from sources | |
| 6 | Family of graph | Review of the relevant pages from sources | |
| 7 | Digraphs | Review of the relevant pages from sources | |
| 8 | Mid-Term Exam | Review of the topics discussed in the lecture notes and sources again | |
| 9 | Eulerian Graphs | Review of the relevant pages from sources | |
| 10 | Hamilton Graphs | Review of the relevant pages from sources | |
| 11 | Path Algorithms | Review of the relevant pages from sources | |
| 12 | Connectivity | Review of the relevant pages from sources | |
| 13 | Hamiltonian Digraphs | Review of the relevant pages from sources | |
| 14 | Matrices of Digraphs | Review of the relevant pages from sources | |
| 15 | Matrices of Digraphs | Review of the relevant pages from sources | |
| 16 | Term Exams | Review of the topics discussed in the lecture notes and sources again | |
| 17 | Term Exams | Review of the topics discussed in the lecture notes and sources again |
Assessment (Exam) Methods and Criteria
| Assessment Type | Midterm / Year Impact | End of Term / End of Year Impact |
|---|---|---|
| 1. Midterm Exam | 100 | 20 |
| General Assessment | ||
| Midterm / Year Total | 100 | 20 |
| 1. Final Exam | - | 80 |
| Grand Total | - | 100 |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 114 | ||
| Total Workload / 25 (h) | 4,56 | ||
| ECTS | 5 ECTS | ||