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Information
| Code | ISB111 |
| Name | Discrete mathematics |
| Term | 2023-2024 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 |
| Label | E Elective |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. SELAHATTİN KAÇIRANLAR |
| Course Instructor |
Prof. Dr. SELAHATTİN KAÇIRANLAR
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
This course aims to help students acquire a powerful background on Counting Rules, permutations, combinations and probability.
Course Content
Counting Rules , permutations, combinations, ordered and unordered fragmentation, probability
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 | Knows 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 Probability, Statistics and Mathematics | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Emphasize the importance of Statistics in life | |
| 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 | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Use proper methods and techniques to gather and/or to arrange the data | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Utilize computer systems and softwares | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Construct the model, solve and interpret the results by using mathematical and statistical tehniques for the problems that include random events | 3 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Apply the statistical analyze methods | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Make statistical inference(estimation, hypothesis tests etc.) | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Generate solutions for the problems in other disciplines by using statistical techniques | |
| PLO11 | Bilgi - Kuramsal, Olgusal | Discover the visual, database and web programming techniques and posses the ability of writing programme | |
| PLO12 | Bilgi - Kuramsal, Olgusal | Construct a model and analyze it by using statistical packages | |
| PLO13 | Beceriler - Bilişsel, Uygulamalı | Distinguish the difference between the statistical methods | |
| PLO14 | Beceriler - Bilişsel, Uygulamalı | Be aware of the interaction between the disciplines related to statistics | |
| PLO15 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Make oral and visual presentation for the results of statistical methods | |
| PLO16 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Have capability on effective and productive work in a group and individually | |
| PLO17 | 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 | |
| PLO18 | 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 | ||