Welcome
to the Home Page of Emeritus Professor Barry Hughes
I am a member of
the School
of Mathematics and Statistics of the University of Melbourne.
I retired from my position as a professor in the School in May 2021,
but continue my association with the school as Emeritus Professor. You can e-mail me at
barrydh @ unimelb.edu.au.
The caricatures were provided by undergraduate students.
My books
I am the author of the
following books:
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B.D. Hughes, Random
Walks and Random Environments. Volume 1: Random Walks.
Clarendon
Press, Oxford, 1995 (xxi+631pp.) ISBN 0 19 853788 3.
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B.D. Hughes, Random
Walks and Random Environments. Volume 2: Random Environments.
Clarendon
Press, Oxford, 1996 (xxiv+526 pp.) ISBN 0 19 853789 1.
Research last century
Links to selected papers published before the year 2000 can be found here.
Research this century
My current or recent research
interests are in
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modelling cell motion in developmental biology and in other contexts
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stochastic modelling
(including random walk processes, random environments,
power-law phenomena, and stochastically evolving networks)
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methods of applied mathematics
(especially transform methods and asymptotics)
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continuuum
modelling (most recently in biological contexts, but formerly using continuum mechanics methodologies in colloid and interface science)
I have worked in a variety of other areas including
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academic timetabling
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actuarial mathematics
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data analysis and interpretation in nanotechnology
Here are my
papers published from 2001 onwards.
REVIEW ARTICLES AND EXPOSITORY ARTICLES
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B.D. Hughes,
Conduction and diffusion in percolating systems,
Encyclopedia of Complexity and Systems Science,
edited by R. Meyers, Part 3, pp.1395-1424 (New York, Springer-Verlag, 2009).
(link to publication details)
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M.J. Simpson, K.A. Landman and B.D. Hughes,
Diffusing populations: ghosts or folks?
Australasian Journal of Engineering Education
15, issue 2 (2009) 59-67. (download)
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B.D. Hughes,
Conduction and diffusion in percolating systems,
Encyclopedia of Complexity and Systems Science,
edited by R.A. Meyers (New York, Springer-Verlag, 2014); extensively revised version of the 2009 article listed above
(link to publication details)
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B.D. Hughes and B.W. Ninham,
A correspondence principle,
Physica A 443 (2016) 495-517.
(download link from publisher) (author-formatted preprint)
NON-LOCAL AGGREGATION PROCESSES
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B.D. Hughes and K. Fellner,
Continuum models of cohesive stochastic swarms:
The effect of motility on aggregation patterns,
Physica D: Nonlinear Phenomena 260 (2013) 26-48.
(publisher's download link)
(authors' final text in preprint form)
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K. Fellner and B.D. Hughes,
Solutions of a non-local aggregation equation: Universal bounds, concavity changes, and efficient numerical solutions,
Mathematical Methods in the Applied Sciences 43 (2020) 5398-5249.
(open access download)
STOCHASTIC MODELLING
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B.D. Hughes,
Anomalous
diffusion, stable processes, and generalized functions, Physical Review
E 65 (2002) 035105(R), 4 pp.
download
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B.D. Hughes and W.J.
Reed, A problem in paleobiology, arXiv:
physics/0211090 (20 November 2002, 4 pages).
(download link)
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W.J. Reed and B.D. Hughes,
On the size distribution of live genera, Journal
of Theoretical Biology 217 (2002)
125-135. (download link)
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W.J. Reed and B.D. Hughes,
From
gene families and genera to incomes and internet file sizes: why power-laws
are so common in nature, Physical Review E
66 (2002) 067103, 4 pp.
download
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W.J. Reed and B.D. Hughes,
On
the distribution of family names, Physica
A319 (2003) 579-590.
(download link)
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W.J. Reed and B.D. Hughes,
Power-law
distributions from exponential processes: an explanation for the occurrence
of long-tailed distributions in biology and elsewhere, Scientiae
Mathematicae Japonicae Online e8 (2003) 329-339
(link to issue Table of Contents);
equivalent paper version Scientiae
Mathematicae Japonicae 58 (2003) 473-483.
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D.Y.C. Chan, B.D. Hughes, A.S. Leong and W.J. Reed,
Stochastically evolving networks,
Physical Review E 68 (2003) 066124, 24 pp.
download
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W.J. Reed and B.D. Hughes,
A model explaining the size
distribution of gene and protein families,
Mathematical Biosciences 189 (2004) 97-102.
(download link)
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J.L. Slater, B.D. Hughes and K.A. Landman,
Evolving mortal networks,
Physical Review E 73 (2006) 066111.
download
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W.J. Reed and B.D. Hughes,
Theoretical size distribution of fossil taxa: analysis of a null model',
Theoretical Biology and Medical Modelling
4:12 (2007), 12pp., doi:10.1186/1742-4682-4-12.
(download link)
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A.Q. Cai, K.A. Landman, B.D. Hughes and C.M. Witt,
T cell development in the thymus:
from periodic seeding to constant output,
Journal of Theoretical Biology
249 (2007) 384-394.
(download link)
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J.L. Slater, K.A. Landman, B.D. Hughes, Q. Shen and S. Temple,
Cell lineage tree models of neurogenesis,
Journal of Theoretical Biology 256 (2009) 164-179.
(download link)
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W. Fulgenzi, A. Melatos and B.D. Hughes,
Radio pulsar glitches as a state-dependent Poisson process,
Monthly Notices of the Royal Astronomical Society 470 (2017) 4307-4329.
(download link from publisher)
(preprint of accepted version)
BIOLOGICAL CELL MOTILITY: CONTINUUM MODELLING, PROBABILISTIC MODELLING
AND AGENT-BASED SIMULATION
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A.Q. Cai, K.A. Landman and B.D. Hughes,
Modelling directional guidance and motility regulation in cell migration,
Bulletin of Mathematical Biology 68 (2006) 25-52.
(download link)
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M.J. Simpson, K.A. Landman, B.D. Hughes and D.F. Newgreen,
Looking inside an invasion wave of cells using continuum models:
proliferation is the key,
Journal of Theoretical Biology
243 (2006) 343-360. (download link)
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A.Q. Cai, K.A. Landman and B.D. Hughes,
Multiscale modelling of a wound healing assay,
Journal of Theoretical Biology
245 (2007) 576-594. (download link)
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K.A. Landman, A.Q. Cai and B.D. Hughes,
Travelling waves of attached and detached cells in a wound healing
cell migration assay,
Bulletin of Mathematical Biology
69 (2007) 2119-2138.
(download link)
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M.J. Simpson, A. Merrifield, K.A. Landman and B.D. Hughes,
Simulating invasion with cellular automata: connecting individual and macroscopic
cell-scale and population-scale properties,
Physical Review E 76 (2007) 021918.
download
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A. Tremel, A. Cai, N. Tirtaatmadja, B.D. Hughes, G.W. Stevens, K.A. Landman and A.J. O'Connor,
Cell migration and proliferation during monolayer
formation and wound healing,
Chemical Engineering Science 64 (2009) 247-253.
(download link)
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M.J. Simpson, K.A. Landman and B.D. Hughes,
Multi-species simple exclusion processes,
Physica A 388 (2009) 399-406.
(download link)
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M.J. Simpson, K.A. Landman and B.D. Hughes,
Distinguishing between directed and undirected cell
motility within an invading cell population,
Bulletin of Mathematical Biology 71(2009) 781-799.
(download link)
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M.J. Simpson, K.A. Landman and B.D. Hughes,
Pathlines in exclusion processes,
Physical Review E
79 (2009) 031920 (5pp.).
download
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M.J. Simpson, K.A. Landman, B.D. Hughes and A.E. Fernando,
A model for mesoscale patterns in motile populations,
Physica A 389 (2010) 1412-1424.
(download link)
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M.J. Simpson, K.A. Landman and B.D. Hughes,
Cell invasion with proliferation mechanisms motivated by time-lapse data,
Physica A 389 (2010) 3779-3790.
(download link)
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C.J. Penington, B.D. Hughes and K.A. Landman,
Building macroscale models from microscale probabilistic models: a general
probabilistic approach for nonlinear diffusion and multi-species phenomena,
Physical Review E 84 (2011) 051909 (16pp.).
download
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C.J. Penington, K. Korvasova, B.D. Hughes and K.A. Landman,
Collective motion of dimers,
Physical Review E 86 (2012) 041120 (12pp.).
download
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C.M. Baker, B.D. Hughes and K.A. Landman,
Random walks in non-uniform environments with local dynamic interactions,
Physical Review E 88 (2013) 042113 (13pp.).
download
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C.J. Penington, B.D. Hughes and K.A. Landman,
Interacting motile agents: taking a mean-field approach beyond monomers and nearest-neighbor steps,
Physical Review E 89 (2014) 032714 (12pp.).
download
- R.H. Chisholm, B.D. Hughes and K.A. Landman,
Erosion by a one-dimensional random walk,
Physical Review E 90 (2014) 022140 (11pp.).
download
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A.A. Almet, M. Pan, B.D. Hughes and K.A. Landman,
When push comes to shove: exclusion processes with nonlocal consequences,
Physica A 437 (2015) 119-129.
(publisher download link) (author-formatted preprint)
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H. Perfahl, B.D. Hughes, T. Alaracon, P.K. Maini, M.C. Lloyd, M. Reuss and H.M. Byrne,
3D hybrid modeling of vascular network formation,
Journal of Theoretical Biology 414 (2017) 254-268.
(publisher download link) (arXiv preprint of earlier version)
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P. Nan, D.M. Walsh, K.A. Landman and B.D. Hughes,
Distinguishing cell shoving mechanisms,
PLoS ONE 13(3): 0193975 (2018), 21 pp.
(download link)
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B.D. Hughes,
Watching the internal clock of cells while they move and divide,
Biophysical Journal 13(2018) 1007-1008.
(preprint) (publisher download link)
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S. Zhang, A. Chong and B.D. Hughes,
Persistent exclusion processes: Inertia, drift, mixing and correlation,
Physical Review E 100 (2019) 042415, 16 pp.
download
NEUROSCIENCE
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J.R. Caffrey, B.D. Hughes, J.M. Britto and K.A. Landman,
An in silico agent-based model demonstrates Reelin function in directing lamination of neurons during cortical developmen,
PLoS ONE 9(10): e110415 (2014), 11pp.
(download link)
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D.M. Walsh, P.T. Röth, W.R. Holmes, K.A. Landman, T.D. Merson and B.D. Hughes,
Is cell migration or proliferation dominant in the formation of linear arrays of oligodendrocytes?,
Journal of Theoretical Biology 406 (2016) 17-30.
(publisher download link) (author-formatted preprint)
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D.M. Walsh, T.D. Merson, K.A. Landman and B.D. Hughes,
Evidence for cooperative selection of axons for myelination by adjacent oligodendrocytes in the optic nerve,
PLoS ONE 11(11): e0165673 (2016), 9pp. + supplementary material
(download including supplementary material)
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D.M. Walsh, K.A. Landman and B.D. Hughes,
What is the optimal distribution of myelin along a single axon?',
Neuroscience Letters 658 (2017) 97-101.
(publisher download link) (author-formatted preprint)
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D.G Gonsalvez, G.A Craig, D.M. Walsh, B.D. Hughes, R.J Wood, S.W. Yoo, S.S. Murray and J. Xiao
The dynamics of oligodendrocyte generation: how distinct is the mouse from the human?
bioRxiv preprint first posted online Dec. 23, 2019 doi: http://dx.doi.org/10.1101/2019.12.23.887174
OTHER AREAS OF MATHEMATICAL BIOLOGY
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J.R. Caffrey, B.D. Hughes and K.A. Landman,
Dispersal, settling and layer formation,
Mathematical Biosciences
232 (2011) 42-56. (download link)
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R.H. Chisholm, B.D. Hughes and K.A. Landman,
Building a morphogen gradient without diffusion in a growing tissue,
PLoS ONE 5(9): e12857 (2010), 9pp.
(download link)
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R.H. Chisholm, B.D. Hughes, K.A. Landman, G. Mayer and P.M. Whitington,
When are cellular oscillators sufficient for sequential segmentation?
Journal of Theoretical Biology
279 (2011) 150-160. (download link)
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R.H. Chisholm, B.D. Hughes, K.A. Landman and J. Hutson,
Mathematical modelling of gubernaculum during inguino-scrotal migration shows limb bud characteristics,
Journal of Pediatric Surgery 48 (2013) 1762-1766.
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R.H. Chisholm, B.D. Hughes, K.A. Landman and M.H. Zaman,
Analytic study of three-dimensional single cell migration with and without proteolytic enzymes,
Cellular and Molecular Bioengineering 6 (2013) 239-249.
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F. Frascoli, B.D. Hughes, M.H. Zaman and K.A. Landman,
A computational model for collective cellular motion in three dimensions: general framework and case study for cell pair dynamics,
PLoS ONE 8(3): e59249 (2013), 16pp.
(download link)
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F. Frascoli, P.S. Kim, B.D. Hughes and K.A. Landman,
A dynamical model of tumour immunotherapy,
Mathematical Biosciences 253 (2014) 50-62.
(download link from publisher) (author-formatted preprint)
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C.M. Baker, B.D. Hughes and K.A. Landman,
Length-based connectivity metrics and their ecological interpretation,
Ecological Indicators 58 (2015) 192-198.
(download link from publisher) (author-formatted preprint)
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T. Lorenzi, R.H. Chisholm, L. Desvillettes and B.D. Hughes,
Dissecting the dynamics of epigenetic changes in phenotype-structured populations exposed to fluctuating environments,
Journal of Theoretical Biology 386 (2015) 166-176.
(download link from publisher) (author-formatted preprint)
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R.H. Chisholm, T. Lorenzi, L. Desvillettes and B.D. Hughes,
Evolutionary dynamics of phenotype-structured populations: from individual-level mechanisms to population-level consequences,
Zeitschrift für angewandte Mathematik und Physik 67 (2016) 100 (34pp.).
(on-screen read-only version of published article)
(download link from publisher)
(author-formatted preprint)
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T. Leung, B.D. Hughes, F. Frascoli and J.M. McCaw,
Periodic solutions in an SIRS model with immune boosting and cross-immunity,
Journal of Theoretical Biology 410 (2016) 55-64.
(download link from publisher) (arXiv preprint of earlier version)
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T. Leung, B.D. Hughes, F. Frascoli, P.T. Campbell and J.M. McCaw,
Infection-acquired versus vaccine-acquired immunity in an SIRWS model,
Infectious Disease Modelling 3 (2018) 118-135.
(open access: download link from publisher)
(arXiv preprint of earlier version)
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R.D. Cousens, B.D. Hughes and M.B. Mesgaran,
Why we do not expect dispersal probability density functions based on a single mechanism to fit real seed shadows,
Journal of Ecology 106 (2018) 903-906.
(on-screen read-only version of published article)
(download link from publisher)
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A.A. Almet, B.D. Hughes, K.A. Landman, I.S. Näthke and J.M. Osborne,
A multicellular model of intestinal crypt buckling and fission,
Bulletin of Mathematical Biology 80 (2018) 335-359.
(publisher download link)
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L. Almeida, P. Bagnerini, G. Fabrini, B.D. Hughes and T. Lorenzi,
Evolution of cancer cell populations under cytotoxic therapy and treatment optimisation: insight from a phenotype-structured model,
ESAIM: Mathematical Modelling and Numerical Analysis 53 (2019) 1157-1190.
(publisher download link) (author-formatted preprint)
NANOTECHNOLOGY
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J.E. Sader, J. Sanelli, B.D. Hughes, J.P. Monty and E.J. Bieske,
Distortion in the thermal noise spectrum and quality factor
of nanomechanical devices due to finite frequency resolution with applications to the
atomic force microscope,
Review of Scientific Instruments 82 (2011) 095104 (10pp.).
download
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J.E. Sader, B.D. Hughes, J.A. Sanelli and E.J. Bieske,
Effect of multiplicative noise on least-squares parameter estimation
with applications to the atomic force microscope,
Review of Scientific Instruments 83 (2012) 055106 (6pp.).
download
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J.E. Sader, B.D. Hughes, F. Huber and F.J. Giessibl,
Interatomic force laws that corrupt their own measurement,
arXiv:1709.07571v1 [cond-mat.mes-hall] 22 Sep 2017
(download link)
J.E. Sader, B.D. Hughes, F. Huber and F.J. Giessibl,
Interatomic force laws that evade dynamic measurement,
Nature Nanotechnology 13 (2018) 1088-1091.
(read-only link)
MISCELLANY
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L. Merlot, N. Boland, B.D. Hughes and P.J. Stuckey,
A hybrid algorithm
for the examination timetabling problem, in
Practice and Theory of Automated Timetabling IV,
edited by E. Burke and P. De Causemaecker,
Lecture Notes in Computer Science, Volume 2740,
pp.207-231 (Berlin, Springer-Verlag, 2003).
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N. Boland, B.D. Hughes, L.T.G. Merlot and P.J. Stuckey,
New integer linear programming approaches for course timetabling,
Computers and Operations Research
35 (2008) 2209-2233. (download link)
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D.C.M. Dickson, B.D. Hughes and Zhang Lianzeng,
The density of the time to ruin for a Sparre Andersen process
with Erlang arrivals and exponential claims,
Scandinavian Actuarial Journal 2005 (2005) 358-376.
(download link)
Teaching
I created from scratch for semester 2 of 2008
a new analysis-based subject for students who were high achievers in
the highest level year 12 school mathematics subject and I continued to refine and teach the subject
(currently known as MAST10009 Accelerated Mathematics 2) for 15 years. That long-term assignment
and opportunities to teach complex analysis, integral transform and asymptotic methods at third year level
have provided the most rewarding experiences, but I have also enjoyed teaching a wide variety of
other subjects, including those devoted to ordinary and partial differential equations, vector analysis,
continuum mechanics,
mathematical modelling, and probability.
Academic
Administration
From 2005 to 2014 inclusive I was Chair of the University of Melbourne Academic Board's
Selection Procedures Committee and retain from that time interest 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 was a member of the University of Melbourne Academic Board's Academic Programs Committee and of its Examinations Subcommittee, and
a member of the University's Project Coordination group for its response to the Melbourne Metro Rail Project. I was a University of Melbourne Council Fellow elected by the professors
for the period 2015−2017.
I have also had extensive commitee experience concerning teaching infrastructure, academic timetabling, and equal employment
opportunity for women.
National Strategic Review of Mathematical Sciences Research in Australia
I was the Executive Director of a
National Strategic Review of
Mathematical Sciences Research in Australia, which reported in December 2006.
Decadal Plan for the Mathematical Sciences in Australia
I was a member of the Steering Committee, the chair of the
Working Party on Mathematics and Statistics Education and training in Universities,
and a member of the Working Party on Mathematics and Statistics Education in Schools and Colleges
(main web site www.science.org.au/mathematics-plan-2016-25: download the plan in PDF form here).
Other Reviewing Activities
I have been invited to act as an external reviewer for the following universities:
- University of Newcastle, Australia 2008: member of Review Panel for Mathematics and Statistics programs
- University of Newcastle, Australia 2012: member of Review Panel for the Bachelor of Science
- King Abdulaziz University, Jeddah, Saudi Arabia 2006: member of Pilot Review panels for the University as a whole, and also specifically
for the Mathematics Program
- Qassim University, Qassim Province, Saudi Arabia 2009: chair of Developmental Review Panel for the Mathematics Program
(photo on site)
- Al Imam Muhammad ibn Saud Islamic University, Riyadh, Saudi Arabia 2010: chair of Developmental Review Panel for the Applied Mathematics Program
(photo at Al Musmak (the Old Fort))
- Gulf College, Oman 2018: member of Review Panel for the General Foundation Program (download report))
The reviews of Saudi universities were undertaken on behalf of the National Commission for Academic Accreditation and Assessment.
I held an appointment to the panel of external reviewers for the
Oman Academic Accreditation Authority, formerly known as the Oman Accreditation Council, from 2007 to the end of 2023.
Created: 19 May 2003
Last modified: 30 January 2023
Authorised
by: Barry Hughes, School of Mathematics and Statistics.
Maintained
by: Barry Hughes, School of Mathematics and Statistics.
Email:
barrydh @ unimelb.edu.au