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| BIL2015 | Discrete Mathematics | 3+0+0 | ECTS:4 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of COMPUTER ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Prof. Dr. Vasif NABİYEV | | Co-Lecturer | | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | Objects studied in discrete mathematics are largely countable sets such as integers, finite graphs, and formal languages. The aim of this course is to teach mathematical basics of computer applications. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | describe mathematical basics of computer science and fundamental concepts of discrete systems | 1.1 - 1.2 - 1.3 - 5.3 | 1 | | LO - 2 : | apply mathematical methods to computer science related and other engineering problems | 1.1 - 1.2 - 1.3 - 5.3 | 1 | | LO - 3 : | describe combinatorical computation principles | 1.1 - 1.2 - 1.3 - 5.3 | 1,3 | | LO - 4 : | use graph theory in modeling of discrete systems.
| 1.1 - 1.2 - 1.3 - 5.3 | 1,3 | | 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 | | |
| Sets. Functions. Logic and Proofs. discrete and continuous probability. Enumerative combinatorics. Recurrence Relations. Graph Theory, Representing graphs. The 4-color problem. Boolean Algebra and Combinatorial Circuits. Sets. Formal systems. Hamilton and Euler loops. Counting and relations. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Introduction. Sets and Relations | | | Week 2 | Models. relations and Their properties. Representing Relations. Discrete and continuous probability. | | | Week 3 | Boolean algebra. Boolean Functions Properties. | | | Week 4 | Completenesss. | | | Week 5 | Boole Function Applications. Minimization of Circuits | | | Week 6 | Introduction to Graphs | | | Week 7 | Representing Graphs and Graph Izomorphism | | | Week 8 | Mid-term exam | | | Week 9 | Connectivity | | | Week 10 | Euler and Hamilton Paths | | | Week 11 | Graf Coloring | | | Week 12 | Shortest Path Problems. Planar Graphs | | | Week 13 | short exam | | | Week 14 | Application problems | | | Week 15 | Characterization. Forbidden figurs | | | Week 16 | End-of-term exam | | | |
| 1 | Özel Ders notları, Nabiyev V. 2009, Algoritmalar. Kombinatorika, Seçkin Y. , 864 s. | | | |
| 1 | Kenneth H. Rosen, 2000, Handbook of Discrete and Combinatorial Mathematics CRC Press. ISBN 0-8493-0149-1. | | | 2 | Richard Johnsonbaugh, 2005, Discrete Mathematics 6th ed. Macmillan. ISBN 0-13-045803. | | | 3 | Ralph P. Grimaldi,2003, Discrete and Combinatorial Mathematics: An Applied Introduction 5th ed. Addison Wesley. ISBN 0-20-172634 | | | 4 | Kenneth H. Rosen, 2000, Discrete Mathematics and Its Applications 6th ed. McGraw Hill. ISBN 0-07-288008-2. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 8 | 28/03/2014 | 120 | 30 | | Quiz | 13 | 02/05/2014 | 110 | 20 | | End-of-term exam | 16 | 30/05/2014 | 2 | 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 | 10 | 1 | 10 | | Arasınav | 2 | 1 | 2 | | Kısa sınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 14 | 1 | 14 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 100 |
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