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MA40037: Galois theory

Follow this link for further information on academic years Academic Year: 2012/3
Follow this link for further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Follow this link for further information on credits Credits: 6
Follow this link for further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Follow this link for further information on period slots Period: Semester 2
Follow this link for further information on unit assessment Assessment: EX 100%
Follow this link for further information on supplementary assessment Supplementary Assessment: MA40037 Mandatory Extra Work (where allowed by programme regulations)
Follow this link for further information on unit rules Requisites: Before taking this unit you must take MA30204 or take MA30237
Follow this link for further information on unit content 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.
Follow this link for further information on programme availabilityProgramme availability:

MA40037 is Optional on the following programmes:

Department of Computer Science
  • USCM-AFB20 : BSc (hons) Computer Science and Mathematics (Full-time) - Year 3
  • USCM-AKB20 : BSc (hons) Computer Science and Mathematics (Full-time with Thick Sandwich Placement) - Year 4
  • USCM-AAB20 : BSc (hons) Computer Science and Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USCM-AFB13 : BSc (hons) Computer Science with Mathematics (Full-time) - Year 3
  • USCM-AKB14 : BSc (hons) Computer Science with Mathematics (Full-time with Thick Sandwich Placement) - Year 4
  • USCM-AAB14 : BSc (hons) Computer Science with Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USCM-AFM14 : MComp (hons) Computer Science and Mathematics (Full-time) - Year 3
  • USCM-AFM14 : MComp (hons) Computer Science and Mathematics (Full-time) - Year 4
  • USCM-AKM14 : MComp (hons) Computer Science and Mathematics with Industrial Placement (Full-time with Thick Sandwich Placement) - Year 4
  • USCM-AKM14 : MComp (hons) Computer Science and Mathematics with Industrial Placement (Full-time with Thick Sandwich Placement) - Year 5
  • USCM-AAM14 : MComp (hons) Computer Science and Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USCM-AAM14 : MComp (hons) Computer Science and Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 5
Department of Mathematical Sciences
  • USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 3
  • USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 4
  • USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 3
  • USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 4
  • USMA-AFB01 : BSc (hons) Mathematics and Statistics (Full-time) - Year 3
  • USMA-AKB02 : BSc (hons) Mathematics and Statistics (Full-time with Thick Sandwich Placement) - Year 4
  • USMA-AAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 3
  • USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 4
  • USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USMA-AFM14 : MMath Mathematics (Full-time) - Year 3
  • USMA-AFM14 : MMath Mathematics (Full-time) - Year 4
  • USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • TSMA-AFM09 : MSc Mathematical Sciences (Full-time) - Year 1
  • TSMA-APM09 : MSc Mathematical Sciences (Part-time) - Year 1
  • TSMA-APM09 : MSc Mathematical Sciences (Part-time) - Year 2
Department of Physics
  • USXX-AFM01 : MSci (hons) Mathematics and Physics (Full-time) - Year 4

Notes:
* This unit catalogue is applicable for the 2012/13 academic year only. Students continuing their studies into 2013/14 and beyond should not assume that this unit will be available in future years in the format displayed here for 2012/13.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.