Using maths to understand the world

Research in mathematics contributes to advances in a wide range of disciplines. From understanding how cells divide to predicting extreme weather to the development of new financial tools, many of today’s challenges are being addressed using applied and industrial mathematics. Using mathematical models and techniques, applied mathematics is used for real-world problem-solving. It can help explain observed phenomena and predict new, unobserved phenomena that may occur in the future.

In almost all industriesmathematics opens the way to virtual experiments, the analysis and simulation of multiple scenarios for a given phenomenonand control and optimisation. Applied mathematicians working alongside industry may develop or enhance mathematical methods to solve industrial problems. Using mathematical modelling and numerical analysis, possible solutions to these problems can be identified and tested for accuracy, validity, and reliability and interpreted in relation to the original real-world problem. By breaking down the problem into mathematical variables, organisations can optimise efficiencies, maximise profitability, improve safety outcomesand reduce uncertainty.

Impact and successful applications

We employ a vast range of mathematical and statistical techniques and computational science to investigate a diverse range of fundamental and real-world problems. The interdisciplinary nature of our work and the constraints imposed by dealing with genuine practical problems make this a challenging and rewarding area for research.

Our strengths lie in:

  • Bushfire dynamics and combustion modelling:
    • to better understand the dynamics and impact of large bushfires driven by extreme fire weather
    • to better understand the complex behaviour of flame fronts, particularly at the onset of instabilities.
  • Ecological modelling:
    • statistical: modelling the survival of Little Penguins noting the impact of climate change and banding and tag recovery studies of Southern Bluefin Tuna
    • deterministic and stochastic: developed and analysed models for stressed ecosystems and environments with nutrient enrichment and depletion.
  • Nonlinear dynamics
    • chemical and bio-reactor engineering – determine efficient operating conditions for reactors using nonlinear dynamical systems theory
    • complex warfighting – the development, simulation, and analysis of mathematical models of warfighting to provide insight into the organisational design best suited to optimise Command and Control and success in contested environments.

Our bushfire research has been incorporated into the Australian curriculum for firefighter training and into the standard operating procedures for fire behaviour analysts working in the country’s rural fire agencies. Our research is also being used to develop operational tools for fire managers. We provide technical expertise to various inquiries, including those concerning the disastrous 2019/20 Australian bushfires.

Competitive advantage

The quality and impact of our research is made possible by our success in obtaining competitive grants and attracting graduating HDR students. We regularly collaborate with national and international researchers who enhance our world-wide reputation. Anextensive number of our publications appear in important international journals.

We seek to improve the understanding of bushfire and associated processesand their relation to firefighter and community safety. This is achieved by conducting fundamental and applied research into bushfire behaviour and propagation, including coupled and dynamic effects, and developing scientifically rigorous models that integrate with fire safety and risk management systems. We are the only research group with a dedicated focus on understanding how dynamic fire behaviours influence firestorm development.

Research for complex warfighting is done in collaboration with the Defence Science and Technology Group (DST) of Australia and is linked to the DST STaR Shots (Science, Technology and Research Shots) strategy, specifically the agile Command and Control STaR shot.

    • McRae, R.H.D., Sharples, J.J., Fromm, M. (2015).Natural Hazards and Earth System Sciences, 15(3), 417-428.DOI:

    • Sharples, J.J., Cary, G.J., Fox-Hughes, P., Mooney, S., Evans, J.P., Fletcher, M.S., Fromm, M., Grierson, P.F., McRae, R.H.D., Baker, P. (2016)..Climatic Change,139(1), 85-99.DOI:

    • Sharples, J. J., McRae, R., & Wilkes, S. (2012)..International Journal of Wildland Fire,21(3), 282-296.

    • T.A. McLennan-Smith, D.O. Roberts, H.S Sidhu, ‘Emergentbehaviorin an adversarial synchronization and swarming model’,Submitted to Physical Review E (2020)

    • T.A. McLennan-Smith, A.C.Kalloniatis, Z. Jovanoski, H.S. Sidhu, D.O. Roberts, S. Watt, I.N. Towers‘A mathematical model of humanitarian aid agencies inattritionalconflict environments', Submitted to Operations Research (2020)

    • Chambers MS; Sidhu LA; O'Neill B; Sibanda N, 2017, ',Ecology and Evolution, vol. 7, pp. 9818 - 9844,

    • Quill R; Sharples JJ; Sidhu LA, 2020, '', EnvironmentalModelingand Assessment, vol. 25, pp. 231 - 250,

    • Huang Z; Sidhu HS; Towers IN; Jovanoski Z; Watt S;GubernovVV, 2020, '',AppliedMathematical Modelling,vol. 77, pp. 1216 - 1228,

    • Sanni S; Jovanoski Z; Sidhu HS, 2020, '',Operations Research Perspectives, vol. 7,

    • Towers I;GubernovV;KolobovAV;PolezhaevAA; Sidhu HS, 2013, '', Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences, vol. 469, pp. 20130315-1 - 20130315-19,

    • Sutherland, D., Sharples, J.J. and Moinuddin, K.A., 2020.International Journal of Wildland Fire,29(1), pp.70-80.

Research projects

  • Effects of flipper bands and injected transponders on the survival of adult Little Penguins
  • Living in stressed environments: using mathematics to understand ecosystems’ dynamics
  • Computationalmathematical analysisof dynamic firepropagation
  • Humanitarian aid agencies inattritionalconflict environments

Study with us

  • Students undertaking a Bachelor of Science majoring in mathematicscan undertake several courses relatedto Applied and Industrial Mathematics including:

Our researchers

Mathematics Stream Coordinator Zlatko Jovanoski
Mathematics Stream Coordinator
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Professor of Bushfire Dynamics Jason Sharples
Professor of Bushfire Dynamics
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Rector Harvinder Sidhu
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Deputy Head of School (Education) Leesa Sidhu
Deputy Head of School (Education)
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Senior Lecturer Duncan Sutherland
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Undergraduate Coordinator Isaac Towers
Undergraduate Coordinator
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Associate Professor Timothy Trudgian
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Casual Academic Mona Ziaeyan Bahri
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