Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
5MATH361ABSTRACT ALGEBRA4+2510

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Compulsory
Objectives of the Course The aim of this course is to give classifications of groups, symmetric groups, and the groups of small order, and is to teach group isomorphism theorems. It is then aimed to give the ring isomorphism theorems and the field of fractions of an integral domain. Finally, it is aimed to present the properties of principle ideal domains, Euclidean domains, unique factorization domains, and the relationships between these concepts with some counter examples.
Course Content Groups and subgroups. Cosets. Theorem of Lagrange. Homomorphisms. Factor groups. Rings, fields and integral domains. Rings of polynomials. Factor rings. Ideals. Prime and maximal ideals. Unique factorization domains. Euclidean domains. Principal ideal domains. Field extensions. Finite fields.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Prof.Dr. BAŞAK AY SAYLAM
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources D.S. Malik, J.N. Mordeson, M.K. Sen, Fundamentals of Abstract Algebra, 1996.
S. Fraleigh, Introduction to Abstract Algebra , 7th Edition, 2002.

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 50
Quizzes 0 % 0
Homeworks 0 % 0
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 50
Total
3
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 48 48
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 1 88 88
Exams and Exam Preparations 2 83 166
Total Work Load   Number of ECTS Credits 10 302

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 To determine the fundamental properties of groups, subgroups, cyclic subgroups, normal subgroups, permutation groups and Abelian subgroups
2 To state the relations between the orders of groups with its subgroups and the number of residue classes
3 To prove homomorphism theorems and to state the notion of isomorphism
4 To express the definitions of rings, integral domains, zero divisors, invertible and irreducible elements
5 To express ideals, factor rings and ring homomorphisms
6 To describe about polynomial rings
7 To describe about principal ideal domains, unique factorization domains, Euclidean domains


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Groups and subgroups. S. Fraleigh, Introduction to Abstract Algebra , 7th Edition, 2002.
2 Cosets and Lagrange’s Theorem. S. Fraleigh, Introduction to Abstract Algebra , 7th Edition, 2002.
3 Homomorphisms. Factor groups. S. Fraleigh, Introduction to Abstract Algebra , 7th Edition, 2002.
4 Isomorphism theorems. S. Fraleigh, Introduction to Abstract Algebra , 7th Edition, 2002.
5 1st mid-semester examination. S. Fraleigh, Introduction to Abstract Algebra , 7th Edition, 2002.
6 Rings, fiealds and integral domains. S. Fraleigh, Introduction to Abstract Algebra , 7th Edition, 2002.
7 Ideals. S. Fraleigh, Introduction to Abstract Algebra , 7th Edition, 2002.
8 Prime and maximal ideals. S. Fraleigh, Introduction to Abstract Algebra , 7th Edition, 2002.
9 Prime and maximal ideals. S. Fraleigh, Introduction to Abstract Algebra , 7th Edition, 2002.
10 2nd mid-semester examination. S. Fraleigh, Introduction to Abstract Algebra , 7th Edition, 2002.
11 Euclidean domains, principal ideal domains. S. Fraleigh, Introduction to Abstract Algebra , 7th Edition, 2002.
12 Unique factorization domains. S. Fraleigh, Introduction to Abstract Algebra , 7th Edition, 2002.
13 Field extensions. S. Fraleigh, Introduction to Abstract Algebra , 7th Edition, 2002.
14 Finite fields. S. Fraleigh, Introduction to Abstract Algebra , 7th Edition, 2002.
15 Final 1st week S. Fraleigh, Introduction to Abstract Algebra , 7th Edition, 2002.
16 Final 2nd week S. Fraleigh, Introduction to Abstract Algebra , 7th Edition, 2002.


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 4
C2 4
C3 3
C4 3
C5 4
C6 4
C7 3

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


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