2nd ed.

THE CLOCK TICKS ON MATHS PREREQUISITES Ian Chubb, Alan Finkel, Deb King, Geoff Prince, Scott Ryan & Terry Speed

HIGH-RISE SECURITY

Minimising crime risk with maths & stats

TERRY TAO

Q&A with Fields Medallist & friend of AMSI Professor Terry Tao

COMPLEX NETWORKS

Are YOU in control of your network or is your network in control of YOU?

AUSTRALIAN MATHEMATICAL SCIENCES INSTITUTE WELCOME TO AMSI GROMOV-WITTEN THEORY GAUGE (MISG) ANZIAM MATHEMATICS AMSI Membership THEORY 2016 Full Members IN INDUSTRY The Australian National University & DUALITIES La Trobe University STUDY GROUP Monash University Queensland University of Technology RMIT University The University of Adelaide 4 - 29 JANUARY 6 - 16 JANUARY 1 - 5 FEBRUARY 7 - 11 FEBRUARY The University of Melbourne The University of New South Wales RMIT UNIVERSITY THE AUSTRALIAN NATIONAL UNIVERSITY UNIVERSITY OF SOUTH AUSTRALIA QT CANBERRA HOTEL The University of Newcastle The University of Queensland The University of Sydney The University of Western Australia

Associate Members Australian Defence Force Academy AMSI'S AMSI RESEARCH Curtin University of Technology CAPITAL Deakin University Federation University Australia Flinders University NUMBER James Cook University Macquarie University Swinburne University A DOOR HAS THEORY The University of New England University of South Australia OPENED FOR University of Southern Queensland University of Tasmania MATHEMATICS SCIENTIFIC University of Technology Sydney University of Wollongong 10 - 11 FEBRUARY 8 - 9 APRIL Victoria University AND STATISTICS THE UNIVERSITY OF MELBOURNE THE AUSTRALIAN NATIONAL UNIVERSITY Western Sydney University PHOTOGRAPHY: MICHAEL SHAW

EVENTS Societies & Government Agencies Australian Bureau of Statistics Australian Mathematics Trust Australian Mathematical Society omentous times! New Prime This issue of The Update is bursting with features. Australian and New Zealand Industrial Minister, New Chief Scientist! Both Ian Chubb and Alan Finkel tell us what they MATHEMATICAL and Applied Mathematics And the departure of Ian think about the burning issue of the moment – maths Bureau of Meteorology METHODS FOR Chubb, a great friend of the prerequisites for university science and engineering CSIRO M mathematical sciences who has exercised courses; along with Assistant Cabinet Secretary Defence Science and Technology Group enormous influence on government and Senator Scott Ryan, Terry Speed and Deb King. Fields APPLICATIONS Statistical Society of Australia on the public perception of science. medallist Terry Tao talks about his life in mathematics and tells us why collaboration makes his world go ANZIAM - ZAMA A door has opened for mathematics and statistics, round. We highlight a pilot project, delivered by AMSI JOINT MEETING Director to grow our research capacity and to start turning Intern that investigates the factors influencing the risk Prof. Geoff Prince FAustMS around some of the chronic problems in our education of crime occurrences in high density housing and also [email protected] au 2016 pipeline. But it is not a time to relax. Australian feature a report on the 4th South Pacific Continuous Marketing & Communications Manager governments are grappling with a national strategic Optimisation meeting held at Adelaide’s University of Mari Ericksen [email protected] plan for Science, Technology, Engineering and South Australia in February of this year. 4 - 15 JULY 11 - 14 NOVEMBER Mathematics (STEM). Of course planning is one thing, I hope you enjoy this second edition of our new WWW.AMSI.ORG.AU/SCIENTIFIC Program Manager (Schools) sticking with a STEM plan through multiple electoral look bulletin. Of course the latest news about our THE UNIVERSITY OF QUEENSLAND HANGZHOU, ZHEJIANG PROVINCE, CHINA Janine McIntosh [email protected] cycles is another thing altogether. AMSI has played program areas of Schools, Research, Higher Education a significant part in raising awareness through its and AMSI Intern can be found at amsi.org.au Program Manager (Research & Higher Ed) Simi Henderson advocacy and policy building and we won’t be letting [email protected] up any time soon. Most recently we have made submissions to three major government reviews National Program Manager (Intern) Dr Hannah Hartig (which you can find at amsi.org.au), all of which will AustMS [email protected] have a major impact on education and research. We Marketing & Communications Co-ordinator will continue to pursue transformative change and its Kristin Marriner support from Malcolm Turnbull and Alan Finkel. 2016 [email protected] Multimedia Manager Michael Shaw [email protected] 5 - 8 DECEMBER Subscribe to E-news at www.amsi.org.au/subscribe Graphic Designer THE AUSTRALIAN NATIONAL UNIVERSITY CANBERRA CANBERRA Paul Murphy [email protected] +613 8344 1777 www.amsi.org.au /DiscoverAMSI @discoverAMSI COVER IMAGE: JUSTUS KINDERMANN [email protected]

28 NOV - 2 DEC 28 NOVEMBER  16 DECEMBER THE UNIVERSITY OF ADELAIDE The Update 1 INDUSTRY INTERNSHIPS

efore stepping down as Chief build a computer model to identify weaknesses Dr Giovanni Di Lieto came on board to assist Commissioner of Victoria Police, in buildings and then give them comparative with merging crime prevention literature from Ken Lay urged a move away security scores,” says Dr Davide Ferrari from The criminology in with the statistics. The big challenge, B from traditional policing to more University of Melbourne’s School of Mathematics according to Dr Di Lieto, lay in exchanging the sophisticated approaches. With the changing and Statistics. different research paradigms. “When we managed lifestyles and demographics of Victorians and Working with master’s student Puxue Qiao, to blend our approaches, the significance of this the rapid growth of high-density dwellings, Dr Ferrari has taken a step closer to achieving project became not only its substance, but also such a move is critical. Victoria’s love affair this after building a generalised mixed-effect its methodology. We are able to demonstrate with high-rise apartment living is creating model. These are useful in the social sciences how to effectively interlink industry and different new challenges for law enforcers with a because they are able to take into account both domains of research,". staggering 63 per cent of property related random and fixed effects. For this particular Qiao described the number of crime occurrences offences recorded study, where measurements were to be made on by using a zero-inflated Poisson regression model by Victoria Police clusters of related statistical units repeatedly, with mixed effects. A combination of predictors in 2014. were selected using information theoretical So, how can homebuyers "THE MAIN CONCERN IS THE criteria for model selection and renters be sure their (Akaike and Bayesian property is safe? information criteria). The “Security systems have LACK OF A STANDARD METHOD TO prediction accuracy for the become a very important best two selected models and integral part of both were then assessed using residential and commercial EVALUATE SECURITY LEVELS OF independent samples by living,” says Andrea cross-validation techniques. Baratta, Managing Director Using the selected models, at Epsilon Security. Dr Ferrari and Qiao first “We have identified a BUILDINGS FOR COMPARISONS. TO developed classification gap in how the security of methods for the crime these buildings is managed,” risk rating based on the Andrea says. “The main DO THIS WE NEED TO DEVELOP A Poisson mixture approach. concern is the lack of a This offered the most SECURING A STANDARD IN standard method to evaluate accuracy when predicting security levels of buildings DATA-DRIVEN COMPUTER MODEL the response due to the for comparisons. To do this complexity of the fixed and we need to develop a data- variable factors. driven computer model to TO ASSESS THE SECURITY RISK “The inspiring women HIGH-RISE LIVING assess the security risk and industry internship enabled potential crime exposure of us to collaborate with a building." AND POTENTIAL CRIME EXPOSURE Dr Ferrari and masters As changing lifestyles and demographics of urban populations Andrea proposes a student Qiao to devise a global risk measure be given statistically sound model fuel the rapid growth of high-density housing understanding to all new buildings. He OF A BUILDING." for this project. Qiao also believes this will provide gained valuable industry factors influencing the risk of crime occurrence in such a good starting point for residents seeking to choosing a mixed-effect model was natural. Dr experience – she was able to solve problems understand how their property compares with Ferrai explains that this type of model allowed and produce tangible results that have an actual buildings has become a vital tool for law enforcers. Through others, as well as identify key risks and implement them to make predictions of crime occurrences business context,” says Andrea. “Something safety improvement solutions. while also obtaining security ratings for each not nearly enough Australian students have the an inspiring women industry internship, supported by veski Epsilon Security accessed funding through individual building. opportunity to do.” an initiative by veski and the Victorian State “The data collection was done using an original Universities are drivers of innovation; and and the Office of the Lead Scientist, Epsilon Security and The Government to support Victorian female honours survey through telephone interviews. In the they play a key role in projects like this. Given the and masters STEM students through a short-term analysis of the frequency of crime occurrences, project’s initial success, the team is applying for an University of Melbourne School of Mathematics and Statistics (4 month) tightly focused research internship. we used Poisson regression models. A large ARC Linkage Project grant to continue their work The initiative was delivered by the AMSI proportion (36 per cent) of responses obtained for with the objective of developing a fully automated have joined forces in a pilot project, delivered by AMSI Intern Intern program and, in a pilot project, Epsilon crime occurrences were concentrated at zero. To tool for risk ratings in buildings.  Security has teamed up with statisticians from the avoid failure accounting for these zeroes, the team to establish a standard method to evaluate building crime rates. University of Melbourne to develop modelling to adopted a zero-inflated Poisson model. This model assess property risk and identify safety solutions. allows for not only a discrete random variable Using Victorian crime data the team has been with a Poisson distribution, but also a point mass able to investigate demographic / geographical at zero. We carried our numerical computations Based on the results from the current project, Epsilon and other measureable variables related to of fitting this mixed model using the R package Security and the University of Melbourne School of communication, access and monitoring to evaluate glmmADMB,” says Dr Ferrari. Mathematics and Statistics are preparing an ARC Linkage the safety of apartment complexes. Giovanni States,when creating a model to research proposal that will target the development “By looking at how a building is accessed, assign risk ratings to apartment buildings many of a fully automated tool for risk rating in buildings. how it is managed, its existing protective variables must be taken into account. To ensure the measures and what suburb it is located in we can model was sound, independent legal researcher www.amsiintern.org.au

The Update 3 TERRY TAO

What’s exciting you in mathematics at the moment? FIELDS MEDALLIST It changes a lot from year to year - there are so many things going on in different AND MEMBER OF parts of mathematics, it seems! I can name two recent breakthroughs in the last year or two which have generated a bit of excitement. The first is the recent proof AMSI’S SCIENTIFIC of the Kadison-Singer conjecture by Marcus, Spielman, and Srivastava, which used radically new methods (in particular, interlacing polynomials) to solve a notoriously ADVISORY COMMITTEE, difficult problem in operator algebras and matrix analysis. It looks like there are PROFESSOR TERRY TAO other applications of this method (for instance, to theoretical computer science). The other is the breakthrough result of Matomaki and Radziwill earlier this year TAKES TIME OUT OF in understanding short sums of multiplicative functions in number theory. This has made several open problems in number theory (e.g. the Chowla conjecture, a cousin HIS BUSY SCHEDULE of the twin prime conjecture) look much more within reach. Recently I was able to AT UCLA TO GIVE use the Matomaki-Radziwill theorems to prove some partial results towards the Chowla conjecture, which could in turn be used to settle a long standing conjecture US AN INSIGHT INTO of Erdos on the discrepancy of sequences. I'm confident that we'll be seeing other WHAT’S EXCITING HIM striking applications of Matomaki and Radziwill's results in the near future. IN MATHEMATICS, Why do you think women are underrepresented in mathematics? That's a good question. Up to about the high school level, we seem to have fairly good HIS RECENT parity these days; if anything, female maths students may even be slightly more numerous and a bit stronger. But then there is a lot of attrition at the undergraduate COLLABORATIONS AND level and beyond. It seems there are a lot of reasons for this. One is that nearby THE WAYS IN WHICH disciplines (e.g. the life sciences) have much better gender balance and this can be more attractive than a discipline where one is in the minority. Another is the relative HE APPROACHES lack of high-profile female role models in mathematics, though there are excellent top female mathematicians who do their heroic best to counteract this. Then there is COMPLEX PROBLEMS. the fact that the graduate and postdoctoral portions of one's career in mathematics can be rough on people who are also trying to start or raise a family. There are some little positive steps in these directions (for instance, child care availability is now taken as a serious issue in mathematics departments, institutes, and conferences, and more efforts are being made to overcome conscious or unconscious biases against minority candidates in hiring and in giving presentations), but there is still a long way to go here.  AMSI INTERVEIW

From a personal perspective what are your top three open problems You have a very different approach to Andrew Wiles say, did you ever in mathematics? What are their prospects for resolution? make a conscious decision to have broad mathematical interests? Well, this is very subjective, and depends a lot on what you mean by "top". Actually I think it was my co-authors that helped me broaden the most. When I There are statements which would have enormous implications if they could be was a postgraduate student I was initially rather narrowly focused on harmonic definitively proved (e.g. the six remaining Millennium prize problems), but the analysis. But my co-author Allen Knutson got me interested in algebraic likelihood of actually doing so is so remote, I don't think these are the problems combinatorics and representation theory. My co-author Mark Keel got me into that we should be devoting the bulk of our mathematical manpower to attacking. PDE, my co-author Ben Green got me into analytic number theory and additive (Though I do like to keep tinkering with an approach I have to disproving global combinatorics, my co-author Emmanuel Candes got me into signal processing, regularity for the Navier-Stokes equations...) My philosophy is to focus on those and so forth. I have a great respect for those mathematicians who drill deeply open problems that are only a little bit out of reach of current techniques and into a single field and extract some very profound results as a consequence, but I methods - problems that require "only" one new breakthrough to solve, rather have always been more comfortable with entering a new field (usually with the than a half-dozen. In number theory, I think the twin prime conjecture is getting assistance of a collaborator in that area) and seeing if any ideas or results from a close to this level of feasibility; in analysis, the Kakeya conjecture has already previous one can be profitably applied to this new one. AMSI “MY PHILOSOPHY IS TO FOCUS ON THOSE OPEN PROBLEMS THAT ARE ONLY A LITTLE BIT OUT OF REACH OF CURRENT TECHNIQUES AND METHODS - PROBLEMS THAT REQUIRE "ONLY" ONE NEW BREAKTHROUGH TO SOLVE, RATHER THAN A HALF-DOZEN.” had much headway made against it from the previous four or five breakthroughs What advice would you give to a philanthropist with deep pockets in the area, and one can hope that just one more is needed to finish it off. More who wanted to invest in mathematics? ambitiously, I think the soliton resolution conjecture in PDE would be a fantastic Well, that is certainly very admirable! I think as far as greatest need is result to settle, though this is currently well out of reach except in very special concerned, prizes, scholarships and grants for junior mathematicians, e.g. to cases (e.g. completely integrable equations, perturbative data, or other very be able to attend conferences and have the opportunity to work with leaders symmetric and special equations). in the field, are the most important. But unfortunately these don't get nearly as much publicity and notice as the larger prizes that go to more established I read somewhere recently that as a child you thought that research people for more visible accomplishments. It seems that a good compromise is was driven by a committee posing problems. Do you think the free to combine the two - to couple a larger prize with some smaller prizes aimed ranging, creative side of mathematics comes off second best to at junior mathematicians. problem solving for kids and adolescents with an interest in maths? Well, I think even problem solving comes off as second best to the computation- Which parts of maths do you think pay the greatest social The ACE network offers universities easy to use, intensive mathematics one sees in schoolwork. Certainly when I was a child, dividend? Should we divert talent from say, the finance accessible means to facilitate research collaboration, the only glimpses I saw of true mathematical research were in some more sector, into these areas and if so how? advanced level books I got from the library, or the informal discussions I had Well, progress in mathematics isn't just a matter of throwing money and re- and sharing of honours courses, seminars and short with some active and retired mathematicians in Adelaide. One big plus in sources into a given area; sometimes a field is just not yet ripe for dramatic courses through video conferencing. today's world though is that, with the internet, one can now listen to public progress, needing a little bit of serendipity to have someone find the key in- lectures or other talks by some very good mathematical speakers, or see good sight. Even very pure areas of mathematics can unexpectedly have tangible examples of accessible mathematical writing online. Even just the mathematics real world impact; I and several others had done some purely theoretical work section on Wikipedia is a wonderful resource which I would have very much on random matrices, for instance, that ended up being useful for compressed enjoyed as a child. So it seems the hard part is to locate the kids with a potential sensing, which is now used for instance to speed up MRI scans. The other thing interest in mathematics and inspire them to go explore for themselves. is that while we certainly do need good people in mathematical research, not every person who is talented in, say, mathematical finance, would also be suit- When it comes to collaboration are you a workshop person? able for this; there are some qualities (e.g. the need to "play", almost to the Or do you have a different MO? point of obsession, with mathematical concepts and problems) that are useful I love collaboration; most of my papers are joint, and most of the mathematics in research but perhaps not in other areas. So I don't think we should actively I have learnt, I have learnt from my various co-authors. But the style is different try to divert people from a career that they already enjoy and are successful at, for each co-author. One of them, for instance, likes to stick to the famous Hardy- but we can certainly raise awareness that there are many areas of both pure Littlewood rules of collaboration (which include such counterintuitive rules that and applied mathematics which need good people and which can be rewarding there is no obligation to respond to any research communication from the in many ways.  other author). I work with some authors almost exclusively by email, others by trying to secure a week at some conducive location where we can brainstorm at a blackboard. More recently, I've been involved with massively collaborative "polymath" projects where dozens of mathematics communicate through wikis Terry is a long term member of AMSI’s Scientific Advisory Committee and and blogs to attack a single problem. Not every collaboration style is suited for AMSI’s first director, Garth Gaudry, was Terry’s mentor as a student at every problem, but they are all fun! Flinders University. Terry continues to be a strong advocate for the Australian mathematical sciences community.

FOR MORE INFORMATION VISIT RESEARCH.AMSI.ORG.AU/ACE Interested in obtaining a Visimeet licence and becoming part of the ACE network? Contact Maaike Wienk at [email protected]

9

The Update The [Q1: ANY OF THE FOLLOWING - WE WERE ASLEEP, IT’S NOT OUR FAULT, THAT CAN’T BE TRUE, ETC.; Q2: NO; Q3: YES; Q4: NO; Q5: NO; Q6: APPARENTLY NOT; Q7: NO.]

Does it encourage the pursuit of maths in schools? in maths of pursuit the encourage it Does

Q7.

WWW.AMSI.ORG.AU/DISCIPLINE-PROFILE-2015 WWW.AMSI.ORG.AU/DISCIPLINE-PROFILE-2015 IMAGE: JUSTUSKINDERMANN

For further information download AMSI’s Discipline Profile and ‘Vision for a Maths Nation’ Policy document Policy Nation’ Maths a for ‘Vision and Profile Discipline AMSI’s download information further For

completions, learning outcomes? outcomes? learning completions,

Does it improve university pass rates, timely timely rates, pass university improve it Does

Q6.

statisticians alone. statisticians

reversing this 20 year trend. trend. year 20 this reversing the private sector. This is the responsibility of practising mathematicians and and mathematicians practising of responsibility the is This sector. private the 

Is it in our students’ best interests? best students’ our in it Is Our future as a high technology, research driven economy depends on on depends economy driven research technology, high a as future Our of promoting mathematics and statistics to the community, government and and government community, the to statistics and mathematics promoting of

Q5.

that maths saves lives. But most of all we will have to do a much better job job better much a do to have will we all of most But lives. saves maths that

RESTORATION OF MATHS PREREQUISITES MATHS OF RESTORATION

the ATAR gaming that goes on in our schools and convince young women women young convince and schools our in on goes that gaming ATAR the

Did we consider the medium and long term consequences? term long and medium the consider we Did

to start re-training the large number of out-of-field maths teachers, disrupt disrupt teachers, maths out-of-field of number large the re-training start to

Q4. IN PHASE MUST UNIVERSITIES

more than one measure to bring us back from this precipice. We will have have will We precipice. this from back us bring to measure one than more

Of course we need need we course Of

Were market forces responsible? responsible? forces market Were

improving the situation. situation. the improving walk on it again. Unhappy lot.” Unhappy again. it on walk should none that vowed Q3.

and low SES areas. SES low and

advance as a pull factor to to factor pull a as advance

The unavailability of these school subjects in many regional regional many in subjects school these of unavailability The seen one of them – who cursed their feet, cursed the ground, and and ground, the cursed feet, their cursed who – them of one seen

re-introduction well in in well re-introduction

Did we plan it? it? plan we Did

the right kind of genetic instability mutated into birds – you’ve you’ve – birds into mutated instability genetic of kind right the

not stop us announcing a a announcing us stop not Q2.

2015 Discipline Profile), Profile), Discipline 2015

the classes. But this should should this But classes. the

famine. Most of the population died out. Those few who had had who few Those out. died population the of Most famine. mathematics subjects at Year 12. (see Section 2.3 of the the of 2.3 Section (see 12. Year at subjects mathematics

low SES areas, to mount mount to areas, SES low

low SES areas, leading to fewer students in calculus-based calculus-based in students fewer to leading areas, SES low

anything other than shoe shops. Result – collapse, ruin and and ruin collapse, – Result shops. shoe than other anything science degrees have Year 12 intermediate maths as a prerequisite? a as maths intermediate 12 Year have degrees science

in regional, remote and and remote regional, in

fied secondary school teachers, especially in regional and and regional in especially teachers, school secondary fied

aren’t enough, especially especially enough, aren’t Horizon, and it became no longer economically possible to build build to possible economically longer no became it and Horizon,

Australia’s of 14% only that pass to come it did How - quali of numbers reduced and programs training teacher

Q1.

teachers for so long there there long so for teachers

of the place passed what I believe is the termed the Shoe Event Event Shoe the termed the is believe I what passed place the of Reduced intake of mathematically qualified graduates into into graduates qualified mathematically of intake Reduced

starved of maths-qualified maths-qualified of starved

and the more the shops proliferated until the whole economy economy whole the until proliferated shops the more the and

couldn’t cope. It has been been has It cope. couldn’t

cipline Profile), Profile), cipline

the education system system education the to wear, the more people had to buy to keep themselves shod, shod, themselves keep to buy to had people more the wear, to

- Dis 2015 the of 4.2 Section (see training research for base

after. Why? Because Because Why? after.

number of institutions dangerously narrowing the support support the narrowing dangerously institutions of number

and more unwearable they became. And the worse they were were they worse the And became. they unwearable more and our retreat from prerequisites. Take his quiz then read on. read then quiz his Take prerequisites. from retreat our

next year or the year year the or year next

and a concentration of university based research to a small small a to research based university of concentration a and

shops there were, the more shoes they had to make and the worse worse the and make to had they shoes more the were, there shops

prerequisites tomorrow, tomorrow, prerequisites AMSI Director Geoff Prince exposes the consequences of of consequences the exposes Prince Geoff Director AMSI

Stagnating interest in engineering and science courses, courses, science and engineering in interest Stagnating

certainly can’t bring back back bring can’t certainly phenomenon but tragic to see it in operation, for the more shoe shoe more the for operation, in it see to tragic but phenomenon

wait that long but we we but long that wait

(see Table 3.23 of the 2015 Discipline Profile), Profile), Discipline 2015 the of 3.23 Table (see

of these shoe shops were increasing. It’s a well-known economic economic well-known a It’s increasing. were shops shoe these of

20 years! We can’t can’t We years! 20

the more apparent when seen in an international context context international an in seen when apparent more the

have thought necessary. And slowly, insidiously, the numbers numbers the insidiously, slowly, And necessary. thought have

prerequisites in another another in prerequisites

(see Section 3.3 of the 2015 Discipline Profile), which is all all is which Profile), Discipline 2015 the of 3.3 Section (see

almost universal maths maths universal almost

these cities there were slightly more shoe shops than one might might one than shops shoe more slightly were there cities these

Reduced graduation rates in the mathematical sciences sciences mathematical the in rates graduation Reduced

the re-introduction of of re-introduction the

cities, shops, a normal world. Except that on the high streets of of streets high the on that Except world. normal a shops, cities,

This would mean mean would This

creasing numbers of less mathematically literate students, students, literate mathematically less of numbers creasing

can be run backwards. backwards. run be can Many years ago, this was a thriving, happy planet – people, people, – planet happy thriving, a was this ago, years Many “

- in with cope to realignments course university Widespread

the maths hole equation equation hole maths the

Let’s suppose that that suppose Let’s

by dubious “assumed knowledge” advice, advice, knowledge” “assumed dubious by

MATHS HOLE! MATHS an almighty almighty an

U E R T

se r nive he t of nd he t t a t an r au t es he Widespread removal of prerequisites and their replacement replacement their and prerequisites of removal Widespread

will cross it and drop into into drop and it cross will

side of the equation we we equation the of side

DOUGLAS ADAMS ADAMS DOUGLAS OVER 20 YEARS WE HAVE SEEN SEEN HAVE WE YEARS 20 OVER

terms into the right hand hand right the into terms

we put some repelling repelling some put we

any maths! I’m not sure that we can estimate when it will occur, but unless unless but occur, will it when estimate can we that sure not I’m maths! any mathematics courses at Year 12 level. 12 Year at courses mathematics

can no longer communicate with the outside world because we don’t know know don’t we because world outside the with communicate longer no can from their historic low and in turn increase the declining interest in advanced advanced in interest declining the increase turn in and low historic their from

So what is the Maths Event Horizon? It’s the point in time at which we we which at time in point the It’s Horizon? Event Maths the is what So Highest priority must be placed on the restoration of maths prerequisites prerequisites maths of restoration the on placed be must priority Highest implements its ‘Vision for a Science Nation’. Science a for ‘Vision its implements

unthinking devotion to market forces. market to devotion unthinking T bodies. These priorities must be addressed as the Commonwealth plans and and plans Commonwealth the as addressed be must priorities These bodies.

removing maths prerequisites and all consequences of of consequences all and prerequisites maths removing key priorities for intervention by Australian governments and for action by peak peak by action for and governments Australian by intervention for priorities key

, paints a grim picture about about picture grim a paints , Universe the of end the Vision for a Maths Nation Maths a for Vision ’ identified identified ’ ‘ document policy AMSI’s this, on Based

The Restaurant at at Restaurant The Adams’ Douglas from excerpt he Australia’s future skills base. base. skills future Australia’s

levels far outstrips supply. This poses an immense challenge to securing securing to challenge immense an poses This supply. outstrips far levels

2015 data shows the demand for mathematical and statistical skills at all all at skills statistical and mathematical for demand the shows data 2015

research, research training and engagement with industry. Broadly, the the Broadly, industry. with engagement and training research research,

highlighting trends as they apply to school education, higher education, education, higher education, school to apply they as trends highlighting

released its annual Discipline Profile of the Mathematical Sciences Sciences Mathematical the of Profile Discipline annual its released

In August this year, The Australian Mathematical Sciences Institute Institute Sciences Mathematical Australian The year, this August In

PREREQUISITES D

Australian STEM leaders discuss theirviews onmathematics prerequisites for science degrees. This reactive policyhassent anegative andmisleading message to schoolsaboutthevalue of these subjects. continues to beanassumption that students obtain still thiscontent knowledge. many for instudy, disappointment andinlife. at thelevel of theirpotential andsetting upfar too of thefuture, discouraging students from performing literacy to study commerce? universities do not indicate a need for mathematical enrol inascience degree? study mathematics, at even themost basiclevel, to Australian universities do not require a student to influence student choices. attached to university courses sendsignals that for further education; and that the pre-requisites school education should adequately prepare you at least agree pipelineislong;that that theskills somehow too hard, surely we ought to beableto intentioned people. are thought soimpossible by somany well- science, mathematics orICTclassroom. ina person qualifiedinthesubject; well-equipped mathematics andICTclass shouldbetaught by a training andcareer-long support. value profession, andinvesting inthebest possible habit of mind:like recognising teaching asahigh- efficiently andambitiouslyif we madethefuture a disciplines sovitalto ourfuture prosperity. test withflying colours; andmost inthe of all STEM to theneedsof adifferent world. measure of our capacity to think beyond ourselves society can strive to answer, because it is really a It isperhapsthemost important question that any centuries what thepurposeof education shouldbe. 10 EXPERT OPINIONS EXPERT AUSTRALIA’S CURRENT It says to methat thiscountry isfailing thetest What does it say to you that 18Australian What does itsay to you that nofewer than12 But even ifthese eminently sensiblethingsare I have never understood why these two things We could go so far as to say that every science, We would domany thingsalot more intelligently, If we were sensible, we would want to pass that greatMany minds have contemplated over the CHIEF SCIENTIST We canandought dobetter. a prerequisite withonlyVictoria andQueenslandrequiring thisstandard, yet there Alarmingly, only14percent of science degrees have intermediate mathematics as mathematics isoneof thegreatest to challenges thehealth of Australia’s STEM disciplines. eclining numbersof Year 12students choosingto study intermediate oradvanced IAN CHUBB IAN Australia’s Chief Scientist mathematics andphysics. likely to be the onlyway to restore prerequisites in Instead, well-considered government intervention is appeal to theiruniversity administration for action. teaching academics at 100%of universities were to corrected by theindustry itself even if100%of recruiting students. Itrepresents amarket failure. finances, necessitating a competitive approach to rarely imposedisrelated to overstretched university that prerequisites inmathematics andphysics are dropped prerequisites inrecent decades. The fact physics. There is no pedagogical benefit in having had asoundbackground inmathematics and their first-yearchallenge students if the students engineering would findit easier to teach and performance. through to theanalysisof statements of financial discussions ranging from return oninvestment rates mental arithmetic gives meanadvantage in the abilityto reason mathematically andperform than thecoal-face periodof my career findthat Istill mathematics andphysics. instrumentation withoutasoundunderstanding of between nerve cells andtheenablingelectronic interests in electrical and chemical signalling have beenimpossible for meto pursuemy particular electronic engineeringandneuroscience. Itwould the underpinningof chemistry andmolecular biology. interactions between atoms andmolecules that are behind. Withoutphysics onecannot express the aircraft carrier’spropellers andthewater itthrusts protons insidethenucleusof anatom orbetween an effects, whether they be between the neutrons and cannot express therelationships between forces and contribution of both. Without mathematics one because Ifeel strongly equally aboutthefundamental the question beingsolelyaboutmathematics and languageof science andengineering. and reading. That is, they are theessential nutrition President, I cannot see how this market failure can be Most academics teaching in science or Even now that Iaminthegovernance rather I didpostgraduate andpostdoctoral research in I refer to both mathematics and physics despite Mathematics andphysics are like mother’s milk AUSTRALIA’S NEXT CHIEF SCIENTIST Australian Academy of Technology &Engineering ALAN FINKEL Chancellor, Monash University Australian MathematicalSciences Institute

SOURCE: DATA COLLECTED BY THE FYIMATHS NETWORK, 2015 The Update leadership that isexpected of us. why itisneeded,we exhibit will the academic how students shouldunderstand mathematics and Butifwe alsoexplainwe make agoodstart. will requirements of courses like science andengineering of urgency. Byclearly stating themathematics students asclients, thissmacks of false advertising. their degrees. limits thepathways that are opento themwithin For others, thelackof mathematical background may carry extra fees, are required to in the gaps. fill may beadditionalto theircourse requirements and underprepared. For some bridging subjects, which studies inscience andengineeringseriously their choices, they commence will theirtertiary their course. Butthisissimplynot true. led students to believe that itisnot important for removing mathematics asaprerequisite we have Universities have allowed thisto happen.By (along withEnglish)astheentry requirement. toat all increase their ATAR score, since it stands advised to take, easier mathematics ornone subjects in constant declineover thisperiod. advanced level mathematics nationally, hasbeen the numberof students studying intermediate and though perhapsunintended, consequence, is that entry to these degrees. Butamore significant, students whomay not have studied mathematics of prerequisites hasbeenseenaspositive, allowing assumed knowledge. In some quarters, the removal now considered asrecommended background or been removed asanentry requirement andis (that is,whichinvolves asubject calculus) has enrolments, intermediate level mathematics and engineeringdegrees. Inanattempt to increase their mathematics entry requirements for science of Australianmajority universities have relaxed and data analysisplay increasingly essential roles. to engineering to biology, mathematical modelling rely onhigh-level mathematics From skills. physics What may not besoclear isthat these innovations the globe, scientific advances are clearly evident. food we eat to the way we communicate around facet of modern life. From the production of the of Mathematics andStatistics, TheUniversity of Melbourne We needto changeourmessaging asamatter In aneducational environment that refers to What students aren’t told isthat asaresult of studentsMany now choose to take, or are In spite of this, over thelast two decades the Science andtechnology impact onalmost every Coordinator of Learning &Teaching Innovation, THE ACADEMIC THE DEB KING DEB School School

knowledge to dowell intheimportant first year goontoand will tertiary education withoutkey secondary not students realise will itsnecessity without mathematics asanofficial pre-requisite, definitelyin thesubject is.It concerns methat isnot anofficialsubject prerequisite, knowledge model. So, whilemathematics asayear 12 instead opting for an‘assumed knowledge’ mathematics as a prerequisite to science degrees, AustralianMany universities have dropped the importancere-establishing of mathematics. secondary schoolstudents. value andimportance of mathematics amongst This hasalsocontributed to aperceived fall inthe prerequisite requirements at tertiary institutions. of factors, butwe cannot dismiss changes to concerning. Thiscanbeattributed to anumber higher levels of secondary schoolisparticularly this, thedeclineinstudy of mathematics at This declineisconcerning. is now outperformed by twelve other countries. forward just underadecadeto 2012andAustralia only five significantly outperformed Australia. Fast- mathematical literacy. Out of the countries tested, than most of ourinternational counterparts in years insecondary education. students seethemthrough that will to theirfinal to embedthe passion for mathematics inyoung a language, or mathematics go a long way will graduate ineitherscience, withaspecialisation initiative inrequiring primaryschoolteachers to can achieve inaclassroom. TheGovernment’s have seen first-hand what the passion of a teacher help drive thestudy of mathematics inlater years. I primary schools.We know that agreat teacher will elevate theimportance of mathematics inour of transition from school. Liberal Senator for Victoria, Assistant Cabinet Secretary, former Parliamentary Secretary for Education & Training Itistherefore important that we commit all to Whilethere isnosilver to bullet address In 2003, Australia was performing better Another important step isto continue to THE SENATOR THE SCOTT RYANSCOTT

mathematics prerequisites.  of theformulae they use. Thisiswhy we need we needpeoplethat understand thederivations of science, commerce andengineering.Thisiswhy formula was predicated.” differed from theassumptions from whichthe because thecircumstances of itsapplication known that theformula was inappropriate pipe failed. We know alsothat we could have that theformula usedwas becausethe wrong, and easy to understand anduse. We know now he usedaformula. Thisformula was well known at Flixborough did not just guess its dimensions: engineer (D. Andrews) said: about engineeringrisks afew years later, an temporary At bypass asymposium pipecausedit. people and seriously injured 36; the rupturing of a chemical plant inEngland1974, 28 which killed underlie these tasks. inthemathematicalunskilled derivations that resources distributed, ourrisks controlled by people ourpowermanaged, ourskyscrapers built, the theorybehindformulae they use? assets priced by individualswhodonot understand portfolios managed, ourcurrencies traded, our science Australia needs. not understand. Thisisnot thekindof biological belimitedwill to clickingonoptions that they do users of thetools andtechniques of bioinformatics mathematical, statistical andcomputational skills, rests squarely onmathematics. Withoutstrong deal thisDNAdata, andthat withall subject of bioinformaticsThe subject helpsbiologists bacteriology, zoology, botany, thelist goes on. evolution, ecology, molecular biology, virology, data onthegenomes of organisms: genetics, disciplines of biologymake extensive useof DNA is beingdone. of data, andwe needpeoplewhounderstand what computational, reliant onlarger andlarger volumes areas isbecoming increasingly quantitative, more Because almost every aspectof these broad subject Why? good idea, important. itisfundamentally commerce and engineering degrees is not just a Catastrophes like thiscanoccur inmany areas “The man who designed the notorious pipe The Flixborough disaster was anexplosion at a Think of engineering.Dowe want ourtraffic Think of financialdata. Do we want our Think of genome science. of the sub- All Having mathematics pre-requisites for science, THE RESEARCHER PREREQUISITES Laboratory head, TERRY SPEED Institute of MedicalResearch Walter &ElizaHall 11 SCHOOL PREREQUISITES: A TALE OF TWO SECTORS PREREQUISITES

rom industry, health, agriculture and business to climate change, mathematics continues to play a key role in shaping our world and how we live in it. As we seek to skill Australia for the future, the F demand for STEM skills is on the rise, with over 75 per cent of the PRIMARY SECTOR SECONDARY SECTOR nation’s fastest growing job areas, including IT, Engineering and Bioinformatics requiring high level science, technology, engineering and mathematics. Why Sara Borghesi Greg Carroll then, with the possibilities seemingly endless, are we seeing a decline in the number of Australian students pursuing high-level mathematics? Do we need to better equip teachers with the skills to educate for the future, is it time to re-think university pre-requisites, or does maths simply have a PR problem? Most of us can point to at least one teacher whose “So what do you do?” my young female optometrist asked. AMSI looks at the state of mathematics education within the primary and ability to illuminate their subject with passion I began to explain I worked at AMSI and one of our goals was to work with mathematics and depth of knowledge, inspired and shaped secondary education sectors. teachers across Australia to … Before I got a chance to go any further she chimed in, our learning. These teachers know that effective Choose Maths Outreach Officers and former primary and secondary classroom outcomes require not just confidence and “Well, that is really necessary as I stopped listening in mathematics when I was about 14.” skill, but also a deep understanding of the subject I explained that keeping capable young women like herself studying mathematics was teachers, Sara Borghesi and Greg Carroll, provide prospective from matter and curriculum. Why then, despite the clear one of our main targets and she replied, two education sectors to tackle these questions. link between content knowledge and classroom teaching standards, are we not equipping teachers “It will be hard to combat the peer pressure. My group of friends did not think mathematics to educate students for a future where skills such as was cool and being cool was very important. Anyway, none of us were planning on going mathematics will be vital? into the careers where we would be going to use mathematics anyway.” Perhaps some of the problem lies with current Why was that I asked, university pre-requisites, which mean maths experience and expertise cannot be assumed in Australian pre- “Mathematics was only required for engineering and the hard sciences, which are of no service primary teachers. Acceptance into Australian interest to girls” she said. teaching degrees varies from state to state, with most This was an intelligent young woman and yet she still had a very limited view of how undergraduate degrees not requiring students to have mathematics supported study in so many fields. undertaken any level of mathematics on entry. In The reality is it is not only girls who are abandoning STEM subjects. As a Year 11 and Victoria students only need a satisfactory completion of 12 coordinator and then campus principal in a senior school, I have been involved in many Units 1 and 2 of any mathematics, while in Queensland similar conversations with both male and female students over the years. entry requires four units of mathematics. A Master of Education, the most popular entry pathway for teaching “The course I want to do only requires a 25 in any mathematics, why would I do the hard in Australia, also has no mathematics pre-requisites. So mathematics? I will get a better mark in the lower mathematics with less effort. No need how do we address this gap in mathematical knowledge to do the advanced mathematics.” amongst our educators? A first priority must be to retain students in the study How and why do these ideas arise and what factors are perpetuating this notion? One of of mathematics, something that could be achieved the obvious determiners in the subject selection of Year 11 and 12 students are university by making mathematics required learning in the later prerequisites, or rather the lack of pre-requisites in many cases. Understandably individual years of secondary school for intending teachers. This is students, careers advisors and schools have short horizons and the focus is upon achieving an particularly important for primary teachers, as improving ATAR that will enable students to be accepted into their tertiary course of choice. Any content content knowledge may help reduce anxiety around knowledge they may require for successful tertiary study is rarely a consideration. mathematics. We also need to look at how we sell The removal of prerequisites for many courses has assisted the tertiary sector to increase mathematics, not only to potential teachers but also enrolments. At the same time, however, there has been an alarming drop in the number of current educators, parents and students, to increase students choosing to study high-level mathematics in Year 12. Australia has witnessed an awareness of mathematical career pathways. increasing number of enrolments in the lower level Year 12 mathematics subjects. Whilst Importantly, the release of recommendations from there are many contributing factors, it is hard to ignore the numbers. the Ministerial Advisory Group on Teacher Education’s The then Victorian Minister for Education Martin Dixon said, “One reason for the shift report Action Now: Classroom Ready Teachers has away from the more challenging mathematics subjects was that universities had changed highlighted the need to provide pre-service teachers their pre-requisites for some courses.” with opportunities to become education leaders. As a The lack of students studying high-level mathematics is “an issue of national first step, the Australian Government will introduce a importance”, according to Australia’s Chief Scientist Ian Chubb. Choose Maths will be national test for pre-service teacher education students working with individuals and schools to educate them about the potential of mathematics from 2016. This will require future teachers to pass a to increase career options for young Australians. literacy and numeracy test prior to commencing their The worry is that the attitude of schools and students may not change without a lead from final professional experience placement, ensuring they the Universities. Universities placing a higher value on the study of mathematics will provide a graduate with levels at least equivalent to those of the tangible reason for selecting Year 12 mathematics units with more mathematical rigour.  top 30 per cent of the population.

AMSI and the BHP Billiton Foundation is actively working with schools to deliver Choose Maths will have a focus on mathematics education in primary and secondary Choose Maths, a five-year national program that will turn around public perception of schools and will contribute to the health of the mathematics pipeline in Australia from mathematics and statistics as a career choice for girls and young women. school through university and out to industry and the workplace.

TO READ MORE ABOUT THE CHOOSE MATHS PROGRAM VISIT WWW.CHOOSEMATHS.ORG.AU

The Update 13 NETWORKS COMPLEX A one of their friends, since most edges lead to a vaccinate therandom individualsbutdovaccinate strategy ispossible: take arandom sample, don’t Even ifthese individuals are unknown aclever those most responsible for disease transmission. that publichealth measures canbedirected at suchdistributions offact, connectedness canmean diseases suchasHIVAIDScannot becontrolled. In rather panickyconclusion that sexually-transmitted networks for example ledearly theoreticians to the again profound, thepresence of hubsinsexual in humansociety asSixDegrees of Separation. whichistheconceptyou’d popularlyknown think, (iii) they are mucheasier all to `get around’ than and and A->Cthenitishighlylikely that B->C, connectedare mega-enormous hubs, (ii)ifA->B nodes withfew connections andsomenodes that have acommon topology: (i)they consist of many stunning discovery real that all complex networks to theInternet to food webs inecology, ledto the ranging from gene-regulation networks inbiology network data. applies mathematical andstatistical tools to large the mathematical sciences that develops and networks muchlike avirusdoes. and obesity spreads through humansocial asifinfectious,can bemathematically modelled profound outcome that diseases suchasobesity social network affects ourbehaviour hashadthe role thanyou realise. social network probably plays amuchlarger friends andfamily? Theanswer isthat your what isnormaland`right’ isdictated by your social context whereby your perception of what anormalhealthy weight is, orisityour 14 discrete andrelatable entities, School AMSISummer explains 2016 WHAT MAKES YOU, YOU? YOU, MAKES WHAT The consequences for health anddisease are Research into networks from disparate fields, Complex Networks isanemerging area in In thestudy of health anddisease, theway our The world around us is brimming with structures consisting of withstructures aroundThe world usisbrimming Senior Lecturer Dr StephenSenior Lecturer Dr Davis, University. RMIT beliefs andyour perception of political opinions, your religious really you whodetermines your re you really you? Imean, isit flu vaccine! you are asocialbutterfly, make sure you get the to get sickwhensomething isgoingaround. Soif more likely to get sickandyou’ll beoneof thefirst your socialnetwork) itisnow known that you are in hand.Ifyou are ahighlysocialperson(ahubin `hitting’ thehubsinnetwork. highly connected personchances are that you start about themselves. as peopleconsider what they have just learnt is apauseintheclass, amoment of self-reflection there isawiderange of values, andsecondly there of peopleinvariably two thingshappen.Firstly easily calculated as(1/2)m(m-1). the numberof possible contacts between themis apartandseparate.all Ifyou have mcontacts, then opposite, that you tend to keep your relationships where alow value (closeto 0)indicates just the town’ effect (everybody knows everybody) and scale where highvalues closeto 1indicate a`small- possible links between your contacts putsyou ona number of links you draw dividedby thenumberof would know each other on afirst-name basis.The links between your contacts ifyou thinkthey with spokes coming outwards. that your nodelooks like thecentre of awheel, draw links between yourself andyour contacts such for more Next, thanoneminute inthepast week. restrict yourself to peopleyou have spoken with Depending onhow many there are you might or colleagues that you interact withregularly. circles around you that represent family, friends that represents yourself andthenplace similar relationships. Start by drawing asolidcircle about yourself andtheway you manageyour network andalongtheway tell you something The following exercise characterise will your local YOUR EGO NETWORK Connectedness anddisease dogohand actually

When thisexercise iscarried outwithagroup Now Draw themore difficult bit. additional Australian MathematicalSciences Institute

PHOTOGRAPHY: MICHAEL SHAW was openingup! Kevin hadnoidea what sortof canof worms he between two nodes hasto pass through you. Dear oritisthenumberof times apath the network, function that would ensueifyou were deleted from connections you have, oritistheloss of network it iswhoyou are connected to not how many of levels andthere haslongbeendebate that they appear in.Thisisdissatisfying at anumber their publications oractors by araw count of films is akinto ranking academicsby araw count of count thenumberof links each nodehas, which ranked interms of closeness. to beterribly true, heisn’tinthetop 100actors one ortwo `hops’away from him–turnedoutnot in themovie-actor network –that every actor is Networks. Thecentrality that Kevin Bacon claimed MAKE SUREYOUGETTHEFLUVACCINE! SO IFYOUAREASOCIALBUTTERFLY, WHEN SOMETHINGISGOINGAROUND. YOU’LL BEONEOFTHEFIRSTTOGETSICK YOU AREMORELIKELY TOGETSICK SOCIAL NETWORK)ITISNOWKNOWNTHAT HIGHLY SOCIALPERSON(AHUBINYOUR DO GOHANDIN CONNECTEDNESS ANDDISEASEACTUALLY is oneof thekey questions that ariseinComplex film. the same to Kevin Bacon viaactors whohave appeared in Hollywood actor andyou must thenlinktheactor aficionados. Thelatter has your opponent namea Six Degrees of Kevin Bacon, popularamongst film Universe", Bacon numbersandthetriviagame titled "Kevin Bacon istheCenter of theHollywood prompted alengthy newsgroup thread amusingly someone who'sworked withthem.Thestatement he hadworked witheverybody inHollywood or interview, actor Kevin Bacon commented that In January1994, duringaPremiere magazine YOUR IMPORTANCE The simplest measure of importance isto How to identify `important’ nodes inanetwork COMPLEX NETWORKS us, aboutsociety andaboutourselves. networks next will reveal abouttheworld around network ismadeupof. repeatedly asbuildingblocks that thelarger of motifs, whichare subgraphs small that recur structure types of andall networks have sets already real that all networks have community and brain function.Indeed,ithasbeendiscovered online socialsites asthey are to gene regulation self-organising structure, principles asrelevant to light onthefundamental principles that govern real complex networks istheirabilityto shed some combination of these fitness values. model thechances of alinkappearing dependson are allocated anintrinsic fitness. In the latter model, the`goodget richer’modelwhere nodes somewhat reassuringly sodoes analternative for thenumberof links each nodehas, but heavy-tailednetworks withso-called distributions preferential attachment does generate realistic quality papers!We canmathematically prove that quality. Surely, for example, citations goto high and that there isnoroom for any measures of - butstrange to thinkthat thingsare thissimple preferential ortherichget richer. attachment, that are already well connected. Thisisknown as preferentially links to thosenodes inthenetwork time. Second, whenanew nodeemerges thenit realthat all networks are not static butgrow over mechanism was responsible. they noted First, ubiquitous, alsoargued that aparticular networks, i.e. that thepresence of hubswas commonality intopological structure of real The researchers that first discovered the DEEPER TRUTH It will befascinatingIt will to seewhat complex Perhaps most exciting aboutthestudy of The concept isbiblical–seeMatthew 25:29 . IFYOUAREA AND

 15 SPCOM FEBRUARY 2015 SPCOM 2015 TECHNICAL REPORT

FITZPATRICK WORKSHOP STOCHASTIC VARIATIONAL INEQUALITIES & OTHER STOCHASTIC PROBLEMS Simon Fitzpatrick was an outstanding Australian mathematician. His contributions have an increasing Variational inequality modeling, analysis and computations impact in functional analysis, both in theoretical and are important for many applications, but most of the subject has th applied aspects. The now celebrated Fitzpatrick function, been developed in a deterministic setting. In recent years research has proceeded on a track to incorporate stochasticity in one way or another. However, the main focus has been on a rather limited idea of what a stochastic variational inequality might be. As where T is a maximally monotone map, has been cited and used variational inequalities are especially tuned to capturing conditions extensively in wide range of applications from PDEs to modern for optimality and equilibrium, stochastic variational inequalities economic theory. It has become a fundamental tool in maximal ought to provide such service for problems of optimisation and 4 monotone theory. The Fitzpatrick function was unnoticed for several equilibrium in a stochastic setting. Therefore they ought to be years until Martínez-Legaz and Théra rediscovered it in 2001. This able to deal with multistage decision processes involving recourse SOUTH PACIFIC CONTINUOUS function provides a bridge between certain monotone phenomena actions, which has so far hardly been the case. Terry Rockafellar and convex functions. This allows use of powerful variational showed it is possible to accommodate this by bringing in the tools techniques for studying problems such as (i) first-order monotone of nonanticipativity and its martingale dualisation. Roger Wets flows, (ii) nonlinear evolutionary PDEs and (iii) quasilinear models then put these new contributions into a historical perspective in OPTIMISATION MEETING in continuum mechanics, electromagnetism and heat conduction. In his plenary talk, which described the highlights of Rockafellar’s a surprisingly different field, Flam has recently given an economic results. To reinforce the stochastic flavor, Claudia Sagastizábal’s Prof. Henri Bonnel, University of New Caledonia, Noumea, New Caledonia Prof. Jonathan M. Borwein, University of Newcastle, AustMS and ANZIAM member interpretation of the Fitzpatrick function in terms of a supply curve, plenary talk covered a new variant of bundle methods, which has Assoc. Prof. Regina S. Burachik, University of South Australia, AustMS and ANZIAM member Dr C. Yalçın Kaya, University of South Australia, AustMS and ANZIAM member which couples prices to quantities in a non-Walrasian market. “on-demand” accuracy, and Jong Shi Pang’s plenary talk concerned In terms of theoretical advances, the Fitzpatrick function has Nash equilibria for games with stochastic recourse functions. ith one of Australia’s most the numerical approaches to several types of frameworks. Dontchev spoke of recent advances led to considerable simplifications of the proofs of some classical beautiful regions at their optimisation problems. in the study of Lipschitz properties of solutions, properties involving maximally monotone operators. For example, THEORY & APPLICATIONS OF doorstep and a rich scientific The meeting started with the two warm-up of paramount importance in sensitivity studies of Simons and Zalinescu used it to obtain a new and short proof of program exploring continuous tutorials by José Mario Martínez and Claudia Sa- constrained optimisation problems. NUMERICAL OPTIMISATION W Rockafellar's characterisation of maximal monotone operators. optimisation, global research leaders and gastizábal. Martínez delivered the morning tutorial The Fitzpatrick Workshop was certainly another students gathered at Adelaide’s University of on numerical smooth optimisation. The afternoon highlight and celebrated 25 years of the publication Within the theory of maximally monotone maps, Burachik and A common denominator in most talks at SPCOM was the South Australia for SPCOM 2015. Organising tutorial, on numerical non-smooth optimisation, of a seminal paper on maximal monotone Svaiter used it to define a one-to-one correspondence between a numerical approaches to several types of optimisation problems. committee members Assoc. Prof. Regina was delivered by Sagastizábal. operators by the late Australian mathematician family of convex functions associated with a maximally monotone Some talks encompassed theory, some applications, and some Burachik and Dr Yalcin Kaya shared some of Terry Rockafellar, a world leader in convex Simon Fitzpatrick. Fitzpatrick’s paper introduced operator, and a family of enlargements of these operators. These others both theory and applications. An example of the latter the meeting’s highlights with AMSI. analysis and optimisation, opened the second day a key tool in functional analysis, with important enlargements, in turn, generated a new way for the efficient type was Bot˛’s plenary talk, which showed us how duality of the conference with a stellar talk on how sto- implications in mathematical optimisation. An Broadly speaking, the mathematical field of chastic variational inequalities can provide the right objective of this workshop was to understand, after approximation and analysis of variational inequality problems. can be exploited for solving complexly structured nonsmooth optimisation involves determining an optimal framework for studying problems of optimisation a quarter of a century, what open questions posed Marques Alves and Svaiter have used it recently to define a optimisation problems. Jeya Jeyakumar presented new results in scenario (relative to some criteria) among a new constraint qualification ensuring maximality of the sum of global polynomial optimisation. José Mario Martínez presented collection of alternatives. maximally monotone operators in non-reflexive Banach spaces. new results on sequential optimality conditions for differentiable For example, the determination of the most The conference was a spectacular Stephen Simons opened the workshop with a plenary talk constrained optimisation. Helmut Maurer spoke about optimal efficient route between two locations, where success scientifically and socially, “route” and “location” can have many abstract and in which, using concepts emanating from Fitzpatrick’s work, he control problems from biology and biomedicine whose solutions concrete meanings, or the most economical use and of course especially for me! obtained a generalisation of Rockafellar's theorem on the maximal exhibit bang-bang and singular control. Xiaoqi Yang presented first- of resources in production processes. Optimisation Emeritus Professor Terry Rockafellar, University of Washington monotonicity of subdifferentials, and, among other results, he and second-order necessary conditions for nonlinear programming problems can involve thousands of variables and obtained an extension of Brezis-Browder theorem to non-reflexive problems from the viewpoint of exact penalty functions. He minimise or maximise many “objective functions”. Banach spaces (Brezis-Browder theorem proves that, in a reflexive also presented an interior point method to solve the L relaxed Mathematical optimisation is a broad and rich and equilibrium in a stochastic setting. (The word in this paper have been solved, and what questions p research area in its own right and it has equally stochastic here refers to problems with a degree of remain open. Stephen Simons gave a keynote talk Banach space, the adjoint of a linear monotone mapping with closed penalty problem, together with promising numerical experiments. broad application. In economic terms it is critical randomness or indeterminacy. For more detail see on Fitzpatrick’s contributions to functional analysis, graph is monotone if and only if the original mapping is maximally to productivity growth and competitive advantage. the Technical Report opposite.) The attendees also introducing a new theoretical framework, which monotone). The plenary talk was followed by four 20-minute talks In social terms it is important in health care, had a chance to celebrate Terry Rockafellar’s 80th gives a generalisation of Brezis-Browder theorem by Jonathan Borwein, Samir Adly, Radu Bot˛ and Regina Burachik. transport planning and communication networks, birthday (not a random event!) during the meeting on linear relations. Most of the results Simons Borwein’s talk introduced the strong Fitzpatrick inequality and used The meeting was generously sponsored by University of South Australia to name just a few. banquet, by means of live piano performances, presented are consequences of Simon Fitzpatrick’s The fourth edition of the successful South Pacific singing and dancing. seminal 1988 paper. Simons’ fascinating talk was it to define a gap function for the monotone inclusion problem (UniSA), School of Information Technology and Mathematical Sciences meetings, this year’s event addressed a diverse Boris Mordukhovich and Asen Dontchev gave followed by Adly, Borwein, Bot˛ and Burachik. and variational inequalities. Bot˛ then furnished new duality results (ITMS) at UniSA, Centre for Industrial and Applied Mathematics audience, from those early in their career to senior talks at the leading edge of research in variational SPCOM 2015 not only covered insightful scientific for certain convex optimisation problems. Adly showed how non- (CIAM) at UniSA, Australian Mathematical Sciences Institute (AMSI), researchers. Featuring lectures, the Fitzpatrick analysis. This subject grew from the classical research and outcomes. It also gave the guests smoothness naturally arises in dynamical systems, such as those Centre for Computer Assisted Research Mathematics (CARMA) at the Workshop, two half-day tutorials on numerical calculus of variations where differential equations, much needed time to meet and socialise with fellow induced by electrical circuits, and some problems from mechanics University of Newcastle, University of New Caledonia, Australian optimisation, and a student poster session, the topics such as Newton’s equations in mechanics, are colleagues and field experts. The mid-week winery ranged from variational analysis, optimal control framed as a variational principle which identifies the tour to McLaren Vale was a great success. and lastly Burachik presented a new family of enlargements, which is Mathematical Society (AustMS), Australian and New Zealand theory, convex analysis, numerical optimisation, solution of the differential equations as providing a The event attracted plenty of praise from inspired by Fitzpatrick’s 1988 paper and every member of this family Industrial and Applied Mathematics (ANZIAM), and ARC Centre vector optimisation, stochastic optimisation, minimum of some “action integral”. Mordukhovich attendees for its perfect blend of scientific research is structurally closer to the epsilon-subdifferential enlargement. of Excellence for Mathematical and Statistical Frontiers (ACEMS). functional analysis, and their applications. discussed a new application of variational analysis and social gatherings and the chance to explore A common theme at this year’s SPCOM was to monotonicity properties in both global and local some of the best of South Australia. 

THIS IS AN EDITED VERSION OF ASSOC. PROF. REGINA BURACHIK AND DR C. YALÇIN KAYA’S REPORT ON THE 4TH SOUTH PACIFIC CONTINUOUS OPTIMISATION MEETING

16 Australian Mathematical Sciences Institute The Update 17 HIGHERED.AMSI.ORG.AU

JULY 2016 THE UNIVERSITY OF QUEENSLAND

SCHOLARSHIPS

NOV - DEC 2016 BEGINNING JANUARY 2017 THE UNIVERSITY OF ADELAIDE DECEMBER 2016 THE UNIVERSITY OF SYDNEY COMING SOON RESEARCH TRAINING SCHOOLS, SCHOLARSHIPS AND GRADUATE COURSES