TÜRKÇE
ENGLISH
Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| ARTIFICIAL INTELLIGENCE AND MACHINE LEARNING PR. (ENGLISH) | |
| Code | YZZ106 |
| Name | Discrete Mathematics |
| Term | 2025-2026 Academic Year |
| Semester | 2. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | İngilizce |
| Level | Belirsiz |
| Type | Normal |
| Label | BS Basic Science Courses C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. GÜZİN YÜKSEL |
| Course Instructor |
The current term course schedule has not been prepared yet.
|
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 | Explains the basic principles of logic. |
| LO02 | Recognize the basic principles and operations of sets. |
| LO03 | Uses mathematical proof methods in problem solving. |
| LO04 | Expresses relations and properties of relations. |
| LO05 | Describes distribution problems. |
| LO06 | Solves the distributing problems using counting principles. |
| LO07 | Explains functional difficulty. |
| LO08 | Uses division algorithm. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | It provides a broad range of knowledge about fundamental Computer Science concepts, algorithms and data structures. | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Learns basic computer topics such as software development, programming languages, and database management. | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Understands advanced computing fields such as data science, artificial intelligence, and machine learning. | |
| PLO04 | Belirsiz | Learn about topics such as computer networks, cyber security, and database design. | |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Develops skills in designing, implementing and analyzing algorithms. | 4 |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Gains the ability to use different programming languages effectively | |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Learns data analysis, database management and big data processing skills. | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Gains practical experience by working on software development projects. | |
| PLO09 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Strengthens collaboration and communication skills within the team. | 3 |
| PLO10 | Yetkinlikler - Alana Özgü Yetkinlik | It provides a mindset open to technological innovations. | 4 |
| PLO11 | Yetkinlikler - Öğrenme Yetkinliği | Encourages continuous learning and self-improvement competence. | 4 |
| PLO12 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Develops 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 and 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-1 | 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 | 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-2 | 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 | ||