 Academic Year: | 2017/8 |
| 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: |
- Semester 2
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| Assessment Summary: | EX 100% |
| Assessment Detail: | |
| Supplementary Assessment: |
- MA40054 Mandatory Extra Work (where allowed by programme regulations)
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| Requisites: |
Before taking this module you must take MA30237
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| 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.
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| Programme availability: |
MA40054 is Optional on the following programmes:
Department of Computer Science
- USCM-AFB20 : BSc(Hons) Computer Science and Mathematics (Year 3)
- USCM-AAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 4)
- USCM-AKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 4)
- USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 3)
- USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 4)
- USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 4)
- USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 5)
- USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 4)
- USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 5)
Department of Economics
- UHES-AFB04 : BSc(Hons) Economics and Mathematics (Year 3)
Department of Mathematical Sciences
- USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
- USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
- USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
- USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
- USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
- USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
- USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
- USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
- USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
- USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
- USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)
- USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
- USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
- USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
- USMA-AFB05 : BSc(Hons) Statistics (Year 3)
- USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
- USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
Department of Physics
- USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 4)
- USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 5)
- USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 5)
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