68105 Algebra
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particular session, location and mode of offering is the authoritative source
of all information about the subject for that offering. Required texts, recommended texts and references in particular are likely to change. Students will be provided with a subject outline once they enrol in the subject.
Subject handbook information prior to 2025 is available in the Archives.
Credit points: 6 cp
Result type: Grade and marks
Requisite(s): 68102 Mathematics for Secondary Education Foundations
These requisites may not apply to students in certain courses. See access conditions.
Anti-requisite(s): 37233 Linear Algebra
Description
This subject enhances your grasp of algebra and linear algebra theory and application. Students tackle topics such as working with complex numbers, solving linear equations, matrix operations, inverses, determinants, LU factorisation, diagonalisation, vector spaces, span, dimension, linear independence, as well as applications to practical problems.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 1. | apply fundamental concepts of mathematics to solve problems involving linear algebra |
|---|---|
| 2. | apply knowledge of the conceptual development of linear algebra to explain procedures and calculations |
| 3. | use mathematical terminology and symbols to define concepts |
| 4. | apply mathematical knowledge and skills in a variety of situations, in both familiar and new contexts |
| 5. | communicate mathematical knowledge clearly, logically and critically |
Contribution to the development of graduate attributes
1.0 Disciplinary knowledge
The lecture content and workshop activities will allow students to develop practical and theoretical skills in Algebra.
2.0 Research, inquiry and critical thinking
The collaborative approach to problem formulations and solutions used in the workshops helps students develop skills in identifying and evaluating alternative approaches to solving problems.
4.0 Reflection, innovation, creativity
The assessment items require students to think about how to present material creatively, precisely and engagingly, and feedback provided after each item allow students to reflect on the effectiveness in communicating the concepts in their responses.
5.0 Communication
Presentation of written and oral solutions to problems using appropriate professional language is emphasised in the workshops and assessment. Assessment tasks require the appropriate presentation of information, reasoning and conclusions and require students to gain meaning from instructions and problem statements.
Teaching and learning strategies
Students should actively engage with the lecture material/subject content, delivered via Canvas, attend and actively participate in the workshops each week, and spend several hours each week working on additional homework problems.
Workshops consist of working in small groups collaboratively on problems.
Assessment Item 3 which assesses progress, understanding and skills will be conducted during the workshop time on campus in weeks 1-11.
Content (topics)
- Complex numbers
- Vector spaces
- Basis, dimensions, span
- Linear spaces and subspaces, linear dependence/independence
- Linear transformations
- Systems of linear equations
- Determinant, elementary matrices, eigenvectors, eigenvalues and invariant subspaces
- LU factorisation
- Applications
Assessment
Assessment task 1: Assessment item 1
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary Knowledge 2. Research, inquiry and critical thinking 4. Reflection, Innovation, Creativity 5. Communication |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 3, 4 and 5 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 2.1 and 4.1 |
| Type: | Quiz/test |
| Groupwork: | Individual |
| Weight: | 45% |
| Length: | 1A: 1 hour 10 minutes 1B: 1 hour 10 minutes |
| Criteria: | Correct mathematics, clarity of exposition, appropriate choice of mathematical techniques/proof methods. |
Assessment task 2: Assessment item 2
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary Knowledge 2. Research, inquiry and critical thinking 4. Reflection, Innovation, Creativity 5. Communication |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2, 3, 4 and 5 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 2.1, 4.1 and 5.1 |
| Type: | Quiz/test |
| Groupwork: | Individual |
| Weight: | 35% |
| Length: | 1 hour 10 minutes |
| Criteria: | Correct mathematics, clarity of exposition, appropriate choice of mathematical techniques/proof methods. |
Assessment task 3: Assessment item 3
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary Knowledge 2. Research, inquiry and critical thinking 4. Reflection, Innovation, Creativity 5. Communication |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 2, 3 and 5 This assessment task contributes to the development of course intended learning outcome(s): 2.1 and 4.1 |
| Type: | Presentation |
| Groupwork: | Group, individually assessed |
| Weight: | 20% |
| Criteria: | Correct mathematics, clarity of exposition, appropriate choice of mathematical techniques/proof methods. |
Required texts
Oliveira, Lina (2022) Linear algebra. Taylor & Francis, first edition.
Available at no cost online from the UTS Library
https://search.lib.uts.edu.au/permalink/61UTS_INST/19joism/alma991007186874105671
Recommended texts
Axler, Sheldon (2024) Linear Algebra Done Right, Springer, forth edition.
PDF available to download without cost at https://linear.axler.net/ or
https://search.lib.uts.edu.au/permalink/61UTS_INST/19joism/alma991007326774705671