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Information
| Code | BBZ104 |
| Name | Discrete Mathematics |
| Term | 2024-2025 Academic Year |
| Semester | 2. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Belirsiz |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. GÜZİN YÜKSEL |
| Course Instructor |
1 2 |
Course Goal / Objective
To teach mathematical and logical structures which are basis of computer science.
Course Content
Starting with logic, methods of proof, sets, functions, inductive proofs, basics of counting, Pigeon's Nest Principle, permutations, combinations, inclusion-exclusion principle,relations and properties, tree diagrams are studied.
Course Precondition
None
Resources
Kenneth H. Rosen, Discrete Mathematics and Its Applications, Fifth Edition, McGraw-Hill.
Notes
Lecture notes.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Understands the basic principles of Logic. |
| LO02 | Understand the basic principles of sets and operations in sets. |
| LO03 | Understand methods of mathematical proofs, and be able to apply them in problem solving. |
| LO04 | Demonstrate relations and determine their properties. |
| LO05 | Describes distribution problems. |
| LO06 | Solves the distributing problems using counting principles. |
| LO07 | Realises functional difficulty. |
| LO08 | Realises division algorithm. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Gain comprehensive knowledge of fundamental concepts, algorithms, and data structures in Computer Science. | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Learn essential computer topics such as software development, programming languages, and database management | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Understand advanced computer fields like data science, artificial intelligence, and machine learning. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Acquire knowledge of topics like computer networks, cybersecurity, and database design. | |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Develop skills in designing, implementing, and analyzing algorithms | 4 |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Gain proficiency in using various programming languages effectively | |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Learn skills in data analysis, database management, and processing large datasets. | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Acquire practical experience through working on software development projects. | |
| PLO09 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Strengthen teamwork and communication skills. | 3 |
| PLO10 | Yetkinlikler - Alana Özgü Yetkinlik | Foster a mindset open to technological innovations. | 4 |
| PLO11 | Yetkinlikler - Öğrenme Yetkinliği | Encourage the capacity for continuous learning and self-improvement. | 4 |
| PLO12 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Enhance the ability to solve complex problems | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Logic | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme, Beyin Fırtınası |
| 2 | Methods of Proof | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 3 | Set Operations; Functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 4 | The Integers and Division | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 5 | Mathematical Induction | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 6 | Permutations and Combinations; Inclusion-Exclusion, | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Soru-Cevap |
| 7 | General problem solving | Review of the relevant pages from sources | Öğretim Yöntemleri: Soru-Cevap, Problem Çözme |
| 8 | Mid-Term Exam | Review of the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Relations and Their Properties | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 10 | Representing Relations; Recurrence Relations | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 11 | Equivalence Relations | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 12 | Distrubution problems | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 13 | The Basics of Counting; The Pigeonhole Principle | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 14 | Axiomatic Structure of Real Numbers | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 15 | General problem solving | Review of the relevant pages from sources | Öğretim Yöntemleri: Beyin Fırtınası, Soru-Cevap, Problem Çözme |
| 16 | Term Exams | Review of the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review of the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
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 | 4 | 56 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 28 | 28 |
| Total Workload (Hour) | 138 | ||
| Total Workload / 25 (h) | 5,52 | ||
| ECTS | 6 ECTS | ||