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.
In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:
- Deduction of 5% of the maximum mark for each calendar day after the due date.
- After ten calendar days late, a mark of zero will be awarded.
If you experience short-term circumstances beyond your control, such as illness, injury or misadventure or if you have essential commitments which impact your preparation or performance in an assessment, you may be eligible for special consideration or special arrangements.
The Current Student website provides information on academic honesty, academic dishonesty, and the resources available to all students.
The University expects students and staff to act ethically and honestly and will treat all allegations of academic dishonesty or plagiarism seriously.
We use similarity detection software to detect potential instances of plagiarism or other forms of academic dishonesty. If such matches indicate evidence of plagiarism or other forms of dishonesty, your teacher is required to report your work for further investigation.
Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University’s graduate qualities and are assessed as part of the curriculum.
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.
Closing the loop
We are continuing to improve the materials and resources for this unit, and thank students for their appreciative comments.
- Science student portal
- Mathematics and Statistics student portal
Work, health and safety
We are governed by the Work Health and Safety Act 2011, Work Health and Safety Regulation 2011 and Codes of Practice. Penalties for non-compliance have increased. Everyone has a responsibility for health and safety at work. The University’s Work Health and Safety policy explains the responsibilities and expectations of workers and others, and the procedures for managing WHS risks associated with University activities.
General Laboratory Safety Rules
- No eating or drinking is allowed in any laboratory under any circumstances
- A laboratory coat and closed-toe shoes are mandatory
- Follow safety instructions in your manual and posted in laboratories
- In case of fire, follow instructions posted outside the laboratory door
- First aid kits, eye wash and fire extinguishers are located in or immediately outside each laboratory
- As a precautionary measure, it is recommended that you have a current tetanus immunisation. This can be obtained from University Health Service: unihealth.usyd.edu.au/