Mathematics and Engineering have a long and turbulent relationship. Many famous mathematicians in history worked as engineers and much contemporary mathematics originates in engineering. The focus of this lecture will be on a personal interest of mine: the connection of sophisticated mathematics with signal processing. New mathematics has come out of applications, and existing mathematics is being applied into real world signal processing problems. I will illustrate this fascinating interplay with several examples from history, and from recent work by myself and others. In particular I will talk about how you should track a rotating object.
Bill Moran is a Professor in the School of Electrical and Computer Engineering at RMIT. Previously he was a Professor of Pure Mathematics at the University of Adelaide, Professor of Mathematics at Flinders University, and Professor of Electrical Engineer at the University of Melbourne. He has served as Dean of the Faculty of Mathematical and Computer Sciences at the University of Adelaide, and Director of the Defence Science Institute at the University of Melbourne. He started his career as a pure mathematician but moved, over time, to a more applied focus, particularly in radar, sensor scheduling, signal processing, and information theory. While he retains an interest in pure mathematics, he mostly uses mathematical techniques to solve problems in engineering. He has been funded by many organisations including the Australian Research Council, DSTO/Group, the US Defence Advanced Research Projects Agency (DARPA), the US Air Force Research Laboratory, and the US Air Force Office of Scientific Research.
There have been spectacular advances in the study of how 2, 3 and 4 dimensional spaces work over the last several decades, including multiple Field medal winning work. I will survey how geometry and topology interact in exciting ways in `low dimensions’. Physics comes into the picture, especially in dimension 4.
Hyam did his honours in maths and stats at Monash then a PhD at Berkeley. He was a postdoc then lecturer at Melbourne appointed a Professor in 1982. Hyam has been head of department twice, President of the Australian Mathematical Society and Chair if the National Committee for Mathematical Sciences. He has supervised around 25 Masters and Phd students and his research interests are in low dimensional geometry and topology, minimal surfaces, differential geometry, shortest networks, optimisation and machine learning. He is also involved in MineOptima which sells software to design access infrastructure for underground mines
This lecture will attempt to address the following questions/issues:
• Why be a mathematician?
• PhD supervisors want the best for you, so be kind to them
• Industry versus Academia
• Applied versus Pure, or does it matter?
• Depth versus Breadth, and does it matter?
• Learning from your failures
• Mathematical models and product stewardship
• Amadeus & football
Jerzy Filar is a broadly trained applied mathematician with research interests spanning a spectrum of both theoretical and applied topics in Operations Research, Optimisation, Game Theory, Applied Probability and Environmental Modelling. Professor Filar co-authored three research level books and approximately 100 refereed research papers. He is fascinated by the ever expanding impact of mathematics on human society and its dual role as the science that explains both magnitude and relationships. He will comment briefly on the power and limitations on mathematical models. He will also comment on the joy and excitement of a mathematical career.
Late in 1998 when I was working at the University of Adelaide, Derek Abbott, a colleague from the Electrical and Electronic Engineering Department, knocked on my door and showed me some interesting simulations. They were implementations of two games, developed by a Spanish physicist Juan Parrondo, which are both biased against the player. However, if the player alternates between the games or chooses which game to play in a random fashion, the ensuing game is biased in favour of the player.
I was initially sceptical of Derek’s results. However, using only elementary probability theory, it is relatively easy to establish that his conclusions were correct. Since then, a large literature has grown dealing with various extensions and applications of Parrondo’s games. My contributions have included some comments on the definition of what it means for a game to be fair, a rigorous proof that Parrondo’s drift criteria do imply that a game is losing, fair or winning respectively and the observation that the phenomenon observed by Parrondo should be thought of as ubiquitous, rather than unusual. In this talk I will tell the story of my involvement with Parrondo’s games.
Peter Taylor received a BSc (Hons) and a PhD in Applied Mathematics from the University of Adelaide in 1980 and 1987 respectively. In between, he spent time working for the Australian Public Service in Canberra. After periods at the Universities of Western Australia and Adelaide, he moved at the beginning of 2002 to the University of Melbourne. In January 2003, he took up a position as the inaugural Professor of Operations Research. He was Head of the Department of Mathematics and Statistics from 2005 until 2010. Peter’s research interests lie in the fields of stochastic modelling and applied probability, with particular emphasis on applications in telecommunications, biological modelling, healthcare and disaster management. Recently he has become interested in the interaction of stochastic modelling with optimisation and optimal control under conditions of uncertainty. He is regularly invited to present plenary papers at international conferences. He has also acted on organising and program committees for many conferences. Peter is the editor-in-chief of ‘Stochastic Models’, and on the editorial boards of ‘Queueing Systems’, the ‘Journal of Applied Probability’ and ‘Advances in Applied Probability’. He served on the Awards Committee of the Applied Probability Section of the Institute for Operations Research and Management Science (INFORMS) from 2005-2007 and is currently on the committee for the Nicholson Prize, awarded for the best student paper in operations research. In 2008, Peter became one of the five trustees of the Applied Probability Trust. This trust, which is based in Sheffield UK, is the body which publishes the Applied Probability journals plus ‘The Mathematical Scientist’ and ‘Spectrum’.
From February 2006 to February 2008, Peter was Chair of the Australia and New Zealand Division of Industrial and Applied Mathematics (ANZIAM), and from September 2010 to September 2012 he was the President of the Australian Mathematical Society. In 2013 he was awarded a Laureate Fellowship by the Australian Research Council.