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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS IMÖ 2010 FIELD ELC. 3 (ELEMENTARY NUMBER THEORY) ELECTIVE 2 0 0 4

Offered By

ELEMENTARY MATHEMATICS TEACHER EDUCATION

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR DOCTOR SERKAN NARLI

Offered to

ELEMENTARY MATHEMATICS TEACHER EDUCATION

Course Objective

Understanding and solving basic properties of numbers, theorems and problems and relating them to daily life.

Learning Outcomes of the Course Unit

1   Explain divisibility, prime number, congruence concepts and number theorems. 2   Interpret the concepts of Euler's function, Wilson's Theorem, Primitive Root, Index. 3   Relate the learned subjects to daily life. 4   Using methods and techniques learned in elementary number theory in project work. 5   Solve problems encountered in numbers and theory with different problem solving strategies.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Divisibility 2 Division Algorithm 3 Greatest common divisor (Gcd) 4 Euclid's Algorithm, Continuous Fractions 5 Bezout's Theorem, Linear Diophantine equations 6 Uniqueness of factorization,least common Multiple (LCM), Infinity of prime numbers 7 congruences 8 Midterm 9 Linear Congruences 10 Chinese Remainder Theorem 11 Euler Function, Wilson's theorem 12 Quadratic Residual 13 Primitive Roots 14 Index 15 Final Exam

Recomended or Required Reading

Arif Kaya (1988). Sayılar Kuramına Giriş, Ege Üniversitesi Yayınları Bülent Karakaş, Hacı Aktaş (1998). Sayılar Teorisi, Tokat Ismail Naci Cangül, Basri Çelik (2014). Sayılar Teorisi Problemleri, Dora Yayıncılık

Planned Learning Activities and Teaching Methods

Lecture, discussion, question-answer, problem solving, active learning techniques, group work.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 VZ Midterm 2 FN Semester final exam 3 BNS BNS Student examVZ * 0.40 + Student examFN * 0.60 4 BUT Make-up note 5 BBN End of make-up grade Student examVZ * 0.40 + Student examBUT * 0.60

Further Notes About Assessment Methods

None

Assessment Criteria

Assessment of students is measured by midterm exams, assignments and final exams in line with the learning outcomes.

Language of Instruction

Turkish

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

serkan.narli@deu.edu.tr

Office Hours

Dönem başında ilan edilecektir.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 2 26 Preparations before/after weekly lectures 13 2 26 Preparation for midterm exam 2 10 20 Preparation for final exam 2 10 20 Midterm 1 1 1 Final 1 1 1 TOTAL WORKLOAD (hours) 94

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 PO.12 PO.13 PO.14 PO.15 LO.1 3 5 3 3 5 4 4 5 4 4 LO.2 3 3 3 4 5 5 4 5 4 5 LO.3 3 4 5 3 4 5 4 4 5 5 4 LO.4 4 3 5 5 5 4 4 5 5 4 LO.5 4 4 5 4 5 4 4 5 4 4