Matematica | GALOIS THEORY
Matematica GALOIS THEORY
cod. 0512300021
GALOIS THEORY
| 0512300021 | |
| DIPARTIMENTO DI MATEMATICA | |
| MATHEMATICS | |
| 2013/2014 |
| YEAR OF COURSE 3 | |
| YEAR OF DIDACTIC SYSTEM 2010 | |
| SECONDO SEMESTRE |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/02 | 6 | 48 | LESSONS |
| Objectives | |
|---|---|
| THE GOAL IS TO STUDY THE ALGEBRAIC EQUATIONS. FOLLOWING GALOIS'S THEORY, IT WILL BE CHARACTERIZED THE EQUATIONS THAT ARE SOLUBLE BY RADICALS. CONNECTIONS WITH OTHER AREAS OF MATH WILL BE HIGHLIGHTED. |
| Prerequisites | |
|---|---|
| FULL KNOWLEDGE OF ELEMENTARY ALGEBRA IS REQUIRED |
| Contents | |
|---|---|
| IRRIDUCIBLITY OF A POLINOMIAL. EXTENDED ISOMORPHISM THEOREMS. SPLITTING FIELD OFA POLINOMIAL. ORDINALAND CARDINAL NUMBERS: TRASFINITY INDUCTION. ALGBRICALLY CLOSED FIELDS, AND ALGEBRIC CLOSURE OF A FIELD. CYCLOTOMIC POLINOMIALS, THEOREM OF GAUSS. NORMAL AND SEPARABLE EXTENSIONS. THE CARDANO'S FORMULAS FOR DETERMINE THE ROOTS OF AN EQUATION OF THIRD OR FOURTH DEGREE. GALOIS EXTENSIONS AND THEIR CARACTERIZATION GALOIS APPLICATIONS: FOUNDAMENTAL THEOREM OF GALOIS THEORY. RISOLUBILITY BY RADICALS OF A GIVEN EQUATION,AND THEIR CARACTERIZATION. CONSTRUCTIONS BY STRAIGHTEDGE AND COMPASS. |
| Teaching Methods | |
|---|---|
| USUAL |
| Verification of learning | |
|---|---|
| THERE ARE MORE ELEMENT THAT GIVE CONTRIBUTION FOR THE VALUTATION OF A STUDENT. 1) INTERACTION DURING LECTURES 2) CHECK AND DISCUSSION OF THE HOMEWORKS 3) WRITING EXAMS 4) ORAL EXAM |
| Texts | |
|---|---|
| 1)ARTIN, ALGEBRA, BOLLATI-BORINGHIERI 2) NOTES GIVEN DURING THE LESSONS |
BETA VERSION Data source ESSE3 [Ultima Sincronizzazione: 2016-09-30]
