MATHEMATICS
Bachelor TR-NQF-HE: Level 6 QF-EHEA: First Cycle EQF-LLL: Level 6

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT3003 Algebra I Fall 3 0 3 5
The course opens with the approval of the Department at the beginning of each semester

Basic information

Language of instruction: En
Type of course: Must Course
Course Level: Bachelor
Mode of Delivery: Face to face
Course Coordinator : Instructor MOHAMED KHALIFA
Course Objectives: The aim of the course is to handle fundamental concepts in the theory of groups and modules. It is first aimed to handle the class equation of a finite group, Sylow’s Theorems, and their applications, and at the end to examine the structure of free groups. Afterwards, it is aimed to introduce the ring of endomorphisms, and so to give the notion of a module. Finally, it is aimed to examine the basic concepts of module theory, isomorphism theorems, and free modules

Learning Outputs

The students who have succeeded in this course;
Be able to understand and interpret different algebraic concepts and structures
Be able to handle the relations between abstract algebraic structures and problems
Be able to apply the ability of abstract thinking to solving problem
Be able to write down the class equation of a finite group
Be able to give examples of class equation
Be able to determine the simplicity of a finite group with the help of Sylow’s theorems
Be able to determine the ring of endomorphisms of an abelian group
Be able to determine the simplicity and the maximality of a submodule
Be able to represent a module as sum of its submodules

Course Content

Reminders about groups, conjugacy and G-sets; G-sets and class equation; Sylow’s theorems; Free Groups; Rings; Ring of Endomorphisms; Submodules and their sums; Quotient modules; Finitely generated modules; Free Modules; Simple modules and maximal submodules

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Course description: Conjugacy and G-sets
2) G-sets and class equation
3) Sylow’s Theorems
4) Applications of Sylow’s Theorems
5) Free Groups
6) Rings, Rings of Endomorphisms
7) Submodules and Ideals
8) Direct sum and direct product of submodules
9) Relations between the direct sum and direct product of submodules
10) Quotient modules
11) Isomorphism theorems for modules
12) Finitely generated modules Free modules
13) Maximal submodules
14) Maximal submodules

Sources

Course Notes: Hungerford, T.W. “Abtract Algebra(An Introduction)”, Thomson Learning,(1997) Bhattacharya P. B., Jain S. K. Nagpaul “ Basic Abtract Algebra”, Cambridge University Pres, 1986
References:

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Attendance 16 % 0
Laboratory % 0
Application % 0
Field Work % 0
Special Course Internship (Work Placement) % 0
Quizzes 2 % 5
Homework Assignments 2 % 5
Presentation % 0
Project % 0
Seminar % 0
Midterms 2 % 50
Preliminary Jury % 0
Final 1 % 40
Paper Submission % 0
Jury % 0
Bütünleme % 0
Total % 100
PERCENTAGE OF SEMESTER WORK % 60
PERCENTAGE OF FINAL WORK % 40
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Laboratory 0 0 0
Application 0 0 0
Special Course Internship (Work Placement) 0 0 0
Field Work 0 0 0
Study Hours Out of Class 0 0 0
Presentations / Seminar 0 0 0
Project 0 0 0
Homework Assignments 2 10 20
Quizzes 2 10 20
Preliminary Jury 0
Midterms 2 14 28
Paper Submission 0
Jury 0
Final 1 15 15
Total Workload 125

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution