MATH2022: Semester 1, 2025
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Unit outline_

Unit outlines now display a small icon AI Allowed = AI allowed restricted AI = restricted AI to indicate which assessments allow you to use AI tools such as Microsoft Copilot Chat. Make sure you are aware of how AI can be used, as unauthorised use is a breach of academic integrity.

MATH2022: Linear and Abstract Algebra

Semester 1, 2025 [Normal day] - Camperdown/Darlington, Sydney

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

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

Available to study abroad and exchange students

Yes

Teaching staff

Coordinator Sam Jeralds, samuel.jeralds@sydney.edu.au
Lecturer(s) Sam Jeralds, samuel.jeralds@sydney.edu.au
The census date for this unit availability is 31 March 2025
Type Description Weight Due Length
Supervised exam
? 
Final exam
Multiple-choice, short and/or extended answer questions
60% Formal exam period 2 hours
Outcomes assessed: LO1 LO2 LO3 LO4 LO5
Participation AI Allowed Tutorial participation
Collaborative problem solving
2% Multiple weeks 1 hr
Outcomes assessed: LO1 LO5 LO4 LO3 LO2
Online task Early Feedback Task Early Feedback Task
Multiple choice #earlyfeedbacktask
2% Week 03
Due date: 14 Mar 2025 at 23:59

Closing date: 14 Mar 2025
40 minutes
Outcomes assessed: LO1
Assignment Assignment 1
Extended written answers
6% Week 05
Due date: 28 Mar 2025 at 23:59

Closing date: 07 Apr 2025
3-5 pages
Outcomes assessed: LO1 LO2 LO3 LO4
Small test Quiz 1
Multiple choice
12% Week 07
Due date: 10 Apr 2025 at 15:00

Closing date: 10 Apr 2025
40 minutes
Outcomes assessed: LO1 LO4 LO3 LO2
Assignment Assignment 2
Extended written answers
6% Week 11
Due date: 16 May 2025 at 23:59

Closing date: 26 May 2025
3-5 pages
Outcomes assessed: LO1 LO2 LO3 LO4
Small test Quiz 2
Multiple choice
12% Week 13
Due date: 29 May 2025 at 15:00

Closing date: 29 May 2025
40 minutes
Outcomes assessed: LO1 LO4 LO3 LO2
AI allowed = AI allowed ?
early feedback task = early feedback task ?

Early feedback task

This unit includes an early feedback task, designed to give you feedback prior to the census date for this unit. Details are provided in the Canvas site and your result will be recorded in your Marks page. It is important that you actively engage with this task so that the University can support you to be successful in this unit.

Assessment summary

Detailed information for each assessment can be found on Canvas.

Assignments: There are two assignments. Each must be submitted electronically, as one single typeset or scanned PDF file only, by the deadline. Note that your assignment will not be marked if it is illegible or if it is submitted sideways or upside down. It is your responsibility to check that your assignment has been submitted correctly and that it is complete (check that you can view each page). Late submisions will receive a penalty. A mark of zero will be awarded for all submissions more than 7 days past the original due date. Further extensions past this time will not be permitted.

Early Feedback Task: This is an online quiz held in Week 3. 

Quizzes: Two quizzes will be held in person at the time of the seminar in Weeks 7 and 13, at the location appearing in your timetable. 

Tutorial Participation: This is a satisfactory/non-satisfactory mark assessing whether or not you participate in class activities during the tutorials. It is 0.25 marks per tutorial class up to 8 tutorials (there are 12 tutorials in total).

Final Exam: There is one examination during the examination period at the end of Semester. Further information about the exam will be made available at a later date on Canvas. If a second replacement exam is required, this exam may be delivered via an alternative assessment method, such as a viva voce (oral exam). The alternative assessment will meet the same learning outcomes as the original exam. The format of the alternative assessment will be determined by the unit coordinator.

Assessment criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

Result name

Mark range

Description

High distinction

85 - 100

Representing complete or close to complete mastery of the material.

Distinction

75 - 84

Representing excellence, but substantially less than complete mastery.

Credit

65 - 74

Representing a creditable performance that goes beyond routine knowledge and understanding, but less than excellence.

Pass

50 - 64

Representing at least routine knowledge and understanding over a spectrum of topics and important ideas and concepts in the course.

Fail

0 - 49

When you don’t meet the learning outcomes of the unit to a satisfactory standard.

For more information see guide to grades.

Use of generative artificial intelligence (AI) and automated writing tools

Except for supervised exams or in-semester tests, you may use generative AI and automated writing tools in assessments unless expressly prohibited by your unit coordinator. 

For exams and in-semester tests, the use of AI and automated writing tools is not allowed unless expressly permitted in the assessment instructions. 

The icons in the assessment table above indicate whether AI is allowed – whether full AI, or only some AI (the latter is referred to as “AI restricted”). If no icon is shown, AI use is not permitted at all for the task. Refer to Canvas for full instructions on assessment tasks for this unit. 

Your final submission must be your own, original work. You must acknowledge any use of automated writing tools or generative AI, and any material generated that you include in your final submission must be properly referenced. You may be required to submit generative AI inputs and outputs that you used during your assessment process, or drafts of your original work. Inappropriate use of generative AI is considered a breach of the Academic Integrity Policy and penalties may apply. 

The Current Students website provides information on artificial intelligence in assessments. For help on how to correctly acknowledge the use of AI, please refer to the  AI in Education Canvas site

Late submission

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.

Academic integrity

The Current Student website provides information on academic integrity 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 integrity breaches seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

Support for students

The Support for Students Policy 2023 reflects the University’s commitment to supporting students in their academic journey and making the University safe for students. It is important that you read and understand this policy so that you are familiar with the range of support services available to you and understand how to engage with them.

The University uses email as its primary source of communication with students who need support under the Support for Students Policy 2023. Make sure you check your University email regularly and respond to any communications received from the University.

Learning resources and detailed information about weekly assessment and learning activities can be accessed via Canvas. It is essential that you visit your unit of study Canvas site to ensure you are up to date with all of your tasks.

If you are having difficulties completing your studies, or are feeling unsure about your progress, we are here to help. You can access the support services offered by the University at any time:

Support and Services (including health and wellbeing services, financial support and learning support)
Course planning and administration
Meet with an Academic Adviser

WK Topic Learning activity Learning outcomes
Week 01 Modular arithmetic, groups and fields Lecture and tutorial (4 hr) LO1 LO4
Week 02 Groups of symmetries and permutations Lecture and tutorial (5 hr) LO1 LO4
Week 03 Conjugation in symmetric groups, products of groups, group isomorphisms Lecture and tutorial (5 hr) LO1 LO4
Week 04 Groups wrap up, matrix arithmetic over fields, systems of equations Lecture and tutorial (5 hr) LO1 LO4
Week 05 Elementary matrices, invertibility and determinants, rotation and reflection matrices Lecture and tutorial (5 hr) LO1 LO4
Week 06 Eigenvalues and eigenvectors, characteristic polynomials, Cayley-Hamilton theorem Lecture and tutorial (5 hr) LO1 LO4
Week 07 Diagonalization and applications of eigenvalues/eigenvectors Lecture and tutorial (5 hr) LO1 LO4
Week 08 Cartesian space, linear transformations, compositions of maps Lecture and tutorial (4 hr) LO1 LO3
Week 09 Abstract vector spaces, subspaces, linear independence Lecture and tutorial (5 hr) LO1 LO2 LO3
Week 10 Basis and dimension, coordinate systems, rank-nullity Lecture and tutorial (5 hr) LO1 LO2 LO3
Week 11 Linear transformations, representation by matrix, change of basis, matrix exponential Lecture and tutorial (5 hr) LO1 LO2 LO3
Week 12 Inner product spaces, projections, orthonormal bases Lecture and tutorial (5 hr) LO1 LO2 LO3 LO5
Week 13 Gram-Schmidt algorithm, Jordan canonical form, additional topics, revision Lecture and tutorial (5 hr) LO1 LO2 LO3 LO4 LO5

Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

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.

Graduate qualities

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

GQ1 Depth of disciplinary expertise

Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline.

GQ2 Critical thinking and problem solving

Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem.

GQ3 Oral and written communication

Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context.

GQ4 Information and digital literacy

Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies.

GQ5 Inventiveness

Generating novel ideas and solutions.

GQ6 Cultural competence

Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues.

GQ7 Interdisciplinary effectiveness

Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries.

GQ8 Integrated professional, ethical, and personal identity

An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context.

GQ9 Influence

Engaging others in a process, idea or vision.

Outcome map

Learning outcomes Graduate qualities
GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9

This section outlines changes made to this unit following staff and student reviews.

We are continuing to improve the materials and resources for this unit, and thank students for their appreciative comments.

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/

Disclaimer

The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.

This unit of study outline was last modified on 04 Feb 2025.

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