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| MAT3036 | Graph Theory | 4+0+0 | ECTS:6 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Bahadır Özgür GÜLER | | Co-Lecturer | Prof. Dr. Ali Hikmet Değer | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | Graphs enable modeling and practical solutions of problems in many areas from science to technology and industry. The aim of this course is to introduce students to graph structures and to lay the foundations for advanced studies on this subject. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | To have knowledge about the scope, applications, history, problems and methods of mathematics that will be beneficial to humanity as both a scientific and intellectual discipline.
| 2,6 | 1 | | LO - 2 : | Identify, formulate and analyze real-life problems using mathematical techniques. | 2,6 | 1 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome | | |
| History of graph theory, graphs, subgraphs, graph isomorphisms, paths and trees, Euler tour, Hamilton cycles, applications to real life problems |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Basic Principles of Counting, Addition and Multiplication Rules | | | Week 2 | Permutation | | | Week 3 | Combination and Binomial theorem | | | Week 4 | Terminology, Basic Definitions | | | Week 5 | History, Königsberg Bridge Problem | | | Week 6 | Graph Modeling of Real Life Problems | | | Week 7 | Subgraphs and graph isomorphisms | | | Week 8 | Paths and trees | | | Week 9 | Mid-term exam | | | Week 10 | Cycles | | | Week 11 | Directed graphs and Euler tour | | | Week 12 | Planar graphs and the famous 4 color problem | | | Week 13 | Hamilton Cycles and the Travelling Salesman Problem | | | Week 14 | Connectedness | | | Week 15 | Dijkstra shortest path algorithm | | | Week 16 | Final exam | | | |
| 1 | Introduction to Graph Theory, Douglas West, Prentice Hall | | | |
| 1 | Discrete and Combinatorial Mathematics, R. P. Grimaldi, Addison-Wesley | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 25/04/2025 | 1 | 50 | | End-of-term exam | 16 | 05/06/2025 | 1 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 4 | 14 | 56 | | Sınıf dışı çalışma | 5 | 14 | 70 | | Arasınav için hazırlık | 8 | 1 | 8 | | Arasınav | 1 | 1 | 1 | | Uygulama | 2 | 14 | 28 | | Dönem sonu sınavı için hazırlık | 4 | 4 | 16 | | Dönem sonu sınavı | 1 | 1 | 1 | | Total work load | | | 180 |
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