Rings and Fields(MAT205)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| MAT205 | Rings and Fields | 4 | 0 | 0 | 0 | 5 | 8 |
| Prerequisites | |
| Admission Requirements |
| Language of Instruction | French |
| Course Type | Compulsory |
| Course Level | Bachelor Degree |
| Course Instructor(s) | Gönenç ONAY gonay@gsu.edu.tr (Email) |
| Assistant | |
| Objective | - |
| Content | - |
| Course Learning Outcomes | |
| Teaching and Learning Methods | |
| References |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | Rings from examples: integers, modular arithmetic, polynomials, matrices |
| 2 | Units, zero divisors, nilpotents, integral domains |
| 3 | Ideals and quotient rings; prime and maximal ideals |
| 4 | Ring homomorphisms; isomorphism theorems |
| 5 | Polynomial rings; division algorithm; roots and factors |
| 6 | Irreducibility; Eisenstein criterion |
| 7 | Midterm |
| 8 | Principal ideal domains; unique factorization domains |
| 9 | Introduction to field extensions; degree |
| 10 | Algebraic extensions; minimal polynomial; tower law |
| 11 | Finite fields: construction and uniqueness |
| 12 | Structure of finite fields; the multiplicative group is cyclic |
| 13 | Computations and applications |
| 14 | Revision |
Practice Topics
| Week | Weekly Contents |
|---|
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Toplam | 0 | 0 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Toplam | 0 | 0 |
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Total Workload | 0 | ||
| Total Workload / 25 | 0.00 | ||
| Credits ECTS | 0 | ||