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Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| MATHEMATICS PR. | |
| Code | MT411 |
| Name | Number Theory |
| Term | 2017-2018 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
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.
Course Content
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 |
|---|
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | - | Is able to prove Mathematical facts encountered in secondary school. | |
| PLO02 | - | Recognizes the importance of basic notions in Algebra, Analysis and Topology | |
| PLO03 | - | Develops maturity of mathematical reasoning and writes and develops mathematical proofs. | |
| PLO04 | - | Is able to express basic theories of mathematics properly and correctly both written and verbally | |
| PLO05 | - | Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. | |
| PLO06 | - | Expresses clearly the relationship between objects while constructing a model | |
| PLO07 | - | Draws mathematical models such as formulas, graphs and tables and explains them | |
| PLO08 | - | Is able to mathematically reorganize, analyze and model problems encountered. | |
| PLO09 | - | Knows at least one computer programming language | |
| PLO10 | - | Uses effective scientific methods and appropriate technologies to solve problems | |
| PLO11 | - | Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | |
| PLO12 | - | 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 | |
| PLO13 | - | Knows programming techniques and is able to write a computer program | |
| PLO14 | - | Is able to do mathematics both individually and in a group. |
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 | Final exam | Review of the topics discussed in the lecture notes and sources | |
| 17 | Final exam | 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 |