MATH1002: Linear Algebra
MATH1002 is designed to provide a thorough preparation for further study in mathematics and statistics. It is a core unit of study providing three of the twelve credit points required by the Faculty of Science as well as a foundation requirement in the Faculty of Engineering. This unit of study introduces vectors and vector algebra, linear algebra including solutions of linear systems, matrices, determinants, eigenvalues and eigenvectors.
Unit details and rules
| Unit code | MATH1002 |
|---|---|
| Academic unit | Mathematics and Statistics Academic Operations |
| Credit points | 3 |
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Prohibitions
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MATH1012 or MATH1014 or MATH1902 |
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Prerequisites
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None |
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Corequisites
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None |
| Available to study abroad and exchange students |
Yes |
Assessment summary
Below are brief assessment details. Further information can be found in the Canvas site for this unit.
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Weekly online quizzes: There are ten weekly online quizzes (equally weighted) and the marks for the best eight count. Each online quiz consists of a set of randomized questions. You should not apply for special consideration for the quizzes. The better mark principle will apply for the total 8% - i.e. if your overall exam mark is higher, then your 8% for the Webwork quizzes will come from your exam. The deadline for completion of each quiz is 11:59 pm Sunday (starting in week 2). The precise schedule for the quizzes is found on Canvas. We recommend that you follow the due dates outlined above to gain the most benefit from these quizzes.
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Quiz: One quiz will be held online through Canvas. The quiz is 40 minutes and has to be submitted by the closing time of 23:59 on the due date. The quiz can be taken any time during the 24 hour period before the closing time. The better mark principle will be used for the quiz so do not submit an application for Special Consideration or Special Arrangements if you miss a quiz. The better mark principle means that the quiz counts if and only if it is better than or equal to your exam mark. If your quiz mark is less than your exam mark, the exam mark will be used for that portion of your assessment instead.
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Assignments: There are two written assignments which must be submitted electronically, as PDF files only via Canvas, 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. Penalties apply for late submission. A mark of zero will be awarded for all submissions more than 10 days past the original due date. Further extensions past this time will not be permitted.
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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).
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Final Examination: The final exam for this unit is compulsory and must be attempted. Failure to attempt the final exam will result in an AF grade for the course. 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.
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.
You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.
Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.
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.
| WK | Topic | Learning activity | Learning outcomes |
|---|---|---|---|
| Week 01 | Introductions, vectors in the plane, vector algebra, vectors in R3 and Rn. | Lecture and tutorial (3 hr) | LO1 LO2 |
| Week 02 | Length and angle: the dot product, orthogonal vectors, projections | Lecture and tutorial (3 hr) | LO2 LO5 |
| Week 03 | Cross products | Lecture and tutorial (3 hr) | LO5 |
| Week 04 | Lines and planes | Lecture and tutorial (3 hr) | LO2 LO3 |
| Week 05 | Systems of linear equations and Gaussian elimination | Lecture and tutorial (3 hr) | LO6 LO7 |
| Week 06 | Gauss-Jordan elimination, intro to matrices, matrix algebra | Lecture and tutorial (3 hr) | LO6 LO7 LO8 |
| Week 07 | Matrix algebra, inverse of a matrix. | Lecture and tutorial (3 hr) | LO8 |
| Week 08 | Solving systems of linear equations, elementary matrices | Lecture and tutorial (3 hr) | LO6 LO8 |
| Week 09 | Applications to population models and Markov chains | Lecture and tutorial (3 hr) | LO8 LO11 |
| Week 10 | Determinants | Lecture and tutorial (3 hr) | LO8 |
| Week 11 | Eigenvalues and eigenvectors | Lecture and tutorial (3 hr) | LO9 |
| Week 12 | Diagonalisation and more on applications | Lecture and tutorial (3 hr) | LO10 LO11 |
| Week 13 | Revision | Lecture (2 hr) | LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8 LO9 LO10 LO11 |
Attendance and class requirements
- Lecture attendance: You are expected to attend lectures. If you do not attend lectures you should at least follow the lecture recordings available through Canvas.
- Tutorial attendance: Tutorials (one per week) start in Week 1. There is no tutorial in Week 13. You should attend the tutorial given on your personal timetable. Attendance at tutorials and participation will be recorded to determine the participation mark. We strongly recommend you attend tutorials regularly to keep up with the material and to engage with the tutorial questions.
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 3 credit point unit, this equates to roughly 60-75 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. apply mathematical logic and rigour to solving problems;
- LO2. represent vectors both algebraically and geometrically in two and three dimensions, and perform arithmetic with them;
- LO3. use vectors to solve classical geometric problems;
- LO4. determine spanning families and check linear independence
- LO5. perform and manipulate dot and cross products;
- LO6. set up systems of linear equations;
- LO7. solve systems of linear equations using Gaussian elimination;
- LO8. perform matrix arithmetic and calculate matrix inverses and determinants;
- LO9. find eigenvalues and eigenvectors;
- LO10. diagonalise a matrix;
- LO11. express mathematical ideas and arguments coherently in written form.
- Lectures: Lectures are face-to-face and streamed live with online access from Canvas.
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Tutorials: Tutorials are small classes in which you are expected to work through questions from the tutorial sheet in small groups on the white board. The role of the tutor is to provide support and to some extent give feedback on your solutions written on the board.
- Tutorial and exercise sheets: The question sheets for a given week will be available on the MATH1002 Canvas page. Solutions to tutorial exercises for week n will usually be posted on the web by the afternoon of the Friday of week n.
- Ed Discussion forum: https://edstem.org