**Prof Michael Small**

Telephone (+61 8) 6488 3877

This will be an introduction to various areas in modern applied mathematics. Each lecture will cover a separate topic from the areas of chaos and complex systems. Topics will be covered in the following order.

The answer: it depends. It depends on how long your ruler is and how wiggly your string. The dimension of objects turns out to generalise well beyond our intuitive understanding of 1, 2 and 3 dimensional space - not just to higher dimensions, but also to fractional dimensions. I will talk about how these measures can be defined and employed for a variety of problems from measuring the length of coastline, to quantifying abstract art, branching structures in bronchiole and trees (the green leafy type not the ones that graph theorists talk about), lung disease and fluctuations in the stock market. We will start with Iterated Function Systems.

The title is a statement of 'The Friendship Paradox', which is of course, not a paradox but only an apparent paradox. I will explain this paradox (hint: it is due to a form of sampling bias) and other interesting features of social networks. The networks we consider are large irregular graphs and they can be formulated as models of all sorts of interaction from Facebook contacts and co-publication in academic journals to neuronal networks and international air transport. We will look at where these networks come from, how they grow and a few of their more interesting properties.

Along the way to the development of modern chaos theory, several of the early protagonists in this story took an interest in applying their skill and knowledge to games of chance. Gambling games have been a useful source of homework questions for high school, and first year, probability. However, many of these systems are actually, in part, deterministic and that determinism can be employed to gain an edge on the house. I will provide details of how this can be done with the example of Roulette.

Additional information about complex systems, chaos, fractal dimension, newscientist and network theory is available for you.

There will be four mini-classes 45 minutes in duration given at **1pm** on **Tuesdays and Fridays** in the **Blakers Lecture Theatre**. No registration is required, simply turn up on your preferred date listed below.

**Complex systems and chaos : Prof Michael Small**

A*bout the lecturer:*Michael is an applied mathematician with interests in nonlinear dynamical systems theory, complex systems theory, chaos, nonlinear time series analysis, and complex networks. His research has found application in a diverse range of areas: physiology, neuroscience, ecology, granular systems, social networks, disease transmission, finance, gambling, musical composition and engineering for remote operations.

Tuesdays

Week | Dates | Lecturer | Topic |
---|---|---|---|

8 | 15 September | Prof Michael Small | Complex systems and chaos |

Week | Dates | Lecturer | Topic |
---|---|---|---|

9, 10, 11 | 25 September, 9, 16 October | Prof Michael Small | Complex systems and chaos |