Elementary Number Theory
Elementary Mathematics Education
Faculty of Education
First Cycle (Bachelor's Degree)
| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Elementary Number Theory | IMO207 | Compulsory | Bachelor's degree | 2 | Fall | 5 |
Name of Lecturer(s)
Assistant Prof. Dr. Ayşe Arzu ARI
Learning Outcomes of the Course Unit
1) Clarify divisibility rules on integers.
2) Find highest common factor (H.C.F.), lowest common multiple (L.C.M.) relation between prime numbers and products on integers.
3) Define special functions on number theory.
4) Solve exercises related to congruents.
5) Find solution of linear and higher order congruents.
6) Apply properties of primitive roots and indexes to problems.
7) Apply theorems related to concept of quadric residues to basic theorems.
8) Solve problems related to cryptography.
9) Transform rational and irrational numbers to continuous fraction.
Program Competencies-Learning Outcomes Relation
| Program Competencies | ||||||||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | ||
| Learning Outcomes | ||||||||||||||
| 1 | No relation | High | High | High | High | High | High | High | High | High | High | High | High | |
| 2 | High | High | High | High | High | High | High | High | High | High | High | High | High | |
| 3 | High | High | High | High | High | High | High | High | High | High | High | High | High | |
| 4 | High | High | High | High | High | High | High | High | High | High | High | High | High | |
| 5 | High | High | High | High | High | High | High | High | High | High | High | High | High | |
| 6 | High | High | High | High | High | High | High | High | High | High | High | High | High | |
| 7 | High | High | High | High | High | High | High | High | High | High | High | High | High | |
| 8 | High | High | High | High | High | High | High | High | High | High | High | High | High | |
| 9 | High | High | High | High | High | High | High | High | High | High | High | High | High | |
Mode of Delivery
Face to Face
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
Abstract Mathematics
Course Contents
Divisibility on integers, prime numbers, important functions on number theories, congruents, linear congruents, seperating prime products on integers, primitive roots and indexes, quadric residues (second degree), cryptography subjects and usage areas in real life, continuous fractions.
Weekly Schedule
1) Introduction to the Theory of Numbers2) Divisibility
3) Prime numbers
4) Prime numbers
5) Base arithmetic
6) Positive divisors of an integer
7) General review and practice
8) Midterm
9) Diaphone equations
10) Modular arithmetic
11) Solution of linear congruence
12) Solution of linear congruence
13) Euler function
14) Primitive roots and indices
15) Solutions of congruence
16) General review and practice
Recommended or Required Reading
1- SAYILAR TEORİSİNE GİRİŞ, Prof. Dr. Mustafa Balcı, Süret yayınları, İstanbul, 2013
2- SAYILAR TEORİSİ PROBLEMLERİ, Prof. Dr. İ. Naci Cangül, Doç. Dr. Basri Çelik
Planned Learning Activities and Teaching Methods
1) Lecture
2) Question-Answer
3) Discussion
4) Drill and Practice
5) Problem Solving
Assessment Methods and Criteria
Contribution of Midterm Examination to Course Grade |
30% |
|---|---|
Contribution of Final Examination to Course Grade |
70% |
Total |
100% |
Language of Instruction
Turkish
Work Placement(s)
Not Required