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MA30237: Group 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: Honours (FHEQ level 6)
Follow this link for further information on period slots Period: Semester 1
Follow this link for further information on unit assessment Assessment: EX 100%
Follow this link for further information on supplementary assessment Supplementary Assessment: 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 MA20217
Follow this link for further information on unit content Description: Aims:
To provide the students with a solid introduction to group theory and a broad range of examples of finite and infinite groups.

Learning Outcomes:
After taking this unit, the students should be able to demonstrate knowledge and understanding of the basic theory of groups covered in the course. They should be able to work with the various constructions and tools developed like quotient groups, groups actions and Sylow Theory.

Skills:
Numeracy T/F A
Problem Solving T/F A
Written and Spoken Communication F (in tutorials).

Content:
Normal subgroups, congruences and quotient groups. Homomorphisms, isomorphisms and the Isomorphisms Theorems. Simple groups. Permutation groups and the simplicity of the alternating groups. Group actions and the Orbit Stabilizer Theorem. Conjugacy classes (including in Sn). Sylow Theory. The structure of abelian groups. Solvable groups.
Follow this link for further information on programme availabilityProgramme availability:

MA30237 is Optional on the following programmes:

Department of Computer Science
  • USCM-AFM14 : MComp (hons) Computer Science and Mathematics (Full-time) - Year 3
  • USCM-AKM14 : MComp (hons) Computer Science and Mathematics with Industrial Placement (Full-time with Thick Sandwich Placement) - Year 4
  • USCM-AAM14 : MComp (hons) Computer Science and Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
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
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.