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Representation theory is the abstract study of the possible types of symmetry in all dimensions. It is a fundamental area of algebra with applications throughout mathematics and physics: the methods of representation theory lead to conceptual and practical simplification of any problem in linear algebra where symmetry is present. This unit will introduce you to the basic notions of modules over associative algebras and representations of groups, and the ways in which these objects can be classified. You will learn the special properties that distinguish the representation theory of finite groups over the complex numbers, and also the unifying principles which are common to the representation theory of a wider range of algebraic structures. By learning the key concepts of representation theory you will also start to appreciate the power of category-theoretic approaches to mathematics. The mental framework you will acquire from this unit of study will enable you both to solve computational problems in linear algebra and to create new mathematical theory.
Study level | Undergraduate |
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Academic unit | Mathematics and Statistics Academic Operations |
Credit points | 6 |
Prerequisites:
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None |
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Corequisites:
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None |
Prohibitions:
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MATH3966 |
Assumed knowledge:
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Familiarity with abstract algebra, specifically vector space theory and basic group theory, e.g., MATH2922 or MATH2961 or equivalent |
At the completion of this unit, you should be able to:
This section lists the session, attendance modes and locations the unit is available in. There is a unit outline for each of the unit availabilities, which gives you information about the unit including assessment details and a schedule of weekly activities.
The outline is published 2 weeks before the first day of teaching. You can look at previous outlines for a guide to the details of a unit.
Session | MoA ? | Location | Outline ? |
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Semester 1 2024
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Normal day | Camperdown/Darlington, Sydney |
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Session | MoA ? | Location | Outline ? |
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Semester 1 2025
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Normal day | Camperdown/Darlington, Sydney |
Outline unavailable
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Session | MoA ? | Location | Outline ? |
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Semester 1 2020
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Normal day | Camperdown/Darlington, Sydney |
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Semester 1 2021
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Normal day | Camperdown/Darlington, Sydney |
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Semester 1 2021
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Normal day | Remote |
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Semester 1 2022
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Normal day | Camperdown/Darlington, Sydney |
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Semester 1 2022
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Normal day | Remote |
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Semester 1 2023
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Normal day | Camperdown/Darlington, Sydney |
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