Academic Year:
 2012/3 
Owning Department/School:
 Department of Mathematical Sciences 
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 or 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
 USCMAFB20 : BSc (hons) Computer Science and Mathematics (Fulltime)  Year 3
 USCMAKB20 : BSc (hons) Computer Science and Mathematics (Fulltime with Thick Sandwich Placement)  Year 4
 USCMAAB20 : BSc (hons) Computer Science and Mathematics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USCMAFB13 : BSc (hons) Computer Science with Mathematics (Fulltime)  Year 3
 USCMAKB14 : BSc (hons) Computer Science with Mathematics (Fulltime with Thick Sandwich Placement)  Year 4
 USCMAAB14 : BSc (hons) Computer Science with Mathematics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USCMAFM14 : MComp (hons) Computer Science and Mathematics (Fulltime)  Year 3
 USCMAFM14 : MComp (hons) Computer Science and Mathematics (Fulltime)  Year 4
 USCMAKM14 : MComp (hons) Computer Science and Mathematics with Industrial Placement (Fulltime with Thick Sandwich Placement)  Year 4
 USCMAKM14 : MComp (hons) Computer Science and Mathematics with Industrial Placement (Fulltime with Thick Sandwich Placement)  Year 5
 USCMAAM14 : MComp (hons) Computer Science and Mathematics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USCMAAM14 : MComp (hons) Computer Science and Mathematics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 5
Department of Mathematical Sciences
 USMAAFB15 : BSc (hons) Mathematical Sciences (Fulltime)  Year 3
 USMAAKB16 : BSc (hons) Mathematical Sciences (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAFB13 : BSc (hons) Mathematics (Fulltime)  Year 3
 USMAAKB14 : BSc (hons) Mathematics (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAFB01 : BSc (hons) Mathematics and Statistics (Fulltime)  Year 3
 USMAAKB02 : BSc (hons) Mathematics and Statistics (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAAB14 : BSc (hons) Mathematics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAFB05 : BSc (hons) Statistics (Fulltime)  Year 3
 USMAAKB06 : BSc (hons) Statistics (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAAB06 : BSc (hons) Statistics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAFM14 : MMath Mathematics (Fulltime)  Year 3
 USMAAFM14 : MMath Mathematics (Fulltime)  Year 4
 USMAAAM15 : MMath Mathematics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 TSMAAFM09 : MSc Mathematical Sciences (Fulltime)  Year 1
 TSMAAPM09 : MSc Mathematical Sciences (Parttime)  Year 1
 TSMAAPM09 : MSc Mathematical Sciences (Parttime)  Year 2
Department of Physics
 USXXAFM01 : MSci (hons) Mathematics and Physics (Fulltime)  Year 4
