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ANU Postgraduate research

Research is at the core of everything we do. It informs the content of our degrees, influences public policy and solves some of our region’s greatest challenges.

ANU postgraduate research

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Scholarships & Fees

How to apply

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Studying an advanced, research-focused Doctor of Philosophy (PhD) or Master of Philosophy (MPhil) degree at The Australian National University (ANU) is an opportunity to make a substantial and original contribution to your discipline or area of professional practice.

We’ll automatically consider you for a scholarship when we receive your application.

Research areas

Our research priorities reflect the challenges facing the world today.

ANU researchers are currently exploring a range of disciplines and study areas .

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Before you apply

Find a potential supervisor and explore our colleges’ research opportunities. Some colleges have different application requirements – so make sure you’re aware of and follow these before you apply.

1. Find a supervisor

Discover potential supervisors. Explore their research and published works and find their contact details.

Search supervisors

2. ANU college research opportunities

Our colleges can provide you with information about research areas, supervisors and groups, as well as who to contact.

NOTE: More than one college can offer supervision in a particular study area.

• ANU College of Arts & Social Sciences
• ANU College of Asia & the Pacific
• ANU College of Business & Economics
• ANU College of Engineering, Computing & Cybernetics
• ANU College of Health & Medicine
• ANU College of Law
• ANU College of Science

3. Explore college application requirements

If you have found a supervisor you would like to work with and the college that offers this supervision, you will need to find out if there are any pre-application steps that your college would like you to take.

Most colleges would like you to find and secure the support of a potential supervisor before you complete your application. For example, the ANU College of Business & Economics has different arrangements for setting up supervision, so please check in with them before applying.

Some colleges will ask you to send a short description of your proposed area of research as an expression of interest and a summary of your academic qualifications, including grades, to them first.

Visit the ANU college research pages for pre-application advice (see the links under 'ANU colleges’ content above).

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Applying to ANU

You can apply at any time of the year – but if you would like to be considered for a scholarship, you will need to send your application within the scholarship’s application deadline.

Scholarship applicants

Your referees should send their reports before your scholarship’s deadline. Give them as much time as possible by completing your ANU application 2–3 weeks earlier than the scholarship’s deadline. We’ll contact your referees when we get your application.

Application requirements

Your application to study at ANU must meet the following requirements.

1. Minimum admission requirements

Explore our minimum admission requirements.

Requirements for admission to a Doctor of Philosophy degree

• An Australian bachelor’s degree with at least second-class honours (Upper first-class honours may be required by some programs) or the international equivalent, or
• Another degree with a significant research/thesis component, or
• A combination of qualifications, research publications and/or professional experience related to your field of study

Requirements for admission to a Master of Philosophy degree

• An Australian bachelor’s degree or higher, with an overall grade of distinction or higher, or the international equivalent, or
• Another equivalent degree, or
• A combination of qualifications, research publications and/or professional experience that are related to your field of study

2. English language requirements

You must meet our English language requirements to be eligible for admission to ANU. While you can apply without having met them, you will need to show that you do when you get a study offer from us.

Unsure whether you can meet the English language requirements? Contact your research school or the Graduate Research Office before you send your application.

Learn more about ANU English language requirements

3. Research proposal

Your draft research proposal only needs to be short. Check in with your potential supervisor to clarify their expectations for this proposal before you send it in with your application.

Your proposal should present your idea or question in your discipline area clearly. Consider it a statement about the basis of the research you’d like to do.

Your research proposal should:

• establish the relevance of your idea
• show gaps in your field – and how your research would address these
• include how you would go about your research project – your approach, methodologies and resources.

You will be able to change the proposal once you have enrolled in your program.

Learn about research proposals

4. Referees

Referee reports are mandatory when applying for admission to a HDR Program. At least 2 referees reports are required to commence assessment of the application. Academic referees, who are able to comment on the applicant’s ability to undertake the program, are preferred, however, professional references can also be used. The University may request additional referee reports during the assessment of the application.

Ensure their contact details are correct; we will email them a report to complete from within the application portal as soon as we have received your application.

If your referee is unable to access our system-generated referee report, they can contact the Admissions team and ask for another version of the form.

Your referees must send their completed reports confidentially and directly to the University rather than to you.

Reference documents:

• Research Application Referee Report (DOCX, 85.97 KB)

5. Supporting documentation

Upload clear, colour copies of your academic transcripts and graduation certificates with your application. You do not need to certify these documents, but they must be original copies. We will verify their authenticity.

If your academic documents were originally given to you in a language other than English, we will need official copies of the document in that language and original translations for verification purposes.

6. Incomplete qualifications

You can apply to ANU before you complete your current degree if you are in your final year. Advise the Graduate Research office your expected completion date via your application and supply a copy of the qualification when we make you an offer.

For more information, refer to ‘Supporting documentation’.

If you have the approval of a college and a potential supervisor, you can apply for admission to ANU. Without this endorsement, though, we might not be able to assess your application.

Choose the program you want to study from the Program & Courses catalogue

On the program’s page, click 'apply’ to open the application portal

Complete your application

Receiving an offer from ANU

After we assess your application, we will contact you via email about the outcome within 6–8 weeks (about 2 months). This could take longer if we're also considering you for a scholarship.

If you do not hear from ANU within two months, contact your research school or email the Graduate Research Office.

• Contact Graduate Research Office

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Mathematical Sciences Institute ANU College of Science

Research activity at MSI is structured into our research groups.

Algebra & topology

We work on problems of central interest in mathematics.

Analysis & geometry

The Analysis & Geometry research program explores the areas of differential geometry, several complex variables, non-commutative geometry, harmonic analysis, microlocal analysis, partial differential equations, operator theory, spectral theory, convex geometry and statistical learning theory, and banach algebras.

Applied & nonlinear analysis

Current research in the Applied & Nonlinear Analysis research program emphasises elliptic and parabolic partial differential equations, geometric and physical variational problems, geometric partial differential equations, geometric evolutions, geometric measure theory, optimal transportation, affine differential geometry, conformal differential geometry, finite element and difference equation approximations, and geometry of fractals.

Bioinformation science

Group expertise lies in biological mathematics and biostatistics, with current research areas focus on population genetics, phylogenetics, and spatial modelling.

Computational mathematics

The Computational Mathematics research program actively studies theoretical aspects of computational algorithms.

Fusion plasma theory and modelling

The Plasma Theory and Modelling group focuses on understanding these fundamental properties of plasmas through a variety of different academic perspectives.

Mathematical physics

The Mathematics Physics research program spans the ANU College of Science, with several members having joint appointments with the Department of Theoretical Physics in RSPE. The program is active in studying fundamental problems across a broad spectrum of Mathematical Physics.

Stochastic analysis & risk modelling

The Stochastic Analysis & Risk Modelling research program explores the areas of stochastic modelling of financial processes, statistical inference relating to those models, stochastic integration and numerical aspects of partial differential equations, and option pricing models.

Theoretical astrophysics

The Theorectical Astrophysics research program explores the areas of compact stars, radiation processes and transfer mechanisms in accretion flows on to highly magnetic compact stars, modelling of accretion disks, modelling of stars and magnetic atmospheres, cataclysmic variable binaries, and searching for the progenitors of type Ia supernovae.

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PhD in Statistics

The PhD program in Statistics at the Research School of Finance, Actuarial Studies and Statistics (RSFAS) equips graduates with knowledge of developments in theoretical and applied statistics. The PhD program draws upon the diverse expertise of academic staff across the University. The School’s PhD candidates will undertake independent research on a specialised research topic.

The program is focused on developing candidates for a career in academia, government or industry. Positions in government or industry may include researchers in scientific, medical or health research organisations; researchers or analysts within government agencies, such as the Australian Bureau of Statistics and Australian Institute of Health and Welfare, or departments of Health, Agriculture, Education, Finance and Treasury; researchers or quantitative data analysts within the corporate sector, including banking, finance and insurance, pharmaceutical, and energy and mining sectors; and management and statistical consultants.

CRICOS #: 048345A

Duration: 2 to 4 years full time (4 to 8 years part time)

Before you submit an application for entry to the program, you should:

• ensure you meet the admission requirements outlined below
• identify potential supervisors – that is, one or two statistics academics at ANU who conduct research in your area of interest.

You can find information on researchers and their research areas in the  ANU researchers database  and on the  RSFAS Statistics faculty  page.

While other ANU schools may recommend contacting potential supervisors before submitting an application,  this is not required  for entry into RSFAS’s PhD programs. Instead, you only need to list the name(s) of potential supervisors in your online application form.

Potential supervisors cannot guarantee entry into the PhD program. Admission will depend on the strength of your application relative to others in the pool.

After you’ve completed the steps above, you can proceed with an  online application .

Application deadlines

The first semester of the ANU academic year starts in February, and the second semester starts in July. While all applications for first semester entry must be submitted  before 31 October,  international applicants wishing to be considered for an  ANU scholarship  should submit their applications  before   31 August .

To be considered for a scholarship, your application must be accompanied by all the supporting documents listed below, including the referee reports. Request for referee reports are triggered and sent to your nominated referees at the time of submission of program application. It is thus important that you submit your application in advance (2-3 weeks) to allow time for your referees to provide their reports prior to the scholarship deadline.

If you’re currently completing an academic degree and haven’t yet received your final results and transcript, you should still submit all available documents before the deadline, and forward remaining results once you receive them. We won’t make a final decision on your application until we’ve received all the required documents.

The admission requirements for the PhD program in Statistics reflect the advanced knowledge that candidates will need to undertake the coursework component of the degree, and the research experience and skills needed to successfully undertake and complete the research thesis.

The minimum qualification requirement for admission to the PhD program in Statistics is:

• an Australian Bachelor degree (or equivalent) with First Class Honours or Second Class Honours Division A in statistics (or a related discipline), or
• another qualification (e.g. a Master degree) with a substantial research thesis component that the RSFAS HDR (higher degree by research) committee is satisfied is equivalent or superior to a degree mentioned in (a), or
• a combination of qualifications and professional experience that the RSFAS HDR committee is satisfied is equivalent or superior to a degree mentioned in (a).

Admission to the PhD program in Statistics is competitive and we can only admit a limited number of applicants each year. Meeting the minimum entry requirements does not guarantee you a place in the program.

If you don’t have sufficient research experience for entry into the PhD program, you might consider applying to the MPhil program . If you’d like to consider this pathway, contact the RSFAS HDR convenor for more information.

English language requirements

All applicants must satisfy the University’s  English language admission requirements . An international applicant who is not a native English speaker may satisfy these requirements by submitting evidence of an  IELTS  overall score of at least 6.5, and with no component less than 6.0, or a paper-based  TOEFL  score of at least 570, with at least 4.5 in the essay component.

Application and supporting documentation

You must submit your application online via the  ANU Application Manager .

In addition to the standard information required in the online application, you must submit the following supporting documents as part of your application:

• a one-page statement of purpose outlining your motivation to undertake a PhD in Statistics at ANU
• a research proposal – see details below, as well as these guidelines on how to  prepare a persuasive research proposal
• copies of written research work, e.g. honours or Master thesis, research project or published works
• official  TOEFL  or  IELTS  results (where applicable) to demonstrate that you satisfy the University’s  English language requirements .

Research proposal

The online application requires you to submit a research proposal. The proposal should set out an original research idea, provide an introduction or background to your research idea, clearly set out the objectives, data required and expected research methods, and explain why the research is important and the contribution it will make to the discipline. Among other things, the research proposal will require you to demonstrate an understanding of the key literature in your chosen topic area. As a guide, you should aim for between 1,500 and 2,000 words, including a list of key references.

The RSFAS HDR committee uses the research proposal as an indicator to assess the quality and originality of your ideas and your skills in critical thinking. Note that the research proposal does not restrict you to this field of study should you be admitted to the PhD program.

Offers of admission

The RSFAS HDR committee will review all complete applications submitted by the relevant deadline.

If your application is short-listed, you may be required to attend an interview (face to face or online).

We may send you an offer of admission if you satisfy the eligibility criteria and your area of interest matches those of RSFAS academics with supervisory capacity. However, since admission is competitive and supervisory capacity is limited, we won’t send any offers of admission  after the relevant application deadline , irrespective of the date when you submit your application.

The PhD program in Statistics consists of two components –  coursework  and  research .

Candidates undertake the research component after successfully completing the required coursework.

PhD coursework component

PhD candidates may be required to complete up to six semester-length courses during the first year of the program. Required coursework must be completed to a satisfactory level for candidates to progress to the research component. The specific coursework requirements will depend on each candidate’s background and will be determined through discussion with the HDR convenor and the chair of the candidate’s supervisory panel.

Compulsory courses for the PhD in Statistics are:

• STAT8027  Statistical Inference
• STAT8056  Advanced Mathematical Statistics
• STAT7040  Statistical Learning
• STAT7018  Stochastic Modelling

Candidates select up to two electives from graduate-level courses in statistics (or suitable advanced courses from other disciplines) in consultation with the chair of the supervisory panel.

PhD research component

Following the successful completion of coursework, PhD candidates undertake specialised research training and independent research.

Research supervisory panel

When a PhD candidate is admitted to the program, a provisional supervisor is appointed. The provisional supervisor has the responsibility of overseeing the candidate’s progress until a supervisory panel is chosen. During the first year, it is important that candidates start developing their research topic ideas by consulting with their provisional supervisor and other academic staff within RSFAS.

Either in a candidate’s first year of study, or soon after completion of their coursework, a supervisory panel will be chosen. The role of the panel is to assist, advise, and provide support and encouragement to the candidate for a timely and successful completion of the research thesis. The HDR convenor will determine the composition of the supervisory panel in consultation with the candidate.

RSFAS statistics seminar program

The RSFAS statistics seminar program consists of regular seminars presented by national and international researchers. PhD candidates are expected to attend and actively participate in the seminars throughout their candidature.

Research integrity training

Within three to six months of enrolment, all PhD candidates must complete the  Research Integrity Training  and pass the exam. Completion of this course and exam is a compulsory milestone for all PhD candidates.

Thesis proposal review

During the second year, candidates must submit a thesis proposal for review to their supervisory panel and present their proposal as a seminar to the School. The purpose of the thesis proposal review is to assess the originality, significance, adequacy and achievability of the candidate’s thesis plan.

The proposal includes a description of the research to be undertaken in the thesis, and a summary of the thesis structure and time plan.

Successful completion of the thesis proposal review (as determined by the Delegated Authority following consultation with the HDR convenor and supervisory panel) is required to continue in the PhD program.

Annual progress review

It is University policy that each candidate’s progress be reviewed periodically. In each year of their program, PhD candidates are required to submit an  annual plan and report  as a basis for periodic progress review. This document provides details on work completed by the candidate since the previous review, current progress, and any problems that may impact their research. It also outlines the coursework and research the candidate intends to undertake in the following 12 months.

Oral presentation

In their final year, candidates are required to give a final  oral presentation  on their research, usually three months before submitting their thesis.

Read more about  research candidate milestones .

Thesis submission and examination

The culmination of the PhD in Statistics is a written thesis which, upon completion, is submitted for examination. The thesis is examined by examiners who are experts in the relevant field.

For more information on the process, visit our page on  submitting a thesis .

For information about scholarships available to HDR candidates, visit our page on  scholarships and fees .

Read details of some of our alumni’s recent  job placements .

See our list of current  Statistics PhD students .

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Paul Leopardi

Visiting fellow.

Brief history

Academic: BSc (Hons in Computer Science), University of New South Wales, 1983-10-05. MCom (Information Systems), University of New South Wales, 1990-05-04. Master of Science and Technology by coursework in Mathematics, University of New South Wales, 2002-04-09. Doctor of Philosophy in Applied Mathematics, University of New South Wales, 2007-05-17, supervised by Professor Ian Sloan and Associate Professor Rob Womersley. Grad. Cert. in Higher Education, Australian National University, 2012-07-12. Working: Telecom Australia 1983-1986 - Computer Systems Officer. Memorex-Telex 1986-1990 - Systems Engineer. Travel Industries Automated Systems 1990-1995 - Systems Analyst. Accenture 1995-2001 - Consultant. UNSW 2001-2002 - Research assistant programmer, Mathematics. University of Sydney 2005-2007 - Scientific Computing Officer, Physics. ANU 2007-2012 - Postdoctoral Research Fellow, Mathematics. ANU 2012-2014 - Research Fellow, Bioinformation Science.

Research interests

Constructive approximation: sparse grids, approximation and quadrature on the sphere and compact manifolds. Clifford algebras: Clifford analysis, new constructions for Hadamard matrices. Combinatorics and statistics: random number generation and testing, combinatorics and statistics of words in sequences. Numerical analysis: object-oriented numerical analysis, parallel linear algebra using ScaLAPACK .

Distributing points on the sphere: Partitions, separation, quadrature and energy , UNSW, 2007. ( Citations ). Accompanying Thesis/Dissertation Sheet.

Publications and preprints

Describes methods used to parallelize code used in optimization on the sphere.

Describes algorithms used in the GluCat C++ software library, for the real representations of real Clifford algebras, having the same order of complexity as the generalized FFTs on finite groups.

Describes the algorithm used in the EQSP software package, which partitions a finite dimensional unit sphere into regions of equal area and small diameter.

Examines the relationship, for a positive weight quadrature rule on the unit sphere, between the the total quadrature weight on any spherical cap and the area of that cap. Uses conjectures from [5] to give improved estimates.

Describes new conjectures on monotonicities of the values and the zeros of functions related to Jacobi polynomials with fixed \alpha and \beta and increasing degree.

Gives bounds for the Coulomb energy of a sequence of well separated spherical designs on the unit sphere, including a conjectured bound comparable to the minimum Coulomb energy.

Describes methods used to parallelize code used in optimization on the sphere, and analyzes performance of the code in relation to the topology of the computer cluster used for testing.

Proves diameter bounds for the sphere partition described in [3], and a modified version of the construction of Feige and Schechtman.

Examines implementations of the overlapping serial tests of Marsaglia and Zaman, and improves them, using accurate calculation of the mean and variance of the number of missing words in a random string.

Describes how the Clifford algebras over the real numbers can be treated as real matrices, except in the case of negative real eigenvalues, when the square root and logarithm functions may take values in a larger Clifford algebra.

Describes a dimension adaptive algorithm for sparse grid quadrature on reproducing kernel Hilbert spaces on the unit torus, and compares this algorithm to the WTP algorithm of Wasilkowski and Wozniakowski.

Shows that a sequence of spherical codes with a well behaved upper bound on discrepancy and a well behaved lower bound on separation, satisfies an upper bound on Riesz s-energy.

Describes work in progress, towards the formulation, implementation and testing of compatible discretization of differential equations, using a combination of Finite Element Exterior Calculus and discrete Geometric Calculus / Clifford analysis.

Describes how the pattern of commuting and anticommuting pairs of basis elements of a real Clifford algebra, and their representation theory, can be used in the construction of Hadamard matrices.

Describes sparse grid quadrature on products of spheres, giving the initial and asymptotic rates of convergence.

Examines the D2 statistic, which counts the number of word matches between two given sequences, under the assumptions of periodic boundary conditions and Markovian dependence. Includes the calculation of the mean of D2 for all Markov orders and the variance for Markov order 1.

Further examines the D2 statistic, which counts the number of word matches between two given sequences, under the assumptions of periodic boundary conditions and Markovian dependence. Includes the calculation of the mean of D2 for all Markov orders and the variance for all Markov orders up to and including the word length. Also includes a comparison of synthetic data with DNA data from human chromosome 1.

Proves that, for a smooth compact connected d-dimensional Riemannian manifold M, if 0 <= s <= d then an asymptotically equidistributed sequence of finite subsets of M that is also well-separated yields a sequence of Riesz s-energies that converges to the energy double integral.

Adapts the techniques of finite element exterior calculus to study and discretize the abstract Hodge-Dirac operator, a square root of the abstract Hodge-Laplace operator considered by Arnold, Falk, and Winther.

Examines a pair of bent functions on and their relationship to a necessary condition for the existence of an automorphism of an edge-coloured graph, whose colours are defined by the properties of a canonical basis for the real representation of a real Clifford algebra.

Constructive approximation

• The Coulomb energy of spherical designs on S^2, 2003.
• A partition of the unit sphere into regions of equal area and small diameter, 2004.
• Partitions of the unit sphere into regions of equal area and small diameter, 2005.
• Movie of the partition EQ(3,99) [MS MPEG4 V2 AVI file], [MPEG4 file], [MPEG4 Quicktime MOV file], 2006.
• The Riesz energy of point sets on the unit sphere under weak-star convergence, 2005.
• Positive quadrature on the sphere and conjectures on monotonicities of Jacobi polynomials, DWCAA06, AustMS, 2006.
• Spherical codes with good separation, discrepancy and energy, HDA, ICIAM, AustMS, 2007. HDA talk handout, 2007.
• Porting a sphere optimization program from LAPACK to ScaLAPACK, CTAC 2008.
• Polynomial interpolation on the sphere, reproducing kernels and random matrices, MASCOS Workshop on Stochastics and Special Functions, 2009.
• Quadrature using sparse grids on products of spheres, HDA, MASCOS AGM, ANZIAM NSW/ACT Branch Mini Meeting, 2009.
• The rate of convergence of sparse grid quadrature on products of spheres, MCQMC, AustMS, 2010.
• The rate of convergence of sparse grid quadrature on the torus, CTAC 2010.
• Sparse grid quadrature as a knapsack problem, HDA 2011.
• Sparse grid quadrature on products of spheres, ANU, University of Canterbury, 2012.
• Discrepancy, separation and energy on spheres and on compact connected Riemannian manifolds, DWCAA, ANU, 2012.
• Discrepancy, separation and Riesz energy of finite point sets on compact connected Riemannian manifolds, Vanderbilt U, ESI Vienna, Bergamo, 2014.
• Applications of equal area partitions of the unit sphere, ORNL, 2014.
• Approximate Fekete points and discrete Leja points based on equal area partitions of the unit sphere, CTAC, ANU, 2014.

Clifford algebras

• Practical computation with Clifford algebras, 2002.
• A generic library of universal Clifford algebra templates, (poster) 2002.
• Quick introduction to Clifford algebras, 2003, ( Citations ).
• A generalized FFT for Clifford algebras, 2003.
• Martin Albrecht, Synergy Effects: a Sage introduction, updated and edited by Paul Leopardi, CLUG, 2008.
• Approximating functions in Clifford algebras, ANZMC 2008.
• Approximation of the square root and logarithm functions in Clifford algebras: what to do in case of negative eigenvalues? (poster) DWCAA09, 2009.
• Approximating functions in Clifford algebras: What to do with negative eigenvalues? AustMS 2009, ( AGACSE 2010 short version ), ( AGACSE 2010 long version ).
• Can compatible discretization, finite element methods, and discrete Clifford analysis be fruitfully combined? ICCA 9, 2011.
• Is a dual mesh really necessary? ICIAM 2011.
• An abstract Hodge-Dirac operator and its stable discretization, IWOTA 2012, CTAC 2012, ICCA 10, 2014.
• Visualization as its own reward: The mathematics of conformal chaos, EViMS 2, ANU, 2014.

Combinatorics and statistics

• Testing the tests: using pseudorandom number generators to improve empirical tests, MCQMC, 2008.
• Accurate computation of the variance of the number of missing words in a random string, 4ICC, 2008.
• A conjecture on the alphabet size needed to produce all correlation classes of pairs of words, 34 ACCMCC, 2010.
• Amicability graphs and Clifford algebras, Hadamard Maximal Determinant Workshop, 2010.
• Constructions for Hadamard matrices, Clifford algebras, and their relation to amicability - anti-amicability graphs, 35 ACCMCC, 2011.
• New constructions for Hadamard matrices, CARMA Seminar, University of Newcastle, 2012.
• Determining the distribution of word matches between Markovian sequences, CTAC 2012.
• Alignment-free comparison of biological sequences, ANZIAM 2013.
• Skew, bent and fractious: a confession, AustMS, 2013.
• Representations of Clifford algebras: skew, bent and fractious, 37 ACCMCC, 2013.
• Twin bent functions and Clifford algebras, ADTHM 2014 (revised), Newcastle, 2014.
• Twin strongly regular graphs: some questions, relayed by Robert Craigen at Algebraic design theory with Hadamard matrices: applications, current trends and future directions (14w2199), 2014.

Other topics

• Lagrange multipliers. Mock lecture, University of Canterbury, 2012.
• SciPy 2013 Austin Texas: The Good, the Bad, and the Ugly (IPython notebook). (IPython notebook in NBViewer). Canberra Python Users Group, July 2013.
• Science Pathways for ANZIAM. Annual NSW/ACT ANZIAM Meeting, Sydney, November 2013.
• EQSP: Recursive Zonal Equal Area Sphere Partitioning Toolbox. ( Citations ).
• GluCat: Generic library of universal Clifford algebra templates. ( Citations ).
• SAFT: Sequence Alignment-Free Tool. (Forked from sylvainforet/saft ).
• Suprangen: Sydney University pseudorandom number generators.
• A129337 : Maximal possible degree of a Chebyshev-type quadrature formula with n nodes, in the case of the constant weight function on [ -1,1], May 2007.
• A152139 : Correlation classes of pairs of different words, November 2008.
• A152959 : Number of correlation classes for pairs of different words in an alphabet of size 4, December 2008.

Research project proposals and grants

• 2010-2013: ARC Discovery DP1095941: Solving problems in physics and engineering involving differential and integral equations by means of mutivariate approximation theory and Clifford algebras (not funded).
• 2011-2014: ARC Discovery DP110101392: Approximating the solution of problems in physics and engineering by means of discrete geometric calculus (not funded).
• 2012-2015: ARC DECRA DE120100028: High performance computation in Grassmann and Clifford algebras, with applications to number theory and partial differential equations (not funded).
• 2013-2015: ARC DECRA DE130100402: New approaches to the discretization of partial differential equations (not funded).
• 2013-2015: ARC Discovery DP130101924: New constructions for Hadamard matrices (not funded).
• 2013 NCI ANU Time Grant xc2: New constructions for Hadamard matrices

Conference, session and user group organization

• Clifford minisymposia at ICIAM 2003, 7-11 July 2003 (Sydney, Australia).
• 8th Australian Space Science Conference (ASSC), 29 September - 1 October 2008 ( ANU ). Public lecture: Life on Mars: Phoenix and Beyond, 1 October 2008 ( ANU ).
• HDA09 - Third Workshop on High-dimensional Approximation, 16-20 February 2009 ( UNSW, Sydney, Australia).
• 34 ACCMCC - Australasian Conference on Combinatorial Mathematics and Combinatorial Computing, 6-10 December 2010 ( ANU ).
• Thematic session on Continuous and discrete Clifford analysis at IWOTA 2012, 16-20 July 2012 ( UNSW, Sydney, Australia).
• NECTAR Early Career Academics Retreat, 4-5 June 2013 (Mt Stromlo, Australia).
• Canberra Python Users Group (2013) (Google+ Community) (Wiki) (with Jay Larson,Ed Schofield and Padarn Wilson).
• Session on Reproducibility in Computational Scientific Research, Mathematics of Plate Earth (MPE) Australia 2013, 8-12 July 2013 (Melbourne, Australia).
• My Google Scholar Citations

Mentions in acknowledgements and elsewhere

• J. Richardson, "The Blockhandler and the Bitfield Package", J. Symbolic Computation (1992) 14, 93-101, [Acknowledgements, p. 100].
• M. Ganesh, I. G. Graham, "A high-order algorithm for obstacle scattering in three dimensions", J. Comput. Phys. 198 (2004), no. 1, 211-242, [Acknowledgements, p. 239].
• D. P. Hardin, E. B. Saff, "Discretizing manifolds via minimum energy points", Notices Amer. Math. Soc. 51 (2004), no. 10, 1186-1194, [mention, p. 1189].
• I. H. Sloan, R. S. Womersley, "Extremal systems of points and numerical integration on the sphere", Adv. Comput. Math. 21 (2004), no. 1-2, 107-125, [Acknowledgements, p. 124].
• P. J. Forrester, N. S. Witte, "Discrete Painlevé equations for a class of PVI tau-functions given as U(N) averages", Nonlinearity 18 (2005), no. 5, 2061-2088, [Acknowledgements, p. 2087].
• G. Bard, "Matrix Inversion (or LUP-Factorization) via the Method of Four Russians, in Theta(n3/log n) Time", (preprint), 2008, [Acknowledgements, p. 6].
• N. J. Higham, Functions of matrices: theory and computation, SIAM, 2008, [reference to GluCat, p. 47 (not seen by Google Scholar)].
• Sacha van Albada, "Mean-Field Analysis of Basal Ganglia and Thalamocortical Dynamics", PhD thesis, University of Sydney, 2009, [Acknowledgements, p. v].
• R. Koekoek, P. A. Lesky, R. F. Swarttouw, Hypergeometric Orthogonal Polynomials and Their Q-Analogues, Springer Monographs in Mathematics, 2010, [reference 244, p. 221 (not seen by Google Scholar).].
• Jorg Arndt, "Generating Random Permutations", PhD thesis, ANU, 2010, [Acknowledgements, p. vii].
• Congpei An, "Distribution of Points on the Sphere and Spherical Designs", PhD thesis, The Hong Kong Polytechnic University, 2011, [Acknowledgements, p. iii].
• Shi Bai, "Polynomial Selection for the Number Field Sieve", PhD thesis, ANU, 2011, [Acknowledgements, p. vii].
• M. Holst, A. Stern, "Geometric Variational Crimes: Hilbert Complexes, Finite Element Exterior Calculus, and Problems on Hypersurface", Foundations of Computational Mathematics, (2012) 12:263-293, DOI: 10.1007/s10208-012-9119-7, [Acknowledgements].
• M. Holst, A. Stern, "Semilinear Mixed Problems on Hilbert Complexes and Their Numerical Approximation", Foundations of Computational Mathematics, (2012) 12:363-387, DOI: 10.1007/s10208-011-9110-8, [Acknowledgements].
• Vikram Sunkara, "Analysis and Numerics of the Chemical Master Equation", PhD thesis, ANU, 2013, [Acknowledgements, p. vii].
• L'Infinit: the unfinished business of mathematics (my mathematical blog).
• My profile on Mendeley.
• My profile on Academia.edu.
• My profile on Linkedin.
• My profile on Google+.
• My articles on arXiv.
• My mathematical genealogy.
• My profile on Facebook.
• Monte Carlo and Massively Parallel Computing (Fred Hickernell's discussion at MCQMC2012 ).

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Dr Priya Dev

Priya holds a PhD in mathematics from ANU and has over ten years experience as a lecturer and researcher at ANU, Columbia University & UNSW. Her research has focussed on mathematics for finance and she has applied this research to consult to ASX listed companies. Priya also co-founded a financial technology startup that provides online ordering and analytics to the hospitality sector. Her current interests involve the valuation of decentralised digital assets and the exploration of decentralised business models. The future of distributed energy production presents interesting opportunities to create digital assets or smart contracts that facilitate the efficient trading of energy at the household level. Priya is collaborating with Spot Energy on a seed linkage project to explore digital assets in this context

Research interests

Priya's current interests involve the valuation of decentralised digital assets and the exploration of decentralised business models. The future of distributed energy production presents interesting opportunities to create digital assets or smart contracts that facilitate the efficient trading of energy at the household level. Priya is collaborating with Spot Energy on a seed linkage project to explore digital assets in this context

• Researcher, Energy economics and policy

Updated:   25 August 2021 / Responsible Officer:   College of Science / Page Contact:   https://iceds.anu.edu.au/contact

ANU College of Science

Master of Mathematical Sciences (Advanced)

A Master of Mathematical Sciences (Advanced) will upgrade your broad skills in the mathematical sciences, while allowing you to develop your own area of expertise. 

You will learn from academics active at the very cutting edge of mathematics research,  and graduate with a degree from Australia's national university, internationally renowned for excellence in mathematical education.

You can tailor the Master of Mathematical Sciences (Advanced) to meet your particular study needs and research interests. Choose from subject areas including pure mathematics, mathematical modelling, bioinformatics, fractal geometry and applications to digital imaging, number theory and cryptography, scientific and industrial modelling, computational mathematics, and applications of mathematics.

You can also pursue study in related disciplines such as statistics, computer science, financial mathematics and econometrics, physics, and the biological sciences.

The program incorporates a year-long research project which you will complete under the supervision of one of our leading researchers. If you are looking for a coursework-only program, consider the Master of Science in Mathematical Sciences also offered by ANU.

Commonwealth Supported Places (CSP) are available for this program.

• #1 in Australia for Mathematics (THE 2024)
• World-class facilities
• Study part time or full time
• Semester 1 & 2 intake
• #1 in Australia for graduate employability ( Times Higher Education )
• Commonwealth Supported Places (CSP) are available for this program
• Available as an advanced degree

Testimonials

Shuaige Qiao

“My favourite thing is the flexibility of choosing courses. If you just went to lectures and exams every semester it would be boring. You need to try other ways to learn, like reading courses or courses in special topics, which only have five or six students, so you can talk to your teacher."

Jiannan Yang

"There were some courses I knew would be challenging before I enrolled in them, but one of those, called Analysis 2, ended up being a favourite of mine. The pace of learning and the problems set for us were appropriate for what we were learning. This course really boosted my confidence from the very first semester."

A Master of Mathematical Sciences (Advanced) is a stepping stone to further academic research, such as for a PhD.

The degree will also make you highly employable in Australia and across the world in fields including:

• Financial, computer, environmental and/or industrial modelling
• Research and analysis
• Science communication
• Lecturing, teaching and education.

Roles our graduates hold include Associate, Quantitative Applications Division at Macquarie Group; Lecturer, Sanata Dharma University (Indonesia); and Visiting Assistant Professor of Managerial Economics and Decision Sciences, Kellogg School of Management (USA).

The Australian National University has been ranked as the top university for graduate employability in Australia in the Global University Employability Ranking 2023-24 . As a student at ANU, you gain access to the ANU CareerHub – an online career development and employability tool that includes a jobs board and careers resources. You also have access to drop-in chats with a career consultant and to attend our career fairs to meet potential employers.

Learning experience

ANU professor solves decades-old maths problem

For twenty years, the best alegbraists in the world tried, and failed, to solve a famously difficult problem.

How a frog-loving maths-hater became a mathematician

Dr Xia Hua is a mathematical biologist at ANU, specialising in evolutionary theory. Find out how she learned to love maths - thanks to frogs.

There's a code built into the ANU maths building - can you crack it?

“People solve Sudoku or crosswords or cryptograms for fun and, in some ways, the skills you need to solve those puzzles are the exact skills that you need as a classical cryptographer.”

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Anand  is an algebraic geometer with broad interests. He is a graduate of Harvard and MIT, and is interested in classical algebraic geometry, enumerative geometry, deformation theory, algebraic stacks, derived categories, among other things.

Watch the webinar

Learn about what it is like to study Mathematical Sciences at ANU. Hear from our current students Ivo Vekemans and Edmund Heng about their experiences and ask them any questions you may have.

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Master of Science in Mathematical Sciences

A single two year graduate award offered by the ANU College of Science

• Length 2 year full-time
• Minimum 96 Units
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Career options, learning outcomes, inherent requirements, further information.

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Admission Requirements

Credit granted, cognate disciplines, scholarships.

• Indicative Fees

Program Requirements

• Capstone Course

The Master of Science in Mathematical Sciences requires completion of 96 units which must consist of:

72 units from completion of the coursework component

A minimum of 24 units from completion of 8000-level courses

A minimum of 36 units must come from completion of courses from the discipline area MATH- Mathematics

The 96 units must include:

A minimum of 24 units from completion of 6000-8000 level MATH courses, excluding MATH6005

A minimum of 12 units from completion of integrative courses from the following list not previously taken:

MATH6209 Special Topic in Mathematical Sciences (6 units)

MATH6211 Topics in Mathematical Physics (6 units)

MATH6216  Advanced Topics in Algebra (6 units)

MATH8201 Topics in Computational Mathematics (6 units)

MATH8702  Mathematics Reading Course (6-24 units, which may be completed more than once under different topics)

MATH8705 Mathematics Special Topic (6 units, which may be completed more than once under different topics)

12 units from completion of Science and Society Courses from the following list:

ENVS6013 Society and Environmental Change (6 units)

SCOM6007 From Creativity to Impact: Science Communication Project Design (6 units)

SCOM6012 Communicating Science Online (6 units)

SCOM6015 Public Speaking About Science (6 units)

SCOM6016 Science, Journalism and Society (6 units)

SCOM6027 Science Politics (6 units)

SCOM6029 Science Communication and Planetary Crises (6 units)

SCOM6031 Misinformation, Disinformation, and Risk (6 units)

SCOM6032 Making Modern Science (6 units)

SCOM6501 Science Communication Strategy and Leadership (6 units)

SCOM8014 Communicating Science with the Public (6 units)

SCNC8000 Science Internship (6 units)

A maximum of 24 units from completion of courses from the following list:

MATH6005 Discrete Mathematical Models (6 units)

ECON6012 Optimisation for Economics and Financial Economics (6 units)

ECON6053 Game Theory (6 units)

EMET8005 Econometric Methods and Modelling (6 units)

6000-, 7000-, or 8000- level from the subject area COMP - Computer Science (maximum 6 units)

6000-, 7000-, or 8000- level from the subject area PHYS - Physics

6000-, 7000-, or 8000- level from the subject area STAT - Statistics

A maximum of 24 units from elective courses offered by ANU

Capstone Courses

Applicants must present a Bachelor degree or international equivalent

• with a minimum GPA of at least 5.0/7.0
• with at least 8 courses in a cognate discipline, which must also have a minimum GPA of 5.0/7.0.

The GPA requirement for this program must be met by both the program as a whole, as well as by the 8 courses in a cognate discipline. Where more than 8 cognate courses have been completed by the applicant, ANU will take the best 8 courses when assessing the cognate GPA.

The GPA for a Bachelor program will be calculated from (i) a completed Bachelor degree using all grades and/or (ii) a completed Bachelor degree using all grades other than those from the last semester (or equivalent study period) of the Bachelor degree. The higher of the two calculations will be used as the basis for admission.

Ranking and English language proficiency: At a minimum, all applicants must meet program-specific academic/non-academic requirements, and English language requirements. Admission to most ANU programs is on a competitive basis. Therefore, meeting all admission requirements does not automatically guarantee entry. In line with the University's admissions policy and strategic plan, an assessment for admission may include competitively ranking applicants on the basis of specific academic achievement, English language proficiency and diversity factors. Applicants will first be ranked on a GPA ('GPA1') that is calculated using all but the last semester (or equivalent) of the Bachelor degree used for admission purposes. If required, ranking may further be confirmed on the basis of:

• a GPA ('GPA2') calculated on the penultimate and antepenultimate semesters (or equivalent) of the Bachelor degree used for admission purposes; and/or
• demonstrating higher-level English language proficiency

Prior to enrolment in this ANU program, all students who gain entry will have their Bachelor degree reassessed, to confirm minimum requirements were met.

Further information: English language admission requirements and post-admission support

Diversity factors: As Australia’s national university, ANU is global representative of Australian research and education. ANU endeavours to recruit and maintain a diverse and deliberate student cohort representative not only of Australia, but the world. In order to achieve these outcomes, competitive ranking of applicants may be adjusted to ensure access to ANU is a reality for brilliant students from countries across the globe.

Assessment of qualifications: Unless otherwise indicated, ANU will accept all Australian Qualifications Framework (AQF) qualifications or international equivalents that meet or exceed the published admission requirements of our programs, provided all other admission requirements are also met.

Where an applicant has more than one completed tertiary qualification, ANU will base assessment on the qualification that best meets the admission requirements for the program. Find out more about the Australian Qualifications Framework:  www.aqf.edu.au .

Unless otherwise indicated, where an applicant has more than one completed tertiary qualification, ANU will calculate the GPA for each qualification separately. ANU will base assessment on the best GPA of all completed tertiary qualifications of the same level or higher.

ANU uses a 7-point Grade Point Average (GPA) scale. All qualifications submitted for admission at ANU will be converted to this common scale, which will determine if an applicant meets our published admission requirements. Find out more about how a 7-point GPA is calculated for Australian universities:  www.uac.edu.au/future-applicants/admission-criteria/tertiary-qualifications .

Applicants with a Bachelor Degree or Graduate Certificate in a cognate discipline may be eligible for 24 units (one semester) of credit.

Applicants with a Graduate Diploma or Honours in a cognate discipline may be eligible for 48 units (one year) of credit.

Mathematics, Statistics, Mathematical Economics, Mathematical Finance, Actuarial Studies, Computer Science, Bioinformatics

Indicative fees

Domestic Tuition Fees (DTF)

For more information see: http://www.anu.edu.au/students/program-administration/costs-fees

For further information on International Tuition Fees see: https://www.anu.edu.au/students/program-administration/fees-payments/international-tuition-fees

Fee Information

All students are required to pay the  Services and amenities fee  (SA Fee)@

The annual indicative fee provides an estimate of the program tuition fees for international students and domestic students (where applicable). The annual indicative fee for a program is based on the standard full-time enrolment load of 48 units per year (unless the program duration is less than 48 units). Fees for courses vary by discipline meaning that the fees for a program can vary depending on the courses selected. Course fees are reviewed on an annual basis and typically will increase from year to year. The tuition fees payable are dependent on the year of commencement and the courses selected and are subject to increase during the period of study.

For further information on Fees and Payment please see: https://www.anu.edu.au/students/program-administration/fees-payments

ANU offers a wide range of  scholarships  to students to assist with the cost of their studies.@

Eligibility to apply for ANU scholarships varies depending on the specifics of the scholarship and can be categorised by the type of student you are.  Specific scholarship application process information is included in the relevant scholarship listing.

For further information see the  Scholarships  website.

Upgrade your expertise in mathematical sciences with a Master of Science in Mathematical Sciences from ANU. In this program you can study a variety of courses tailored to your own interests and needs, ranging from pure mathematics to mathematical modelling, computational mathematics and applications of mathematics to many research areas (such as biology, astronomy, physics and environmental sciences), to related disciplines such as statistics, computer science, and econometrics.

Find out more about mathematical studies, the degree structure, the university experience, career opportunities and student stories on  our website.  Get the inside story on what it’s like to be an ANU student by visiting our  student blog.

ANU ranks among the world's very finest universities. Our nearly 100,000 alumni include political, business, government, and academic leaders around the world.

We have graduated remarkable people from every part of our continent, our region and all walks of life.

Roles our graduates hold include Associate, Quantitative Applications Division at Macquarie Group; Lecturer, Sanata Dharma University (Indonesia); and Visiting Assistant Professor of Managerial Economics and Decision Sciences, Kellogg School of Management (USA).

Areas such as biological sciences and computational science are also becoming increasingly reliant on advanced techniques from the mathematical sciences. The Master of Science in Mathematical Sciences will equip you with quantitative skills applicable to these areas and more.

• demonstrate high level knowledge in mathematical sciences;
• apply acquired knowledge in mathematical sciences to new problems;
• interpret, synthesize and critically analyse published literature of relevance to mathematical sciences;
• demonstrate theoretical and/or practical skills relevant to techniques and research methodology in mathematical sciences;
• critically analyse data within applications of mathematical sciences to reach independent conclusions;
• demonstrate a critical understanding of science in society;
• clearly communicate theory and results in both written and oral formats.

Information on inherent requirements is currently not available for this program.

Program advice:

Students have the option of applying to transfer to the Master of Mathematical Sciences (Adv) and undertaking a 24 unit research project if they satisfy the following requirements:

• have met the published admission requirements of the Master of Mathematical Sciences (Adv)
• achieve a minimum 70% weighted average mark in the initial 48 units of coursework
• have the approval of an identified supervisor, and 
• have completed compulsory courses in the Master Mathematical Sciences (Advanced). 

Students considering a transfer to the Masters of Mathematical Sciences (Adv) should read the program requirements early on to ensure they focus on courses most relevant to their potential areas of research.

Students who have completed 48 units and wish to exit the program have the option of transferring to graduate from a Graduate Diploma of Science.

Students who have completed 24 units and wish to exit the program have the option of transferring to graduate from a Graduate Certificate of Science.

Course offered by the College of Science:

An indicative list of courses offered by the College of Science can be found under current students page on the College website  via this link.

Academic Advice

Back to the Master of Science in Mathematical Sciences page

The first step to enrolling in your new program is to seek academic advice in order to discuss the courses you will be studying. This is done by making an appointment to meet with the program convener (details below).

Your academic advice session is a great opportunity to discuss with the convener the direction in which you want your studies to go. The convener will be able to advise you about course selection and content of courses that you will undertake as part of your program. Ideally you should bring along a copy of your academic record/academic transcripts as these will greatly assist your convener when giving you course advice.

To book an appointment you can email: [email protected]

Detailed enrolment information and instructions can be found at   https://www.anu.edu.au/students/program-administration/enrolment/enrol-for-the-first-time-as-a-coursework-student

Please follow each step carefully, and do not hesitate to reach out to the College Student Services Team if you need help.

There is additional information available from https://students.science.anu.edu.au/program-admin/new-masters-students

An indicative list of courses offered by the College of Science and College of Health & Medicine can be found here: https://students.science.anu.edu.au/program-admin/courses

Responsible Officer: Registrar, Student Administration / Page Contact: Website Administrator / Frequently Asked Questions

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PhD & MPhil Study Options

Doctor of Philosophy (PhD)

Full-time Doctor of Philosophy (PhD) students normally spend a minimum of three years at ANU, while part-time students spend up to six years. Candidates are normally required to submit a thesis of no more than 100,000 words and must meet the internationally recognised standard for the degree in the relevant discipline.

Master of Philosophy (MPhil)

Degrees of Master of Philosophy (MPhil) are designed for students who require an advanced research qualification, but who want a shorter degree program than the PhD. The MPhil program is offered on a full-time and part-time basis. It usually takes students between one and two years full-time, or between two and four years part-time, to complete.  Candidates are normally required to submit a thesis of no more than 60,000 words and must meet the internationally recognised standard for the degree in the relevant discipline.

CASS requires research students to complete coursework as part of their degree. This will include training on research methods, ethics and other topics as deemed appropriate by your supervisory panel.

Finding a supervisor

Identifying a potential primary supervisor is an important part of your graduate research application. Browse the ANU Researchers database to find and contact a potential supervisor to support your application. In most cases the School or Centre location of your potential supervisor will determine which School or Centre within CASS you will reside in. Please note, that once you have found a potential supervisor, any offer of supervision will be subject to you being formally offered admission to the program and meeting any conditions (if applicable).