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Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| MATHEMATICS PR. | |
| Code | MT484 |
| Name | Combinatorics |
| Term | 2017-2018 Academic Year |
| Semester | 8. 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 |
| Label | E Elective |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. HAYRULLAH AYIK |
| Course Instructor |
Prof. Dr. HAYRULLAH AYIK
(Bahar)
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
Understanding counting principles and understanding Generalizations of Counting Principles, Recognizing nth order disarrangement, Recognizing Square polinom and solving problem using Square polinom, Recognizing Generating Functions, Recognizing and using First Order Generating Functions, Recognizing recurrence relations.
Course Content
Counting Principles, Generalized Counting Principles, Applications of Counting Principles, nth order disarrangement, Rook polinomal, Application of Rook polinomial, Generating Functions, First Order Generating Functions, Binomial Cofficient, Applications of Generating Functions, Recurrence relations, Second order linear homogeneous recurrence relations.
Course Precondition
Resources
Discrete and Combinatorial Mathematics an applied introduction, Ralph Grimaldi, Addison-Wesley Publishing Company,1994.<br> Discrete Mathematics and its Applications (Second Edition) , Kenneth H. Rosen
Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Realises counting principles. |
| LO02 | Recognizes generalized counting principles. |
| LO03 | Recognises nth order disarrangement . |
| LO04 | Solving problem by using the Rook polynomial. |
| LO05 | Recognises generating functions. |
| LO06 | Recognises first order generating functions. |
| LO07 | Recognises recurrence relations. |
| LO08 | Recognises second order linear homogeneous recurrence relations. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Understands importance of basic consepts of Algebra, Analaysis and Topology. | 3 |
| PLO03 | Yetkinlikler - Öğrenme Yetkinliği | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 4 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Demonstrates the ability to express the basic theories of mathematics accurately both in writing and orally. | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 4 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | |
| PLO08 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 3 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Comprehends at least one of the computer programming languages. | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 4 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities. | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Understands the programming techniques and shows the ability to do programming. | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Demonstrates the ability to study mathematics both independently and as a group. | |
| PLO15 | Bilgi - Kuramsal, Olgusal | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | 3 |
| PLO16 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | |
| PLO17 | Bilgi - Kuramsal, Olgusal | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | 4 |
| PLO18 | Bilgi - Kuramsal, Olgusal | Gains the ability to use information technologies effectively for contemporary mathematical applications. | 4 |
| PLO19 | Bilgi - Kuramsal, Olgusal | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | 4 |
| PLO20 | Bilgi - Kuramsal, Olgusal | Gains the consciousness of prefesional ethics and responsibility. | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Counting Principles | Review of the relevant pages from sources | |
| 2 | Generalizations of Counting Principles | Review of the relevant pages from sources | |
| 3 | Applications of Counting Principles I | Review of the relevant pages from sources | |
| 4 | Applications of Counting Principles II | Review of the relevant pages from sources | |
| 5 | nth order disarrangement | Review of the relevant pages from sources | |
| 6 | Rook polinomial | Review of the relevant pages from sources | |
| 7 | Application of Rook polinomial I | Review of the relevant pages from sources | |
| 8 | Mid Term Exam | Review | |
| 9 | Application of Rook polinomial II | Review of the relevant pages from sources | |
| 10 | Generating Functions | Review of the relevant pages from sources | |
| 11 | First Order Generating Functions | Review of the relevant pages from sources | |
| 12 | Binomial Cofficients | Review of the relevant pages from sources | |
| 13 | Applications of Generating Functions | Review of the relevant pages from sources | |
| 14 | Recurrence relations | Review of the relevant pages from sources | |
| 15 | Second order linear homogeneous recurrence relations | Review of the relevant pages from sources | |
| 16 | Final Exam | Review | |
| 17 | Final Exam | Review |
Assessment (Exam) Methods and Criteria
| Assessment Type | Midterm / Year Impact | End of Term / End of Year Impact |
|---|---|---|
| 1. Midterm Exam | 100 | 40 |
| General Assessment | ||
| Midterm / Year Total | 100 | 40 |
| 1. Final Exam | - | 60 |
| Grand Total | - | 100 |
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 | ||