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MA40054: Representation theory of finite groups

Follow this link for further information on academic years Academic Year: 2013/4
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6
Further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Further information on teaching periods Period: Semester 2
Further information on unit assessment Assessment: EX 100%
Further information on supplementary assessment Supplementary Assessment: MA40054 Mandatory Extra Work (where allowed by programme regulations)
Further information on requisites Requisites: Before taking this unit you must take MA30237
Further information on descriptions Description: Aims:
The course explains some fundamental applications of linear algebra to the study of finite groups. In so doing, it will show by example how one area of mathematics can enhance and enrich the study of another.

Learning Outcomes:
At the end of the course, the students will be able to state and prove the main theorems of Maschke and Schur and be conversant with their many applications in representation theory and character theory. Moreover, they will be able to apply these results to problems in group theory.

Content:
Topics will be chosen from the following: Group algebras, their modules and associated representations. Maschke's theorem and complete reducibility. Irreducible representations and Schur's lemma. Decomposition of the regular representation. Character theory and orthogonality theorems. Burnside's pa qb theorem.
Further information on programme availabilityProgramme availability:

MA40054 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
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)
  • TSMA-APM09 : MSc Mathematical Sciences (Part-time)
Department of Physics
  • USXX-AFM01 : MSci (hons) Mathematics and Physics (Full-time) - Year 4

Notes:
* This unit catalogue is applicable for the 2013/4 academic year only. Students continuing their studies into 2014/15 and beyond should not assume that this unit will be available in future years in the format displayed here for 2013/14.
* 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.