Useful links
Unit of study_
MATH2022: Linear and Abstract Algebra
2024 unit information
Linear and abstract algebra is one of the cornerstones of mathematics and it is at the heart of many applications of mathematics and statistics in the sciences and engineering. This unit investigates and explores properties of linear functions, developing general principles relating to the solution sets of homogeneous and inhomogeneous linear equations, including differential equations. Linear independence is introduced as a way of understanding and solving linear systems of arbitrary dimension. Linear operators on real spaces are investigated, paying particular attention to the geometrical significance of eigenvalues and eigenvectors, extending ideas from first year linear algebra. To better understand symmetry, matrix and permutation groups are introduced and used to motivate the study of abstract group theory.
Unit details and rules
Managing faculty or University school:
Mathematics and Statistics Academic Operations
| Code | MATH2022 |
|---|---|
| Academic unit | Mathematics and Statistics Academic Operations |
| Credit points | 6 |
|
Prerequisites:
?
|
MATH1061 or MATH1961 or MATH1971 or MATH1X02 or (a mark of 65 or above in MATH1014) |
|---|---|
|
Corequisites:
?
|
None |
| Prohibitions:
?
|
MATH2922 or MATH2968 or (MATH2061 and MATH2021) or (MATH2061 and MATH2921) or (MATH2961 and MATH2021) or (MATH2961 and MATH2921) |
| Assumed knowledge:
?
|
None |
At the completion of this unit, you should be able to:
- LO1. be fluent in analysing and constructing arguments involving matrix arithmetic, permutation and abstract groups, fields and vector spaces
- LO2. understand the definitions, main theorems and corollaries for linearly independent sets, spanning sets, basis and dimension of vector spaces
- LO3. be fluent with linear transformations and operators, and in interpreting, analysing and applying associated abstract phenomena using matrix representations and matrix arithmetic
- LO4. develop appreciation and strong working knowledge of the theory and applications of elementary permutation groups, their decompositions and relationship to invertible phenomena in linear algebra
- LO5. be fluent with important examples, theorems, algorithms and applications of the theory of inner product spaces, including processes and algorithms involving orthogonality, projections and optimisation.
Unit availability
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.
Modes of attendance (MoA)
This refers to the Mode of attendance (MoA) for the unit as it appears when you’re selecting your units in Sydney Student. Find more information about modes of attendance on our website.
