TÜRKÇE
ENGLISH
Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| MATHEMATICS PR. | |
| Code | MT411 |
| Name | Number Theory |
| Term | 2019-2020 Academic Year |
| Semester | 7. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Üniversite Dersi |
| Type | Normal |
| Label | E Elective |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Dr. Öğr. Üyesi ELA AYDIN |
| Course Instructor |
Dr. Öğr. Üyesi ELA AYDIN
(Güz)
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
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
Resources
Prof. Dr. Hüseyin ALTINDİŞ " Sayılar Teorisi ve Uygulamaları",Lazer ofset Press Ankara, 2005.
Notes
İsmail Naci CANGÜL, Basri ÇELİK, " Sayılar Teorisi Problemleri", Paradigma Akademi Press ,Bursa 2002.<br> Prof.Dr.Halil.İ. KARAKAŞ, Doç Dr. İlham ALİYEV," Sayılar Teorisinde Olimpiyat Problemleri ve Çözümleri", Tübitak, 1996
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Knows divisibility the properties of integers. |
| LO02 | Calculates the greatest common divisor using division algorithm. |
| LO03 | Solves problems using Euclidean algorithm. |
| LO04 | Knows factorisation solves related problems. |
| LO05 | Solves congruence equations , systems of equations. |
| LO06 | Solve systems using Chinese remainder theorem. |
| LO07 | Use Fermat and Lagrange Theorems to solve problems. |
| LO08 | Euler functions, Möbius functions, arithmetical functions uses in calculations. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | - | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | 5 |
| PLO02 | - | Understands importance of basic consepts of Algebra, Analaysis and Topology. | 5 |
| PLO03 | - | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 2 |
| PLO04 | - | Demonstrate the ability to express the basic theories of mathematics both correctly. | 1 |
| PLO05 | - | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 1 |
| PLO06 | - | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | 3 |
| PLO07 | - | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 5 |
| PLO08 | - | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 4 |
| PLO09 | - | Comprehends at least one of the computer programming languages. | 0 |
| PLO10 | - | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 0 |
| PLO11 | - | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | 0 |
| PLO12 | - | 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. | 0 |
| PLO13 | - | Understands the programming techniques and shows the ability to do programming. | 0 |
| PLO14 | - | Demonstrates the ability to study mathematics both independently and as a group. | 0 |
| PLO15 | - | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | |
| PLO16 | - | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | |
| PLO17 | - | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | |
| PLO18 | - | Gains the ability to use information technologies effectively for contemporary mathematical applications. | |
| PLO19 | - | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | |
| PLO20 | - | Gains the consciousness of prefesional ethics and responsibility. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Divisibility and the properties of integers | Review of the relevant pages from sources | |
| 2 | Division algorithm | Review of the relevant pages from sources | |
| 3 | The greatest common divisor | Review of the relevant pages from sources | |
| 4 | Euclidean algorithm | Review of the relevant pages from sources | |
| 5 | Unique factorisation into primes and solving related problems | Review of the relevant pages from sources | |
| 6 | Linear Diophantine equations and systems | Review of the relevant pages from sources | |
| 7 | Congruences | Review of the relevant pages from sources | |
| 8 | Mid-Term Exam | Review of the topics discussed in the lecture notes and sources | |
| 9 | Linear Congruences and systems | Review of the relevant pages from sources | |
| 10 | Chinese remainder theorem and its applications | Review of the relevant pages from sources | |
| 11 | Fermat ve Lagrange Theorems | Review of the relevant pages from sources | |
| 12 | Euler functions, Möbius functions | Review of the relevant pages from sources | |
| 13 | Arithmetic functions | Review of the relevant pages from sources | |
| 14 | Convolution products and multiplicative functions | Review of the relevant pages from sources | |
| 15 | Solving problems, final exam | Review of the relevant pages from sources | |
| 16 | Term Exams | Review of the topics discussed in the lecture notes and sources | |
| 17 | Term Exams | Review of the topics discussed in the lecture notes and sources |
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 |