Ext. Number:
  • Applied Mathematical Methods
  • Probability Modelling
  • Mathematical Biology
  • Continuum Modelling
  • Random Walks
  • Random Environments
Recent Publications:
  • 3D hybrid modelling of vascular network formation (2017) more
  • A correspondence principle (2016) more
  • 3D hybrid modelling of vascular network formation. (2016) more
  • Evidence for Cooperative Selection of Axons for Myelination by Adjacent Oligodendrocytes in the Optic Nerve (2016) more
  • Evolutionary dynamics of phenotype-structured populations: from individual-level mechanisms to population-level consequences (2016) more

Selected Publications

Extra Information:
I have been working in applied probability for more than 35 years and am the author of two books in the area:
B.D. Hughes, Random Walks and Random Environments. Volume 1: Random Walks (Oxford University Press, 1995).
B.D. Hughes, Random Walks and Random Environments. Volume 2: Random Environments. (Oxford University Press, 1996).
I have also worked often on deterministic problems that require a variety of techniques.

Some of my work is motivated by general mathematical curiosity, but much of my work springs from questions in a variety of practical contexts. I have collaborated with researchers from many fields and worked on problems motivated by applications from physics and physical chemistry, engineering, actuarial science, social phenomena, and increasingly in recent years, applications from biology and medicine. My interests in academic governanance of universities has led to published research on timetabling and internal reports on admission standards.

More details of my research work and download links for some of my publications can be found on my personal home page (to which a link has been given above).

In recent years I have been privileged to teach introductory real analysis and related mathematics to our best-prepared incoming students in their first year at The University of Melbourne, and I also currently teach methods of applied mathematics based around ordinary and partial differential equations. Over the course of a long career I have taught material from many other areas including integral transforms, asymptotic methods and practical complex analysis, probability and its applications, continuum mechanics, basic calculus, and linear algebra. I am particularly interested in promoting correct conceptual understanding rather than mere rote learning.

**Academic administration
My principal interests have been in undergraduate and postgraduate selection policies and practices, the interface between school and university mathematics education, and the effects of English language background on student progress. I also have considerable experience in academic timetabling, and in equal employment opportunity for women. I am keenly interested in questions of academic governance and collegial decision making.
Past Postgraduate Supervision:
James CAFFREY "Mathematical modelling of layering in nature"
Anna Q CAI "Mathematical modelling of cell populations in experimental systems: migration, proliferation and differentiation"
Rebecca CHISHOLM "Mathematical modelling of cell migration and biological systems driven by cell proliferation"
Liam T G MERLOT "Techniques for academic timetabling"
Catherine PENINGTON "Modelling cell movement in multicellular systems"
Jennifer L SLATER "Growing network models with an application to neurogenesis"
Amy SULLIVAN "Chemical signals in interneuron migration: modelling repulsion and inhibition"
Dimetre TRIADIS "Indentation models for colloid science and nanotechnology"
Past MSc Students:
Bruce RIDING "Plant Spread from a Single Source"
Rebecca CHISHOLM "Cell Proliferation in a Scaffold"
Daniel MENTIPLAY "T Cell Development in the Thymus Modelling Cell Migration"
James WOODCOCK "Mortal Polygamous Networks"
Madeleine HUGGINS
Christopher BAKER
Catherine BROWNE
Alexander ZAREBSKI
Marselinus Ulu F
Phillip BROWN
Subject(s) Currently Teaching:
MAST30021 (620-324) Complex Analysis (Semester 1, 2017)
Recent Grant History:
Year(s) Source Type Title
2014 - 2016 ARC Discovery Building macroscale models from microscale probabilistic models (080075)
2011 - 2013 ARC Discovery From single cell to collective cell migration in multicellular systems: mathematical and computational modelling of real biological systems
2011 - 2013 ARC Discovery Modelling and simulation of self-organised behaviour in biological and bio-inspired systems
2006 - 2009 ARC Discovery Multi-scale modeling of cell migration in developmental biology
Academic Board member
Academic Programs Committee member
Building Renovations Advisor
Course advisors - Upper Undergraduate
University Council Fellow
Math. Sciences Library Users Committee
Strategic Planning Committee
University Council ((Fellow elected by the professors))