| MATHEMATICS | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT3004 | Algebra II | Spring | 3 | 0 | 3 | 6 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | En |
| Type of course: | Must Course |
| Course Level: | Bachelor |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Instructor MAHMOUD JAFARI SHAH BELAGHI |
| Course Objectives: | To provide the necessary basic knowledge of abstract algebra to students majoring in mathematics. |
|
The students who have succeeded in this course; A student who finished this class will have learned the basic concepts of abstract algebra to be able to take a graduate class on the subject. |
| Abelian groups. Abelian group morphisms. Kernel and image. Subgroups and product groups. Cyclic groups. Classification of finite abelian groups. Ideals and their lattice. Prime ideals, primary ideals and maximal ideals. Zorn's Lemma. Quotient rings. Fields and field of fractions. A review of the covered subjects and first exam. Zero divisors. Annihiators. Integral domains. Unique factorization domains. Euclidean domains. Polynomial rings of a single indeterminate over fields. Euclidean division in such rings. Calculating greatest common divisors and least common multiples in such rings. Irreducible polynomials in polynomial rings with one indeterminate over fields. Field extensions. Rings of matrices over fields. Subrings of matrices. Selected topics from matrix groups. |
| Week | Subject | Related Preparation | |
| 1) | Abelian groups. Abelian group morphisms. Kernel and image. | ||
| 2) | Subgroups and product groups. Cyclic groups. Classification of finite abelian groups. | ||
| 3) | Rings. Ring morphisms. Kernel and image. | ||
| 4) | Ideals and their lattice. Prime ideals, primary ideals and maximal ideals. Zorn's Lemma. | ||
| 5) | Zero divisors. Annihiators. Integral domains. | ||
| 6) | Unique factorization domains. Euclidean domains. | ||
| 7) | Quotient rings. Fields and field of fractions. | ||
| 8) | Irreducible polynomials in polynomial rings with one indeterminate over fields. Field extensions. | ||
| 9) | Euclidean division in polynomial rings of a single indeterminate over fields. Calculating greatest common divisors and least common multiples in such rings. | ||
| 10) | Selected topics from polynomial rings over fields. | ||
| 11) | Rings of matrices over fields. Subrings of matrices. | ||
| 12) | Rings of matrices over fields. Subrings of matrices. | ||
| 13) | Selected topics from matrix rings. | ||
| 14) | Selected topics from matrix rings. | ||
| Course Notes: | Instructor's own lecture notes. T. W. Hungerford, "Algebra". I. N. Herstein, "Abstract Algebra". |
| References: |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | 14 | % 0 |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | 3 | % 10 |
| Homework Assignments | % 0 | |
| Presentation | % 0 | |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | 2 | % 40 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 50 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 50 | |
| PERCENTAGE OF FINAL WORK | % 50 | |
| Total | % 100 | |
| 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 | 14 | 6 | 84 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 0 | 0 | 0 |
| Quizzes | 3 | 3 | 9 |
| Preliminary Jury | 0 | 0 | 0 |
| Midterms | 2 | 2 | 4 |
| Paper Submission | 0 | 0 | 0 |
| Jury | 0 | 0 | 0 |
| Final | 1 | 20 | 20 |
| Total Workload | 159 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |