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Information
| Code | ISB491 |
| Name | Combinatorics |
| Semester | 7. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. SELAHATTİN KAÇIRANLAR |
Course Goal
To teach basic ideas of combinatorics
Course Content
Odd rules, permutation, combination, repeated permutation and combination, partitions, the minimax principle, the integer solutions of the special equations , recurrence relations, recurrence relations with constant coefficients, Fibonacci sequence, generating functions, the solutions of recurrence relations using generating functions.
Course Precondition
no
Resources
Balakrishnan, V. K. (1995). Schaums outline of theory and problems of combinatiorics
Notes
Balakrishnan, V. K. (1995). Schaums outline of theory and problems of combinatiorics
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | solve counting rules problems |
| LO02 | solve permutations, combinations, and the problems of fragmentation ordered and unordered |
| LO03 | solve the Principle of Inclusion and Exclusion problems |
| LO04 | find the number of solutions of the equation n unknowns in a set of positive integers, |
| LO05 | write and solve recurrence relations |
| LO06 | understand producer functions |
| LO07 | solve recurrence equations using generating functions |
| LO08 | solve random walk and the problems of ingrown |
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 | 3 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Emphasize the importance of Statistics in life | 2 |
| 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 | 3 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Use proper methods and techniques to gather and/or to arrange the data | 1 |
| 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 | 4 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Apply the statistical analyze methods | 1 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Make statistical inference(estimation, hypothesis tests etc.) | 1 |
| PLO10 | Bilgi - Kuramsal, Olgusal | Generate solutions for the problems in other disciplines by using statistical techniques | 1 |
| 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 | 1 |
| PLO13 | Beceriler - Bilişsel, Uygulamalı | Distinguish the difference between the statistical methods | 1 |
| PLO14 | Beceriler - Bilişsel, Uygulamalı | Be aware of the interaction between the disciplines related to statistics | 3 |
| 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 | 2 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Counting rules, permutations | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 2 | Combination | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 3 | Ordered and Unordered Partitions | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 4 | The Principle of Inclusion and Exclusion | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 5 | solutions of the equation n unknowns on set of positive integers | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 6 | Recurrence relations | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 7 | Solutions of equations of the reduction | 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 | generating functions | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 10 | to solve reduction equations with the help of generating functions | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 11 | to solve reduction equations with the help of generating functions (continue) | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 12 | Random walk and the player goes down | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 13 | Some counting problems I | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 14 | Some probability problems I | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 15 | Some probability problems II | 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 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 114 | ||
| Total Workload / 25 (h) | 4,56 | ||
| ECTS | 5 ECTS | ||