BAHÇEŞEHİR UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
| 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 |
Basic information
| Language of instruction: | English |
| Type of course: | Must Course |
| Course Level: | Bachelor’s Degree (First Cycle) |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Instructor MOHAMED KHALIFA |
| Recommended Optional Program Components: | None |
| 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 Outcomes
|
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 / Textbooks: | 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 |
| Quizzes | 2 | % 5 |
| Homework Assignments | 2 | % 5 |
| Midterms | 2 | % 50 |
| Final | 1 | % 40 |
| 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 |
| Homework Assignments | 2 | 10 | 20 |
| Quizzes | 2 | 10 | 20 |
| Midterms | 2 | 14 | 28 |
| 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 |