Türkçe English Rapo to Course Content
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 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.;
21 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
22 Textbooks, References and/or Other Materials: 1. Sayılar Teorisi Problemleri, İsmail Naci Cangül & Basri Çelik, 2005
23 Assesment
TERM LEARNING ACTIVITIES NUMBER PERCENT
Midterm Exam 1 40
Quiz 0 0
Home Work-Project 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
Information
24 ECTS / WORK LOAD TABLE
Activites NUMBER TIME [Hour] Total WorkLoad [Hour]
Theoretical 14 2 28
Practicals/Labs 14 2 28
Self Study and Preparation 14 5 70
Homeworks 0 0 0
Projects 0 0 0
Field Studies 0 0 0
Midtermexams 1 20 20
Others 0 0 0
Final Exams 1 28 28
Total WorkLoad 194
Total workload/ 30 hr 5,8
ECTS Credit of the Course 6
25 CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS
PQ1 PQ2 PQ3 PQ4 PQ5 PQ6 PQ7 PQ8 PQ9 PQ10
LO1 5 0 2 0 0 0 2 2 0 0
LO2 5 3 0 0 2 0 5 2 0 0
LO3 3 0 0 0 3 0 5 2 2 0
LO4 5 0 0 0 0 0 0 2 2 0
LO5 0 0 0 0 0 0 0 0 0 0
LO6 0 0 0 0 0 5 0 0 0 0
LO: Learning Objectives PQ: Program Qualifications
Contribution Level: 1 Very Low 2 Low 3 Medium 4 High 5 Very High
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