Department of Mathematical Sciences, Unit Catalogue 2011/12 |
|
 Credits:
| 6 |
| Level:
| Masters UG & PG (FHEQ level 7) |
| Period: |
Semester 2 |
| Assessment:
| EX 100% |
| Supplementary Assessment: | MA40037 Mandatory Extra Work (where allowed by programme regulations) |
| Requisites:
| Before taking this unit you must take MA30204 |
| Description:
| NB. This unit is only available in academic years starting in an even year. Aims: To give a thorough treatment of the fundamental theory of Galois on solvability of polynomials and the subtle interplay between group theory and field theory that arises in this context. Learning Outcomes: At the end of the course the students should be able to state and use the fundamental theorem of Galois Theory as well as the various applications given. The students should moreover be able to compute the Galois group of simple polynomials. Content: Revision of rings, integral domains and fields. Field extensions. Algebraic closure. Splitting fields. Normal and separable field extensions. Galois groups. The Galois correspondence and the fundamental theorem of Galois Theory. Solvable groups and the theorem of Galois on solvability of polynomials. The fundamental theorem of algebra. Finite fields. |
| Programme availability: |
MA40037 is only available in academic years starting in an even year. |