- Code MATH6116
- Unit Value 6 units
- Offered by Mathematical Sciences Institute
- ANU College ANU Joint Colleges of Science
- Course subject Mathematics
- Areas of interest Digital Arts, Computer Science, Mathematics, Physics, Algorithms and Data
This course introduces basic mathematical techniques of fractal geometry and dynamical systems, aimed towards understanding and modeling natural shapes and forms from leaves to coastlines. Basic topological and geometrical language to describe and model rough, ("fractal") objects is developed. Relationships between fractal geometry and discrete dynamical systems and chaotic dynamics are emphasized, including symbolic dynamics, stability of attractors, bifurcations and routes to chaos.
The key ideas are introduced in an intuitive way. The key definitions and theorems are stated but few proofs of theorems are given. However, graduate students will have to attend additional lectures which will provide rigorous mathematical foundations and will be assessed separately from undergraduate students.
In computer laboratory sessions students learn how the mathematical results can be applied in practice by running and modifying simple Python programs.
Upon successful completion, students will have the knowledge and skills to:
Upon successful completion of this course, students will have the knowledge and skills to:
1. Be able to construct and analyse a wide range of fractals.
2. Be able to analyse 1-D dynamical systems in terms of attractors, basins and cascades of bifurcations.
3. Understand how to use fractal geometry to model rough data and natural shapes.
4. Be familiar with Hutchinson theory of deterministic fractal sets and measures, and be able to prove basic theorems and solve problems in the area.
5. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from fractal geometry.
6. Ability to use their deep knowledge and understanding of fractal geometry to formulate responses to complex concrete and abstract problems.
7. Ability to communicate their understanding and skills in fractal geometry with colleagues and non-experts and apply their knowledge in an occupational situation.
- Projects 10% (LO 1-4)
- Assignments 30% (LO 1-4)
- In-class Quizzes 20% (LO 1-4)
- Final exam - 40% of total mark (LO 1-4)
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WorkloadThree lectures per week and regular workshops
Requisite and Incompatibility
You will need to contact the Mathematical Sciences Institute to request a permission code to enrol in this course.
Fractals Everywhere, by Michael F. Barnsley, Third Edition (2012, Dover).
Fractal Geometry - Mathematical Foundations and Applications, Kenneth Falconer (Wiley,2000)
Tuition fees are for the academic year indicated at the top of the page.
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- Student Contribution Band:
- Unit value:
- 6 units
If you are an undergraduate student and have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). You can find your student contribution amount for each course at Fees. Where there is a unit range displayed for this course, not all unit options below may be available.
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