| Effective Term: | 2024/05 |
| Institute / School : | Institute of Innovation, Science & Sustainability |
| Unit Title: | Puzzles, Patterns and Proofs (Advanced Level) |
| Unit ID: | MATHS3007 |
| Credit Points: | 15.00 |
| Prerequisite(s): | (At least one intermediate level mathematics unit) |
| Co-requisite(s): | Nil |
| Exclusion(s): | (MA655 and MATHS2005) |
| ASCED: | 010101 |
| Other Change: | |
| Brief description of the Unit |
This unit is aimed at students who are interested in the role of both logic and imagination in mathematics. It would be particularly valuable to prospective teachers of mathematics at primary and secondary level and to students interested in improving their understanding of basic mathematical principles and techniques. In the latter case this unit can be used by students interested in pursuing more advanced mathematical units. |
| Grade Scheme: | Graded (HD, D, C, P, MF, F, XF) |
| Work Experience Indicator: |
| No work experience |
| Placement Component: | |
| Supplementary Assessment:No |
| Supplementary assessment is not available to students who gain a fail in this Unit. |
| Course Level: |
| Level of Unit in Course | AQF Level(s) of Course | | 5 | 6 | 7 | 8 | 9 | 10 | | Introductory | | | | | | | | Intermediate | | | | | | | | Advanced | | |  | | | |
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| Learning Outcomes: |
| Knowledge: |
| K1. | use elementary ideas in number theory; |
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| K2. | explain and be able to carry out proofs by mathematical induction |
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| K3. | describe the proof of the four colour theorem |
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| K4. | apply basic concepts of graph theory |
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| K5. | explain arithmetic operations from a theoretical point of view |
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| Skills: |
| S1. | express concepts, relationships and structures in mathematical form, and draw conclusions about the situations studied by abstract argument |
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| S2. | use elementary ideas about sets and their properties in problem solving |
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| S3. | investigate topological ideas |
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| Application of knowledge and skills: |
| A1. | construct mathematical proofs using a variety of proof techniques |
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| A2. | express in mathematical terms and solve a range of counting problems |
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| A3. | research and impart mathematical knowledge to others |
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| Unit Content: |
This unit introduces a broad range of mathematical concepts of wide applicability. It contains material which will be of interest and relevant to computing students who seek a theoretical understanding of their subject, as well as to mathematics students. Much of the material is starting to appear in secondary mathematics curricula, and the rest provides valuable enrichment material for those students intending to teach mathematics. |
| Graduate Attributes: |
| | Learning Outcomes Assessed | Assessment Tasks | Assessment Type | Weighting | | 1. | K1-5, S1-3, A1, A2 | Participate in class activities | Portfolio of completed work | 0 - 20% | | 2. | A3 | Self directed or group exploration | Projects / Presentation | 30 - 50% | | 3. | K1-5, S1-3, A1, A2 | Review and skills practice | Tests / Examination(s) | 50 - 60% |
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