COURSE SYLLABUS

ABSTRACT ALGEBRA

1	Course Title:	ABSTRACT ALGEBRA
2	Course Code:	MAT3019
3	Type of Course:	Compulsory
4	Level of Course:	First Cycle
5	Year of Study:	3
6	Semester:	5
7	ECTS Credits Allocated:	6
8	Theoretical (hour/week):	2
9	Practice (hour/week) :	2
10	Laboratory (hour/week) :	0
11	Prerequisites:	None
12	Recommended optional programme components:	None
13	Language:	Turkish
14	Mode of Delivery:	Face to face
15	Course Coordinator:	Prof. Dr. İSMAİL NACİ CANGÜL
16	Course Lecturers:	Yrd. Doç. Dr. Musa DEMİRCİ, Yrd. Doç. Dr. Hacer ÖZDEN
17	Contactinformation of the Course Coordinator:	cangul@uludag.edu.tr, 0224 2941756, Fen-Edebiyat Fakültesi, Matematik Bölümü, 16059, Görükle / Bursa
18	Website:	http://www.ismailnacicangul.com/
19	Objective of the Course:	To teach divisibility, congruences, linear Diophant equations, arithmetic functions, and also the applications of those together with the origins of the notions
20	Contribution of the Course to Professional Development

Learning Outcomes:

1	Differentiates between prime and composite numbers and knows the reasons of different situations.;
2	Knows the Notion of divisibility on the ring of integers and related notions.;
3	Knows daily applications of Diophantine equations.;
4	Knows daily applications of congruences.;
5	Knows the origins and history of the main notions.;
6	Knows the corresponding English meanings of the main notions.;

22	Course Content:

Week	Theoretical	Practical
1	Divisibility on integers	Divisibility examples
2	Division and Euclid algorithms and gcd and lcm	Examples of division and Euclid algorithms
3	Linear Diophantine equations	Examples of linear Diophantine equations
4	Fundamental theorem of arithmetic and divisors	Examples of the number and the sum of the divisors of a number
5	Euler ?-function	Calculation of the values of Euler ?-function
6	Properties of Euler ?-function	Examples of properties
7	Congruences	Examples of congruences
8	Operations in Zm and properties of congruences	Examples of properties
9	Midterm exam, Euler and Fermat theorems	Examples of Euler and Fermat theorems
10	Linear congruences with one variable	Examples of linear congruences
11	Linear congruences and linear Diophantine equations	Relation between linear congruences and linear Diophantine equations
12	Congruence systems	Solution of congruence systems
13	Quadratic residues and Legendre symbol	Calculation of quadratic residues
14	Gauss’ quadratic reciprocity law	Applications of reciprocity law

23	Textbooks, References and/or Other Materials:	1. Sayılar Teorisi Problemleri, İsmail Naci Cangül & Basri Çelik, 2005
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	1	40
Quiz	0	0
Homeworks, Performances	0	0
Final Exam	1	60
Total	2	100
Contribution of Term (Year) Learning Activities to Success Grade		40
Contribution of Final Exam to Success Grade		60
Total		100
Measurement and Evaluation Techniques Used in the Course
Information

ECTS / WORK LOAD TABLE

CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High