TÜRKÇE
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Information
| Code | MT407 |
| Name | Number Theory |
| 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 | Dr. Öğr. Üyesi ELA AYDIN |
Course Goal
The aim of this course students known the essentials of integer numbers and prime numbers, solve congruences equations and the systems including them and to recognize Euler and Möbius functions and use them.
Course Content
The contentst of this course is integer numbers and prime numbers, congruences equations and the systems Euler and Möbius functions .
Course Precondition
None
Resources
Sayılar Teorisi ve Uygulamaları, Prof. Dr. Hüseyin ALTINDİŞ,
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | 1) Knows divisibility the properties of integers. |
| LO02 | 2) Calculates the greatest common divisor using division algorithm. |
| LO03 | 3) Solves problems using Euclidean algorithm. |
| LO04 | 4) Knows factorisation solves related problems. |
| LO05 | 5) Solves congruence equations , systems of equations. |
| LO06 | 6) Solve systems using Chinese remainder theorem. |
| LO07 | 7) Use Fermat and Lagrange Theorems to solve problems. |
| LO08 | 8) Euler functions, Möbius functions, arithmetical functions uses in calculations. |
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. | 5 |
| 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. | 2 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to express the basic theories of mathematics both correctly. | 1 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 1 |
| 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. | 3 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 4 |
| 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. | 1 |
| PLO10 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 1 |
| 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 | 1 |
| 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. | 1 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Understands the programming techniques and shows the ability to do programming. | 1 |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Demonstrates the ability to study mathematics both independently and as a group. | 1 |
| PLO15 | Bilgi - Kuramsal, Olgusal | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | 1 |
| PLO16 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | 1 |
| PLO17 | Bilgi - Kuramsal, Olgusal | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | |
| PLO18 | Bilgi - Kuramsal, Olgusal | Gains the ability to use information technologies effectively for contemporary mathematical applications. | 1 |
| 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. | 1 |
| PLO20 | Bilgi - Kuramsal, Olgusal | Gains the consciousness of prefesional ethics and responsibility. | 1 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Divisibility and the properties of integers | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 2 | Division algorithm | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 3 | The greatest common divisor | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 4 | Euclidean algorithm | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 5 | Unique factorisation into primes and solving related problems | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 6 | Linear Diophantine equations and systems | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 7 | Congruences | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Rewiev of the topics dşscussin the lecture notes | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Linear Congruences and systems | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 10 | Chinese remainder theorem and its applications | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 11 | Fermat ve Lagrange Theorems | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 12 | Euler functions, Möbius functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 13 | Arithmetic functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 14 | Convolution products and multiplicative functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 15 | Solving problems, final exam | Rewiev of the topics dşscussin the lecture notes | Öğretim Yöntemleri: Problem Çözme |
| 16 | Term Exams | Ölçme Yöntemleri: Yazılı Sınav |
|
| 17 | Term Exams | 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 | ||