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| Course Description |
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| Course Name |
: |
Number Theory |
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| Course Code |
: |
MT 411 |
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| Course Type |
: |
Optional |
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| Level of Course |
: |
First Cycle |
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| Year of Study |
: |
4 |
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| Course Semester |
: |
Fall (16 Weeks) |
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| ECTS |
: |
5 |
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| Name of Lecturer(s) |
: |
Asst.Prof.Dr. ELA AYDIN
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| Learning Outcomes of the Course |
: |
Knows divisibility and the properties of integers.
Calculates the greatest common divisor using division algorithm.
Solves problems using Euclidean algorithm.
Knows factorisation and solves related problems.
Solves congruence equations and systems of equations.
Solve systems using Chinese remainder theorem.
Is able to use Fermat ve Lagrange Theorems to solve problems.
Recognizes Euler functions, Möbius functions, arithmetical functions and uses them in calculations.
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| Mode of Delivery |
: |
Face-to-Face |
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| Prerequisites and Co-Prerequisites |
: |
None |
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| Recommended Optional Programme Components |
: |
None |
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| Aim(s) of Course |
: |
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.
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| Course Contents |
: |
Division algorithm, Greatest common divisor, Euclidean algorithm, Unique factorisation into primes, Congruences, Linear congruences, Chinese remainder theorem, Higher order congruences, Euler´s f-function, Arithmetic function. |
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| Language of Instruction |
: |
Turkish |
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| Work Place |
: |
Department of Mathematics Classrooms |
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Course Outline /Schedule (Weekly) Planned Learning Activities |
| Week | Subject | Student's Preliminary Work | Learning Activities and Teaching Methods |
|
1 |
Divisibility and the properties of integers |
None |
Lecture and discussion |
|
2 |
Division algorithm |
None |
Lecture and discussion |
|
3 |
The greatest common divisor |
None |
Lecture and discussion |
|
4 |
Euclidean algorithm |
None |
Lecture and discussion |
|
5 |
Unique factorisation into primes and solving related problems |
None |
Lecture and discussion |
|
6 |
Linear Diophantine equations and systems |
None |
Lecture and discussion |
|
7 |
Congruences |
None |
Lecture and discussion |
|
8 |
Mid-term exam |
None |
Written exam |
|
9 |
Linear Congruences and systems |
None |
Lecture and discussion |
|
10 |
Chinese remainder theorem and its applications |
None |
Lecture and discussion |
|
11 |
Fermat ve Lagrange Theorems |
None |
Lecture and discussion |
|
12 |
Euler functions, Möbius functions |
None |
Lecture and discussion |
|
13 |
Arithmetic functions |
None |
Lecture and discussion |
|
14 |
Convolution products and multiplicative functions |
None |
Lecture and discussion |
|
15 |
Solving problems |
None |
Lecture and discussion |
|
16/17 |
Final exam |
None |
Written exam |
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Required Course Resources |
| Resource Type | Resource Name |
| Recommended Course Material(s) |
 Prof. Dr. Hüseyin ALTINDİŞ " Sayılar Teorisi ve Uygulamaları",Lazer ofset Press Ankara, 2005.
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.
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| |
| Required Course Material(s) | |
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Assessment Methods and Assessment Criteria |
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Semester/Year Assessments |
Number |
Contribution Percentage |
|
Mid-term Exams (Written, Oral, etc.) |
1 |
100 |
|
Homeworks/Projects/Others |
0 |
0 |
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Total |
100 |
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Rate of Semester/Year Assessments to Success |
40 |
| |
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Final Assessments
|
100 |
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Rate of Final Assessments to Success
|
60 |
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Total |
100 |
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| Contribution of the Course to Key Learning Outcomes |
| # | Key Learning Outcome | Contribution* |
|
1 |
Is able to prove Mathematical facts encountered in secondary school. |
5 |
|
2 |
Recognizes the importance of basic notions in Algebra, Analysis and Topology |
5 |
|
3 |
Develops maturity of mathematical reasoning and writes and develops mathematical proofs. |
2 |
|
4 |
Is able to express basic theories of mathematics properly and correctly both written and verbally |
1 |
|
5 |
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. |
1 |
|
6 |
Expresses clearly the relationship between objects while constructing a model |
3 |
|
7 |
Draws mathematical models such as formulas, graphs and tables and explains them |
5 |
|
8 |
Is able to mathematically reorganize, analyze and model problems encountered. |
4 |
|
9 |
Knows at least one computer programming language |
4 |
|
10 |
Uses effective scientific methods and appropriate technologies to solve problems |
0 |
|
11 |
Knows programming techniques and is able to write a computer program |
0 |
|
12 |
Is able to do mathematics both individually and in a group. |
0 |
|
13 |
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians |
0 |
|
14 |
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 |
0 |
| * Contribution levels are between 0 (not) and 5 (maximum). |
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| Student Workload - ECTS |
| Works | Number | Time (Hour) | Total Workload (Hour) |
| Course Related Works |
|
Class Time (Exam weeks are excluded) |
14 |
3 |
42 |
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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 |
15 |
15 |
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Final Exam |
1 |
20 |
20 |
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Total Workload: | 119 |
| Total Workload / 25 (h): | 4.76 |
| ECTS Credit: | 5 |
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