MA40037: Galois theory
[Page last updated: 15 October 2020]
Academic Year:  2020/1 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Masters UG & PG (FHEQ level 7) 
Period: 

Assessment Summary:  EX 100% 
Assessment Detail: 

Supplementary Assessment: 

Requisites:  Before taking this module you must take MA30237 
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 Optional on the following programmes:Department of Computer Science

Notes:
