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Year - 2020

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.

Classes

3 x 1hr lecture/week, 1 x 1hr tutorial/week

Assessment

tutorial participation (10%), 2 x homework assignments (40%), final exam (50%)

Assumed knowledge

Familiarity with abstract algebra, specifically vector space theory and basic group theory, e.g., MATH2922 or MATH2961 or equivalent.

MATH3966

Faculty: Science

Semester 1

24 Feb 2020

Department/School: Mathematics and Statistics Academic Operations

Study Mode: Normal (lecture/lab/tutorial) day

Census Date: 31 Mar 2020

Unit of study level: Honours

Credit points: 6.0

EFTSL: 0.125

Available for study abroad and exchange: Yes

Faculty/department permission required? No

Location

Camperdown

More details

HECS Band: 2

Leadership for good starts here

ABN: 15 211 513 464

CRICOS Number: 00026A

TEQSA: PRV12057