MT484 Combinatorics

5 ECTS - 3-0 Duration (T+A)- 8. Semester- 3 National Credit

Information

Code MT484
Name Combinatorics
Term 2024-2025 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
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator Prof. Dr. HAYRULLAH AYIK
Course Instructor
1 2
Prof. Dr. HAYRULLAH AYIK (A Group) (Ins. in Charge)


Course Goal / Objective

The aim of this course is to make students comprehend counting principles, generalizations of counting principles, nth order disarrangement, Rook polynomial and problem solving by using Rook polynomial, generating functions, first order generating functions, recurrence relations.

Course Content

In this course counting principles, generalized counting principles, applications of counting principles, nth order disarrangement, Rook polynomial, application of Rook polynomial I, application of Rook polynomial II, generating functions, first order generating functions, binomial cofficient, applications of generating functions, recurrence relations, second order linear homogeneous recurrence relations are described.

Course Precondition

NONE

Resources

Discrete and Combinatorial Mathematics an applied introduction, Ralph Grimaldi, Addison-Wesley Publishing Company,1994. Discrete Mathematics and its Applications (Second Edition) , Kenneth H. Rosen

Notes

Discrete and Combinatorial Mathematics an applied introduction, Ralph Grimaldi, Addison-Wesley Publishing Company,1994. Discrete Mathematics and its Applications (Second Edition) , Kenneth H. Rosen


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 Öğretim Yöntemleri:
Anlatım, Tartışma
2 Generalizations of counting principles Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
3 Applications of counting principles I Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma, Soru-Cevap
4 Applications of counting principles II Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma, Soru-Cevap
5 nth order disarrangement Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
6 Rook polinomial Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
7 Application of Rook polinomial I Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma, Problem Çözme
8 Mid-Term Exam Review Ölçme Yöntemleri:
Yazılı Sınav
9 Application of Rook polinomial II Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma, Problem Çözme
10 Generating functions Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
11 First order generating functions Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
12 Binomial cofficients Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
13 Applications of generating functions Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
14 Recurrence relations Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
15 Second order linear homogeneous recurrence relations Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
16 Term Exams Review of the topics discussed in the lecture notes and sources again Ölçme Yöntemleri:
Yazılı Sınav
17 Term Exams Review of the topics discussed in the lecture notes and sources again 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

Update Time: 13.09.2024 03:20