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| MATL7460 | Discrete Structures | 3+0+0 | ECTS:7.5 | | Year / Semester | Spring Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Doç. Dr. Tuncay KÖROĞLU | | Co-Lecturer | Prof. Dr. Bahadır Özgür GÜLER | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | Concepts of discrete mathematics is suitable for the problem of computer algorithms, programming languages, cryptography applications and software development. The operation logic of digital computers is discrete. Applications of discrete math are social sciences, electrical engineering, computer sciences, cryptology and business science. Therefore, the aim of this course is to examine discrete structures within discrete mathematics and to give the applications for different disciplines. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | define important algorithms and can make algorithm analysis. | | | | PO - 2 : | define recursive relations. | | | | PO - 3 : | define graphs and classify them. | | | | PO - 4 : | define trees and classify them. | | | | 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), PO : Learning Outcome | | |
| Sets and logic, Proof, Character strings, Relations and functions, Algorithms, Introduction to number theory, Recursive relations, Graphs, Trees. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Sets, Propositions, Inference rules, Qualifiers. | | | Week 2 | Proof techniques, Induction. | | | Week 3 | Arrays, Character strings , Relations, Functions, Equivalence relations, The matrix of relations. | | | Week 4 | Sets, Logic, Evidence, Character strings and application of correlation. | | | Week 5 | Algorithm analysis, Recursive algorithms. | | | Week 6 | The expression of integer, Euclidean algorithm, RSA-public-key encryption system. | | | Week 7 | Give iterative algorithm analysis by solving equations. | | | Week 8 | Algorithms, Number theory and applications of iterative equations. | | | Week 9 | Mid-term exam | | | Week 10 | Paths and cycles, Euler cycle, Hamilton path, Marketers problem. | | | Week 11 | The shortest path algorithm, the expression of Graphs, Isomorphic graphs, Planar graphs. | | | Week 12 | Application of the graphs. | | | Week 13 | Characterization of trees, Spanning trees, Minimal spanning trees, Binary trees. | | | Week 14 | Tree Scan, Decision Trees, Isomorphic Trees, Game trees. | | | Week 15 | Application of trees. | | | Week 16 | Final exam. | | | |
| 1 | Richard Johnsonbaugh, Discrete Mathematics, 7. Ed., Prentice Hall (2009). | | | |
| 1 | Kenneth H. Rosen, Discrete Mathematics and Its Applications, McGraw-Hill Int. Ed. (2007). | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 04/04/2020 | 120 | 50 | | End-of-term exam | 16 | 01/06/2020 | 120 | 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 | 3 | 14 | 42 | | Sınıf dışı çalışma | 2 | 14 | 28 | | Arasınav için hazırlık | 2 | 8 | 16 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 2 | 6 | 12 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 102 |
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