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Information
| Code | MT352 |
| Name | Finite Mathematics |
| Term | 2024-2025 Academic Year |
| Semester | 6. Semester |
| Duration (T+A) | 2-0 (T-A) (17 Week) |
| ECTS | 4 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. HAYRULLAH AYIK |
| Course Instructor |
1 2 |
Course Goal / Objective
The aim of this course is to teach the students how to solve distribution problems by using the basic principles of counting.
Course Content
In this course counting principles, binomial coefficients, cyclic permutations, distrubution problems, Fibonachi Numbers, division algorithm, prime numbers, the least common multiple and the greatest common divisor, surjective functions, Stirling Numbers, special functions, the pigeonhole principle, functional difficulty are described.
Course Precondition
NONE
Resources
1. Discrete and Combinatorial Mathematics an applied introduction, Ralph Grimaldi, Addison-Wesley Publishing Company,1994. 2. Sonlu Matematik Olimpiyat Problemleri ve Çözümleri (Tübitak yayınları) Ünal Ufuktepe, Refail Alizade 3. Sayma, Ali Nesin
Notes
1. Discrete and Combinatorial Mathematics an applied introduction, Ralph Grimaldi, Addison-Wesley Publishing Company,1994.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Describes distribution problems. |
| LO02 | Solves the distributing problems using counting principles. |
| LO03 | Calculates the Binomial coefficients. |
| LO04 | Describes the Fibonacci numbers. |
| LO05 | Recognizes division algorithm. |
| LO06 | Calculates the elements of surjective functions using Stirling numbers. |
| LO07 | Solves problem using the pigeonhole principle. |
| LO08 | Recognizes functional difficulty. |
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. | 4 |
| PLO03 | Yetkinlikler - Öğrenme Yetkinliği | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Demonstrates the ability to express the basic theories of mathematics accurately both in writing and orally. | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 3 |
| 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. | 4 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 3 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 4 |
| 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. | |
| 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. | 4 |
| 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. | 3 |
| PLO15 | Bilgi - Kuramsal, Olgusal | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | |
| 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. | 3 |
| 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. | |
| PLO20 | Bilgi - Kuramsal, Olgusal | Gains the consciousness of prefesional ethics and responsibility. | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Counting rules | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Binom coefficients | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Cyclic permutation | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | Distrubution problems | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | Fibonacci Numbers | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 6 | Division algorithm | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 7 | Prime numbers | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 8 | Mid-Term Exam | Review of the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | The least common multiple and the greatest common divisor | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Surjective functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Stirling Numbers | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | Special functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | The pigeon hole principle | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 14 | Functional difficulty | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | General problem solving | 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 | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review of 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 | 1 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 8 | 8 |
| Final Exam | 1 | 24 | 24 |
| Total Workload (Hour) | 88 | ||
| Total Workload / 25 (h) | 3,52 | ||
| ECTS | 4 ECTS | ||