| Effective Term: | 2024/05 |
| Institute / School : | Institute of Innovation, Science & Sustainability |
| Unit Title: | Secrets of the Matrix |
| Unit ID: | MATHS1005 |
| Credit Points: | 15.00 |
| Prerequisite(s): | Nil |
| Co-requisite(s): | Nil |
| Exclusion(s): | (MA555) |
| ASCED: | 010101 |
| Other Change: | |
| Brief description of the Unit |
This course aims to offer students from diverse backgrounds an introduction to the use of mathematical methods in finding optimal choices in business, industry, economics, and social, behavioural and biological sciences. It introduces students to linear algebra and linear programming that underlie applications in operations research. |
| Grade Scheme: | Graded (HD, D, C, P, MF, F, XF) |
| Work Experience Indicator: |
| No work experience |
| Placement Component: | |
| Supplementary Assessment:Yes |
| Where supplementary assessment is available a student must have failed overall in the Unit but gained a final mark of 45 per cent or above, has completed all major assessment tasks (including all sub-components where a task has multiple parts) as specified in the Unit Description and is not eligible for any other form of supplementary assessment |
| Course Level: |
| Level of Unit in Course | AQF Level(s) of Course | | 5 | 6 | 7 | 8 | 9 | 10 | | Introductory | | |  | | | | | Intermediate | | | | | | | | Advanced | | | | | | |
|
| Learning Outcomes: |
| Knowledge: |
| K1. | proclaim the fundamental structure of matrices and matrix arithmetic; |
|
| K2. | explain the nature of vectors; |
|
| K3. | recognise the basic techniques used for problems in linear programming; |
|
| K4. | demonstrate an understanding of the theoretical basis for such algorithms; |
|
| Skills: |
| S1. | represent and solve systems of linear equations; |
|
| S2. | perform the operations of addition, multiplication, and transposition of matrices; |
|
| S3. | find the determinant and inverse of a matrix; |
|
| S4. | prove simple algebraic statements about vector addition, scalar multiplication and inner products; |
|
| S5. | use vectors and operations involving vectors to solve problems involving lines and planes in 3-space; |
|
| S6. | find eigenvalues and eigenvectors of a 2x2 matrix; |
|
| S7. | graphically represent linear programming problems in 2 dimensions; |
|
| Application of knowledge and skills: |
| A1. | use appropriate algorithms to solve linear programming problems; |
|
| A2. | use appropriate software packages to solve elementary problems of linear programming; |
|
| Unit Content: |
•matrix representations of systems of linear equations;
•vectors and matrices and their algebraic properties;
•determinants and inverses of matrices;
•dot products and cross products of vectors;
•lines and planes in 3-space;
•vector spaces, linear independence, basis, dimension and rank of matrices;
•inner products, orthonormal bases, orthogonal matrices;
•diagonalization of matrices, eigenvalues and eigenvectors;
•the setting of LP problems and the geometry of LP problems;
•the Simplex algorithm;
•duality;
•modern algorithms such as those based on interior point methods;
•transportation problems;
•network flow problems;
•applications of LP;
•software packages for solving LP problems. |
| Graduate Attributes: |
| | Learning Outcomes Assessed | Assessment Tasks | Assessment Type | Weighting | | 1. | K1-4, S1-7, A1 | Participate in class activities | Portfolio of completed work | 0 - 20% | | 2. | K1-4, S1-7, A1, A2 | Self directed or group exploration | Projects | 10 - 30% | | 3. | K1-4, S1-7, A1, A2 | Self directed or group exploration | Presentation | 10 - 20% | | 4. | K1-4, S1-7, A1 | Review and skills practice | Tests/examination(s) | 40 - 60% |
|