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Information
| Code | ISB111 |
| Name | Discrete mathematics |
| Term | 2024-2025 Academic Year |
| Semester | 1. Semester |
| Duration (T+A) | 2-0 (T-A) (17 Week) |
| ECTS | 3 ECTS |
| National Credit | 2 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. SELAHATTİN KAÇIRANLAR |
| Course Instructor |
1 2 |
Course Goal / Objective
This course aims to help students acquire a powerful background on Counting Rules, permutations, combinations and probability.
Course Content
Counting Rules, Permutation, Combination, Ordered and Unordered Partitioning, Probability constitute the content of this course.
Course Precondition
no
Resources
Refail Alizade, Ünal Ufuktepe (2006), Sonlu Matematik, Tubitak Yayınları, Ankara.
Notes
Goldstein-Scheider-Seigel (1998), Finite Mathematics and Its Applications,Prentice Hall. 3. A.Simpson (2002), Discrete Mathematics by example, McGraw Hill.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Explains Counting Rules |
| LO02 | Solve the problems of permutations |
| LO03 | Solve the problems of combinations |
| LO04 | Solve the problems of fragmentation ordered and unordered |
| LO05 | Solve the problems of distributing |
| LO06 | Uses probability of an event, the Rules of Probability Probability Axioms |
| LO07 | Explains conditional Probability, Independent events |
| LO08 | Applies Bayes Theorem |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Explain the essence fundamentals and concepts in the field of Statistics | 3 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Emphasize the importance of Statistics in life | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Define basic principles and concepts in the field of Law and Economics | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Produce numeric and statistical solutions in order to overcome the problems | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Use proper methods and techniques to gather and/or to arrange the data | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Utilize computer programs and builds models, solves problems, does analyses and comments about problems concerning randomization | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Apply the statistical analyze methods | |
| PLO08 | Bilgi - Kuramsal, Olgusal | Make statistical inference (estimation, hypothesis tests etc.) | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Generate solutions for the problems in other disciplines by using statistical techniques and gain insight | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Discover the visual, database and web programming techniques and posses the ability of writing programs | |
| PLO11 | Beceriler - Bilişsel, Uygulamalı | Distinguish the difference between the statistical methods | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Make oral and visual presentation for the results of statistical methods | |
| PLO13 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Have capability on effective and productive work in a group and individually | 4 |
| PLO14 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Professional development in accordance with their interests and abilities, as well as the scientific, cultural, artistic and social fields, constantly improve themselves by identifying training needs | |
| PLO15 | Yetkinlikler - Öğrenme Yetkinliği | Develop scientific and ethical values in the fields of statistics-and scientific data collection |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Counting rules | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 2 | Permutations, circular permutations | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 3 | All objects that are not different from each other permutations | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 4 | Combinations, Pascal convention | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 5 | Repeated combinations | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 6 | Ordered and unordered partitions | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 7 | Distributing | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 8 | Mid-Term Exam | Review the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Distributing II | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 10 | Concept of Probability | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 11 | Concept of Probability II | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 12 | Conditional Probability | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 13 | Additive Rule and Independent Events | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 14 | Probability Distributions | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 15 | Solving Problems | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 16 | Term Exams | Review the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review 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 | 2 | 28 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 2 | 28 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 6 | 6 |
| Final Exam | 1 | 16 | 16 |
| Total Workload (Hour) | 78 | ||
| Total Workload / 25 (h) | 3,12 | ||
| ECTS | 3 ECTS | ||