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•           Information on Degree Programmes

COURSE INFORMATON
Course Title Code Semester L+P Hour Credits ECTS
Number Theory * MT   411 7 3 3 5

 Prerequisites and co-requisites Recommended Optional Programme Components None

Language of Instruction Turkish
Course Level First Cycle Programmes (Bachelor's Degree)
Course Type
Course Coordinator Dr. Lec. Uyesi Ela AYDIN
Instructors
 Dr. Öğr. Üyesi ELA AYDIN 1. Öğretim Grup:A Dr. Öğr. Üyesi ELA AYDIN 2. Öğretim Grup:A

Assistants
Goals
To teach 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.
Content
integer numbers and prime numbers, congruences equations and the systems Euler and Möbius functions .

Learning Outcomes
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Course's Contribution To Program
NoProgram Learning OutcomesContribution
12345
1
Is able to prove Mathematical facts encountered in secondary school.
X
2
Recognizes the importance of basic notions in Algebra, Analysis and Topology
X
3
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
X
4
Is able to express basic theories of mathematics properly and correctly both written and verbally
X
5
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
X
6
Expresses clearly the relationship between objects while constructing a model
X
7
Draws mathematical models such as formulas, graphs and tables and explains them
X
8
Is able to mathematically reorganize, analyze and model problems encountered.
X
9
Knows at least one computer programming language
10
Uses effective scientific methods and appropriate technologies to solve problems
11
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
12
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields
13
Knows programming techniques and is able to write a computer program
14
Is able to do mathematics both individually and in a group.

Course Content
WeekTopicsStudy Materials _ocw_rs_drs_yontem
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
16-17 Final exam Review of the topics discussed in the lecture notes and sources

Recommended or Required Reading
TextbookProf. Dr. Hüseyin ALTINDİŞ " Sayılar Teorisi ve Uygulamaları",Lazer ofset Press Ankara, 2005.
Additional Resources
İsmail Naci CANGÜL, Basri ÇELİK, " Sayılar Teorisi Problemleri", Paradigma Akademi Press ,Bursa 2002.
Prof.Dr.Halil.İ. KARAKAŞ, Doç Dr. İlham ALİYEV," Sayılar Teorisinde Olimpiyat Problemleri ve Çözümleri", Tübitak, 1996