COURSE UNIT TITLE

: NUMBER THEORY

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
LME 5012 NUMBER THEORY ELECTIVE 2 0 0 4

Offered By

Mathematics Teacher Education

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR HASIBE SEVGI MORALI

Offered to

Mathematics Teacher Education

Course Objective

The main aim of this course is to introduce well ordered principle, induction, fibonacci numbers, prime numbers, the fundemental theorem of arithmetics, the method of separation to fermat multipliers, least common multiple, greatest common divisor, the euclidean algorithm, the finite number of finite elements, linear diophant equations, perfect numbers, mersenne numbers, congruences, linear congruences, remainer theorem, Wilson theorem and fermat's small theorem, properties of euler phi function, moebius reversing, continuous fractions.

Learning Outcomes of the Course Unit

1   1. To be able to know well ordered principle, to prove using induction
2   2. To be able to know divisibilty, Fibonacci numbers
3   3. To be able to know prime numbers and properties
4   4. To be able to know least common multiple, greatest common divisor
5   5. To be able to know Euclidean Algorithm, fundamental theorem of arithmetics, applications
6   6 To be able to know Linear diophant equations
7   7. To be able to know and prove properties and theorems about congruences and linear congruences. To be able to apply the Chinese remainder theorem.
8   8. To be able to recognize and apply continued fractions.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Integers, well ordered sets, proof with induction
2 Divisibility, Fibonacci numbers
3 Prime numbers, properties
4 Least common multiple, greatest common divisor
5 Euclidean Algorithm, fundamental theorem of arithmetics
6 Fermat s factoring method
7 Diophant equations
8 Course overview, evaluation and midterm examination
9 Perfect numbers, Mersenne numbers
10 Congruances, chinese remainder theorem
11 Wilson s theorem, Fermat s small theorem
12 Euler phi function, moebius inverse
13 Continuous fractions
14 General exercises, problems
15 Final Exam

Recomended or Required Reading

Prof. Dr. Arif Kaya, Sayılar kuramına Giriş, Ege Üni. Yayınları 1988

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

Midterm and final exams are determined according to the weekly course content within the scope of the learning outcomes of the course

Language of Instruction

Turkish

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

sevgi.morali@deu.edu.tr
Cahit Arf Building Office: 226
Phone: 3012422

Office Hours

Thursday 13.30-15.00

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 1 15 15
Preparation for final exam 1 15 15
Preparing assignments 1 14 14
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 100

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14PO.15PO.16PO.17PO.18
LO.1543323
LO.2543323
LO.3543323
LO.4543323
LO.5543323
LO.6
LO.7
LO.8

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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