2014 - University of Auckland

www.math.auckland.ac.nz

Faculty of ScienceMathematics Postgraduate Handbook

2014Contact

Department of Mathematics

The University of Auckland

Private Bag 92019

Auckland 1142

New Zealand

0800 61 62 63

Phone: +64 9 923 5886

Fax: +64 9 373 7457

Email: [email protected]

Web: www.math.auckland.ac.nz

Physical Address

Department of Mathematics

The University of Auckland

Level 4, Building 303

38 Princes Street, Auckland

New Zealand

| 2014 Mathematics Postgraduate Handbook 2 2014 Mathematics Postgraduate Handbook | 3

Welcome

We extend a warm invitation to all qualified students to consider studying for a postgraduate degree or diploma in Mathematics at the University of Auckland.

If you enjoyed your experience as an undergraduate student in Mathematics and would like to enhance your skills and get a taste of leading edge research, you should consider pursuing graduate studies.

Postgraduate students in Mathematics can specialise in their area of choice and pursue their studies in depth. The department offers four postgraduate programmes – Bachelor of Science (or Arts) Honours, Masters degrees (Master of Science or Arts), a Postgraduate Diploma in Science, and a PhD programme.

A postgraduate qualification in Mathematics will provide you with advanced knowledge in mathematics. The experience of writing a dissertation or thesis provides skills that are in-demand by many employers. Graduates from the department take up positions in business, government, industry, research, planning, environmental organisations.

We will be pleased to welcome you as a postgraduate student in our department.

EAMONN O’BRIEN Head of Department, Mathematics

Disclaimer Although every reasonable effort is made to ensure accuracy, the information in this document is provided as a general guide only for students and is subject to alteration. All students enrolling at the University of Auckland must consult its official document, the University of Auckland Calendar, to ensure that they are aware of and comply with all regulations, requirements and policies.

Contents

Welcome 3

Contact and enquiries 4

Important dates 5

Why study Mathematics at the University of Auckland? 6

Fundamental Mathematics 7

Applied Mathematics 10

Mathematics Education 12

Postgraduate degree programmes 13

Degrees and diplomas in Mathematics and Applied Mathematics 14

Entry requirements 15

Applying for a postgraduate degree or diploma 17

Postgraduate courses 18

Mathematics postgraduate courses overview 19

Further information 23

Student support services 24

Financial support for students 25

Mathematics department staff 26

2014 Mathematics Postgraduate Handbook | 5| 2014 Mathematics Postgraduate Handbook 4

Contact and enquiriesPlease contact one of the following staff members for information about graduate study and research programmes in Mathematics at the University of Auckland.

Postgraduate advisers:

For Honours and Postgraduate Diploma students

Professor Marston Conder Phone: +64 9 923 8879 or ext 88879 Email: [email protected]

For Masters, International and Exchange students

Associate Professor Warren Moors Phone: +64 9 923 4746 or ext 84746 Email: [email protected]

PhD Adviser

Professor Rod Gover Phone: +64 9 923 8792 or ext 88792 Email: [email protected]

Head of the Algebra and Combinatorics Group

Associate Professor Ben Martin Phone: +64 9 923 1816 or ext 81816 Email: [email protected]

Head of the Analysis, Geometry and Topology Group

Semester 1: Associate Professor Tom ter Elst Phone: +64 9 923 7457 or ext 87457 Email: [email protected] Semester 2: Dr Shayne Waldron Phone: +64 9 923 5877 or ext 85877 Email: [email protected]

Head of the Applied Mathematics Unit

Professor Hinke Osinga Phone: +64 9 923 5056 or ext 85056 Email: [email protected]

Head of Mathematics Education Unit

Dr Judy Paterson Phone: +64 9 923 8605 or ext 88605 Email: [email protected]

Deputy Head of Department

Semester 1: Dr Philip Sharp Phone: +64 9 923 8884 or ext 88884 Email: [email protected] Semester 2: Associate Professor Tom ter Elst Phone: +64 9 923 7457 or ext 87457 Email: [email protected]

Head of Department

Professor Eamonn O’Brien Phone: +64 9 923 8819 or ext 88819 Email: [email protected]

2014 Academic Year DatesSummer School - 2014Summer School begins Monday 6 January

Auckland Anniversary Day Monday 27 January

Waitangi Day Thursday 6 February

Lectures end Friday 14 February

Study break Saturday 15 February

Examinations Monday 17 - Wednesday 19 February

Summer School ends Wednesday 19 February

Semester One - 2014Orientation Welcome Monday 24 - Friday 28 February

Semester One begins Monday 3 March

Mid-semester break/Easter Monday 14 - Saturday 26 April

ANZAC Day Friday 25 April

Graduation Monday 5, Wednesday 7, Friday 9 May

Queen’s Birthday Monday 2 June

Lectures end Friday 6 June

Study break Saturday 7 - Wednesday 11 June

Examinations Thursday 12 - Monday 30 June

Semester One ends Monday 30 June

Semester Two - 2014Semester Two begins Monday 21 July

Mid-semester break Monday 1 - Saturday 13 September

Graduation Tuesday 30 September

Lectures end Friday 24 October

Study break Saturday 25 - Wednesday 29 October

Labour Day Monday 27 October

Examinations Thursday 30 October - Monday 17 November

Semester Two ends Monday 17 November

Summer School - 2015Summer School begins Tuesday 6 January

Semester One - 2015Semester One begins Monday 2 March


Fundamental MathematicsStudents planning to take research projects or dissertations with pure mathematicians in the Department have a choice of supervisors amongst researchers at the top of their fields. Fundamental mathematics is represented by two research groups: Algebra and Combinatorics, and Analysis, Geometry and Topology. They conduct research and teach in analysis, algebra, combinatorics, group theory, number theory, topology, geometry, and graph theory.

Every year, the fundamental mathematics groups attract a significant number of international visitors, including world-renowned figures like John Conway, Marcus du Sautoy or Ian Stewart. Most of the visitors give seminars or colloquia talks, whilst some give public lectures or spend part of the semester lecturing a postgraduate course.

5-component link with Jones polynomial (t1/2 - t-1/2)4

Development and use of pure mathematical techniques for distinguishing knotted structures are applied to molecular biology (RNA strands and protein folding) and theoretical physics.

For an updated list of postgraduate research topics in fundamental mathematics, see www.math.auckland.ac.nz/pgresearch-pure-maths

If you are thinking about an honours degree, postgraduate diploma or masters in Mathematics, please get in touch with one or more of the people listed. Students are welcome to join one or several of the ongoing research projects or propose a research topic and choose a supervisor.

Why study Mathematics at the University of Auckland?Further your understanding of mathematics The idealists among us would hope that preparation for employment is not the sole reason for graduate study. There is always a pride in being accomplished in one’s profession, and in keeping up with the latest developments. Graduate-level courses in Mathematics bring you to the cutting edge of the subject, taught by highly qualified staff who are active in research and keen to communicate the background of their specialist field.

The department has particular strengths in pure and applied mathematics, as well as in mathematics education and offers world-class degree programmes at both undergraduate and postgraduate levels, including BSc, MSc and PhD.

Discover the research dimensionDissertations and theses provide a research “apprenticeship”, helping you gain valuable skills, as well as bringing you to the frontiers of knowledge and the thrill of discovery or the satisfaction of seeing mathematics at work.

Students in our department are strongly encouraged to give a research dimension to their graduate studies, through projects and dissertations. It is a requirement that the BSc(Hon) degree includes a 30-point research based component.

Open new career horizonsGraduate study in Mathematics opens up a world of possibilities. It can enable you to indulge your academic enthusiasm or satisfy your intellectual curiosity, at the same time providing you with advanced knowledge and problem-solving skills applicable in any number of fields. In this information-age, a postgraduate qualification in the mathematical sciences places you well for a career in business, education, industry or science. Attractive opportunities exist in biotechnology, computing, finance, meteorology, systems analysis, school and university teaching, and many other fields; and mathematics graduates with honours are particularly sought after.

Interdisciplinary mathematics: Application of finite element analysis, boundary element and collocation techniques are used to model the human heart and other organs.


Associate Professor Jianbei An has received his PhD from the University of Illinois. He has been associated with the Math-ematics Department since 1992 and has been recently working on the Alperin weight conjecture, the

Alperin-McKay conjecture, the Dade conjecture for some finite groups.

Professor Marston Conder is especially interested in combina-torial group theory, graph theory, discrete computation, and the symmetries of maps and surfaces. Marston has won a number of prestigious awards (including the

Senior Mathematical Prize at Oxford, a Fellowship of the Alexander von Humboldt Foundation, and a Hood Fellowship), and was elected a Fellow of the Royal Society of New Zealand in 1998 (and its Vice-President International from 2008) and was awarded a DSc degree by Oxford University the following year.

Associate Professor Steven Galbraith was appointed a Senior Lecturer in 2008. Prior to this appointment, a successful career took him from a Waikato degree in Mathematics, to an Oxford DPhil and culminated with

a Professorship at the Royal Holloway University London. Steven’s main research interests are in number theory and particularly the mathematical aspects of public key cryptography.

Associate Professor Dimitri Leemans completed all his studies at the Université Libre de Bruxelles where he obtained his Doctorate Degree in 1998. He joined the Department as a Senior Lecturer in 2011. His research

interests are in combinatorics, finite group theory, computational algebra and incidence geometry. He has won two awards from the “Classe des Sciences” of the “Académie Royale de Belgique” for his research on the geometry of the sporadic simple groups.

Associate Professor Ben Martin was appointed in 2011. He has a PhD in Mathematics from King’s College London. He did postdoctoral work at universities in Australia, Israel and the UK, then was a lecturer at

the University of Canterbury for seven years. Ben’s main research area is group theory and representa-tion theory, with applications to algebraic groups, infinite trees and asymptotic counting problems. Ben is also interested in applying algebra and geometry to other areas. He has worked on problems from quantum field theory, topology, neural networks and image recognition.

Professor Eamonn O’Brien’s primary research interests are algorithmic and computational aspects of group theory. He has published over 50 research papers in leading international journals, various conference papers,

chapters in books, and is co-author of a “Handbook for Computational Group Theory”. Implementations of his algorithms are distributed worldwide with the leading computational algebra systems.Eamonn re-ceived a PhD from the Australian National University in 1988. He joined the department in 1997.

Associate Professor Arkadii Slinko received his PhD and BSc degrees from the Sobolev Institute of Mathematics and joined the department in 1993. His current research interests are in: Mathematical Economics and,

in particular, Social Choice Theory, Decision Theory and mathematical theories of allocation of discrete resources; cluster analysis and applications; design of experiments and random matrices; mathemat-ics education of gifted students and mathematics competitions.

Analysis, Geometry and Topology research staff Algebra and Combinatorics research staff

Professor David Gauld’s inter-ests are in set theoretic topology, especially applications to non-met-risable manifolds, and topological properties of manifolds near the limit of metrisability. If you are interested in his collection of 100

topological properties equivalent to metrisability for a manifold go to www.math.auckland.ac.nz/d.gauld.

Professor Rod Gover received his MSc from Canterbury and his DPhil from Oxford. He joined the department in 1999, after several years spent in Australian universi-ties. His research interests include differential geometry, twistor theory

and mathematical physics. He is especially focused on a class of differential geometries known as parabolic geometries. This class includes conformal geometries, CR geometries, quaternionic geometries, projective differential geometries and many other structures. Rod coordinates the Geometric Analysis group and informal workshops.

Dr Sina Greenwood’s primary area of research is set theoretic topology and in particular non-metrisable manifolds and discrete dynamical systems. She is currently addressing a question which arises naturally from fixed point theorems

in topology: if f is an arbitrary self-map on a set X and P is some topological property, under what conditions can one endow X with a topology that satisfies P and with respect to which f is continuous? Her present focus is the case where P is connected compact Hausdorff.

Dr Igor Klep hails from the Univer-sity of Ljubljana, Slovenia. A major line of Igor’s studies concerns the classical question of real algebraic geometry: given polynomials p and q, is p positive where q is positive? His work focuses on different alge-

bras of polynomials and different notions of positivity based on various representations of algebras. This includes inequalities on eigenvalues or the trace of a free noncommutative polynomial applied to matrices. Igor heavily employs computer programming in his

research and has gained a remarkable expertise in Mathematica and Matlab.

Dr Sione Ma’u received his PhD from the University of Auckland. He worked at the University of the South Pacific before being ap-pointed as a lecturer at Auckland in 2011. His research interest is in pluripotential theory and its appli-

cations, and functions of several complex variables.

Associate Professor Warren Moors received his PhD from Newcastle in 1992. Warren works on problems that lie at the inter-face between functional analysis and general topology. In particular he has interests in Banach space

theory, Nonsmooth analysis and General Topology. His broad research interests are reflected in his 70 research papers that are published in leading interna-tional journals.

Associate Professor Tom ter Elst received his PhD from Eindhoven and - after a postdoc-toral fellowship at the Australian National University - lectured in this city for 15 years. Tom’s research in-terests are in the fields of harmonic

analysis, operator theory, geometric analysis, PDE, subelliptic and degenerate operators. His research is reflected in his book Analysis on Lie groups with polynomial growth and in over 50 research papers.

Dr Shayne Waldron holds a PhD from the University of Wisconsin-Madison. His research interests are in approximation theory. If one of the two Cartesian coordinates of a battleship is lost, then its position can no longer be determined.

It is possible to give three coordinates, so that its position can still be determined if one is lost. This is an example of what is called a finite tight frame. His recent work involves the theory and application of finite tight frames to areas such as signal analysis, quantum measurements and multivariate orthogonal polynomials.


Dr Robert Chan is a Senior Lecturer in the department. He graduated from Auckland with a PhD under Prof John Butcher and is an active member of the Numerical Analysis team. His interests are in numerical methods

for stiff ordinary differential equations, differential-algebraic equations and oscillator Hamiltonian problems, and scientific computation.

Dr Graham Donovan is an applied mathematician with research interests in both mathematical biology and optical systems. He completed his PhD at Northwestern University, and was a research fellow at the Auckland

Bioengineering Institute before joining the Depart-ment of Mathematics. Current research projects include multiscale modelling of the lung, focusing particularly on asthma; modelling the stochastic movement of T-cells within the lymph node; and simulation of optical communication systems, particularly rare events.

Applied MathematicsApplied Mathematics is an essential part of the development of advances in science and technology. Mathematical and computational techniques are used widely in areas such as the biological sciences, information technology, climatology, combustion and emission control, and finance and investment. The Department of Mathematics has an active research group in Applied Mathematics, and offers postgraduate courses and research supervision in a range of contemporary topics.

In the fields of applied and industrial mathematics, students are welcome to join our staff in exploring topics of the following research areas: non-linear dynamics, sea-ice in Antarctica, numerical methods, radio-carbon dating, cellular physiology, inverse porblems, the solar system, medical imaging, control theory or circuit theory.

In previous years, applied mathematics students have investigated topics such as modelling functions or mechanisms of the human body or modelling distribution of volcanic ashes; they have proposed mathematical techniques in applied neuroscience, generalisations of social laws (eg, Dodgson’s rule), or applications of graph theory to genealogy. They have attended international workshops and some of their work has been published in well-cited international journals.

For a list of postgraduate research topics in applied mathematics, see www.math.auckland.ac.nz/pgresearch-applied-maths

Applied Mathematics research staff

Professor Jari Kaipio’s research interests include all things computational, especially inverse problems. As for applications, he is not choosy and has consid-ered biomedical, industrial and geophysical problems. His current

focus is on the statistical framework of model reduc-tion and modelling of uncertainties in general. He co-authored the book Statistical and computational inverse problems as well as about 100 journal papers. He is a fellow of the Institute of Physics (UK).

Associate Professor Vivien Kirk’s research interests are in dynamical systems, being primar-ily concerned with understand-ing the qualitative behaviour of solutions to nonlinear differential equations. She is interested in

applying dynamical systems techniques to math-ematical models arising in a variety of physical and biological systems, with recent work being particularly in the area of mathematical models of cellular calcium dynamics.

Professor Bernd Krauskopf’s research is in dynamical systems theory and its applications to real-world problems. Topics he works on include: the computation and visualisation of dynamical phenomena, different types of

transitions to chaos, bifurcations as organising cen-tres, chaotic light in laser systems, the influence of delays in balancing tasks, strategies for mechanical hybrid tests, and the dynamics of aircraft as ground vehicles.

Professor Hinke Osinga specialises in the numerical computation and visualisation of invariant manifolds that arise in systems of ordinary differential equations. Her work is based on two guiding principles: 1) a picture

says more than a thousand words; and 2) you only really understand something if you can draw a picture of it. Hinke’s research has contributed to a better understanding of dynamical systems as varied as the chaotic Lorenz equations, models of hormone-secreting neuron cells, intracellular calcium dynamics, and shaking mechanical structures.

Dr Claire Postlethwaite has a PhD in Applied Mathematics from the University of Cambridge, and has since worked as a postdoctoral fellow at Northwestern University and at the University of Houston. Claire’s research interests are

primarily in applied dynamical systems, particularly nonlinear differential equations. More recently, she has started working with biologists on models of animal movement and behaviour.

Dr Philip Sharp received a PhD in fluid dynamics at the University of Canterbury. Philip is an applied mathematician who specialises in the development of numerical integrators for differential equa-tions and the use of simulations

to model the Solar System. He has a passion for Astronomy and gives courses on Astronomy through the Centre for Continuing Education. Philip offers theses and projects supervision in numerical analysis and computational astronomy.

Professor James Sneyd is interested in mathematical physiology, with a particular focus on cell signalling and cell biology. Current project is the study of asthma in airway smooth muscle and the study of how saliva

secretion works, or doesn’t. Mathematically, this involves the construction and numerical solution of reaction-diffusion equations. James works closely with a number of experimental laboratories in the US, which means that his students often get to travel to the US to see how things are done.

Dr Steve Taylor received his PhD from the University of Minnesota. Most of Steve’s research is in three areas of applied maths: Boundary Control Theory for systems modelled by partial differential equations (PDEs), Industrial

Mathematics, and Quantum Chemistry. Most of Steve’s other research is, like these areas, in the more general area of applications of differential equations.

Dr Shixiao Wang completed his PhD at the University of Paris VI, France. His research is in nonlin-ear partial differential equations (PDEs) and theoretical fluid mechanics, focusing on the stability theory of complicated

vorticity-dominant flows. His current projects include developing global and nonlinear stability theory for swirling flow and uncovering the physical mechanism leading to breakdown of a slender vortex. The research has a strong theoretical flavour, but is also combined by numerical and experimental approaches.


Professor Bill Barton’s main research area is mathematics and language (ethnomathematics). This includes fifteen years of research and development of the Māori mathematics vocabulary, which has developed into a considera-

tion of communicating mathematics in non-Indo-European languages. His second research area is undergraduate mathematics teaching and learning, and a further area of interest is mathematical knowl-edge for teaching.

Dr Greg Oates completed his PhD, examining the use of technol-ogy in the undergraduate math-ematics curriculum. His principal research interests are in the teach-ing and learning of undergraduate and bridging mathematics, with

a particular focus on peer tutoring, cooperative learning, technology, the transition from secondary to undergraduate mathematics, and professional development of tertiary mathematics lecturers.

Dr Judy Paterson taught at high schools in South Africa and New Zealand before joining the University in 1997 to establish the secondary diploma course for mathematics teachers. She has had leading roles in a variety of outreach programmes to teachers both in schools and in

a range of tertiary institutions. Her doctoral study and ongoing interest is in professional development with a mathematics content focus and in the ways a teacher or lecturer’s relationship with mathematics impacts on their teaching.

Professor Mike Thomas has been at the University of Auckland since 1993, and has been engaged in research in mathematics education since 1983. He has published 150 refereed research papers in the

fields of secondary algebra, technology, calculus and linear algebra, advanced mathematical thinking, mathematical pedagogy and educational cognitive neuroscience. He has completed the supervision of seven PhD students.

Dr Caroline Yoon spends most of her time wondering about the nature of mathematical knowledge: How do leaps of mathematical insight occur, and what can be done to bring them about more predictably? Her

research involves designing mathematical activities that encourage leaps of mathematical insight, and analysing secondary and tertiary students’ (and sometimes their teachers’) mathematical thinking.

Mathematics EducationThe Mathematics Education Unit (MEU) offers a suite of graduate courses that can be taken either as part of a BSc(Hons), PGDipSci, MProfStuds, MSc or MA programme.

MEU researchers work closely with academics from the Faculty of Education and are able to offer jointly-supervised projects, dissertations or PhD theses.

Mathematics education papers and research are offered under the Mathematics major.

Mathematics Education research staff

For a list of postgraduate research topics in mathematics education, please see www.math.auckland.ac.nz/pgresearch-maths-education

Postgraduate degreeprogrammes

Degrees and diplomas in Mathematics and Applied Mathematics 14

Entry requirements for postgraduate programmes 15

Bachelor of Science and Arts (Honours) 15

Master of Science 16

Postgraduate Diploma in Science 16

Graduate Diploma in Science 17

Research topics for postgraduate studies 17

Applying for a postgraduate degree or diploma 17

Postgraduate courses offered in 2014 18

Mathematics postgraduate courses overview 19


Degrees and diplomas in Mathematics and Applied MathematicsThe Department of Mathematics encourages students to pursue their studies to postgraduate levels and to follow their interests in the field by taking the opportunities provided for self-directed research.

At the University of Auckland, students can start a degree (or a diploma) in either the first or the second semester of a given academic year.

There are a number of possible graduate programmes you can enrol in after getting your BSc or BA in Mathematics or Applied Mathematics, with the most common being BSc(Hons) or BA(Hons) or PGDipSci.

The postgraduate advisers for the Department of Mathematics guide students in their choice of a programme that is most appropriate for their needs and qualifications.

The Mathematics postgraduate advisers establish the eligibility of a student to enrol in a graduate degree or diploma and, once the student is admitted by the University, approve their enrolment in the postgraduate courses of their choice.

The information below summarises the regulations for the various degrees. In the next section you will find a list of graduate courses that are planned to be offered next year.

For further help, you are welcome to contact

Honours and Postgraduate Diploma Coordinator: Professor Marston Conder Phone: +64 9 923 8879 or ext 88879 Email: [email protected]

Masters, International and Exchange students Coordinator: Associate Professor Warren Moors Phone: +64 9 923 4746 Email: [email protected]

Entry requirements The information below summarises the prerequisites and requirements for the postgraduate degrees and diplomas in mathematics, available at the University of Auckland.

A degree (or diploma) is obtained after having passed 120 points worth of postgraduate courses. A regular course is 15 points, while some research-based projects may be worth 30, 45 or 60 points. A major for each of the graduate degrees is 75 points or more in the respective subject (Mathematics or Applied Mathematics).

These guidelines should be read in conjunction with The University of Auckland Calendar, which contains the official regulations and course requirements approved by the University. The Calendar is available at www.auckland.ac.nz/calendar.

Bachelor of Science (Honours) (BSc(Hons)) in Mathematics or Applied Mathematics

Bachelor of Arts (Honours) (BA(Hons)) in Mathematics

To be awarded a BSc(Hon) or a BA(Hons) you need to pass 120 points of 700-level courses, with at least 75 points in Mathematics (or Applied Mathematics).

To be admitted into the BSc(Hons)/BA(Hons) in Mathematics programme, you must have a major in Mathematics including MATHS 332 (Real Analysis) and either MATHS 320 (Algebraic Structures) or MATHS 328 (Algebra and applications), and passed at least 90 points of courses at Stage III (these courses need not all be in Mathematics) and obtained at least a B average over 3 papers in Mathematics above Stage II.

For BA(Hons) students must have passed the major requirements and met the GPA 5.0 (B) or higher in 45 points above Stage II in MATHS.

MSc or MA

PGDipSci

BSc(Hons) orBA(Hons)

Usually at least A- average

Minimum B- average

GradDipSci

Bachelors DegreePhD

Minimum B averagenon Maths major

Maths major


If you are doing a BSc(Hons) in Applied Mathematics, you must pass MATHS 361 and MATHS 340 with preferably a B grade or higher before enrolling in the degree.

For BSc/BA(Hons), you will have to write an honours dissertation, under the supervision of a member of the Mathematics department. You will need to be enrolled in MATHS 776 (Honours dissertation in Mathematics or Applied Mathematics) while doing your dissertation.

You can do an honours degree either full-time over one year or part-time over two years. At graduation, your actual class of honours will depend on the average mark for the courses you attempt for your BSc(Hons), computed over all the papers attempted (passed or failed). An average greater than A- leads to first class honours, an average of B+ leads to 2nd class honours (1st division), an average of B or B- leads to 2nd class honours (2nd division). An average between C- and C+ will secure you a Postgraduate Diploma in Science, and not a BSc(Hons).

Master of Science (MSc) in Mathematics or Applied Mathematics

Master of Arts (MA) in Mathematics

Before being admitted into an MSc programme, you will need to get the approval of the Department of Mathematics, then find a supervisor for your thesis and have him or her complete a thesis proposal form.

The emphasis in an MSc is on original research.

Before you can enrol in an MSc you must have a BSc(Hons) or PGDipSci with sufficiently high marks in the required major. If you obtained your PGDipSci or BSc(Hons) degree from Auckland, you will need a B- average over at least 90 points of your courses, of which at least 75 points must be in 700-level (graduate level) courses.

To get an MSc/MA in Mathematics, you must either do a 120 point thesis or a 90 point thesis and 30 points of other courses. To get an MSc in Applied Mathematics you must do a 120 point thesis.

An MSc/MA can be done part-time over two years.

If your average mark for your masters degree is sufficiently high you will be awarded the degree with honours.

If you require more information about doing an MSc or MA, please contact the masters students coordinator.

Postgraduate Diploma in Science (PGDipSci)

This is a popular graduate programme for part-time study, possibly because you can take up to four years to complete it.

To be admitted into the PGDipSci programme, you must have a major in Mathematics including MATHS 332 (Real Analysis) and either MATHS 320 (Algebraic Structures) or MATHS 328 (Algebra and applications).

You need to pass eight 15-point courses at 700-level, with at least 75 points in the major (Mathematics or Applied Mathematics).

If your average marks for the courses of your PGDipSci are sufficiently high, you will be awarded the degree with distinction or merit.

If you failed your PGDipSci (too many failed courses, or discontinued the diploma without seeking an interruption), you will not be able to take another postgraduate diploma at the University of Auckland.

Graduate Diploma in Science (GradDipSci)

This diploma is at a lower level than a Postgraduate Diploma in Science. Students who enrol in this diploma are often transferring from other universities or hold a degree in another discipline than Mathematics or Applied Mathematics. If you have any questions about the programme, you should contact the undergraduate adviser at [email protected].

To get a GradDipSci, you must pass 120 points at Stage II and above, with at least 75 points (of the 120) Stage III or above.

You can do a GradDipSci in Mathematics or Applied Mathematics. Before you can enrol in a GradDipSci you must have a BSc or an equivalent degree. A GradDipSci can be done part-time over four years.

Research topics for postgraduate studies

Our postgraduate programmes are designed to take students to the cutting edge of their discipline. Postgraduate courses are taught by research-active staff who also supervise student self-directed projects, dissertations and theses.

Research staff in the department offer a broad range of honours dissertation and masters research topics in fundamental and applied mathematics, as well as mathematics education.

A list of proposed research topics is available online at www.math.auckland.ac.nz/postgraduate

Applying for a postgraduate degree or diplomaFor ALL students not enrolled at the University of Auckland in 2013, apply online at www.auckland.ac.nz/applynow. If you are unable to access our website, please call 0800 61 62 63 or visit the Student Information Centre.

Student Information Centre Room 112, Level 1 (Ground Floor) The ClockTower Building 22 Princes Street Auckland City Campus

Phone: +64 9 923 1969 or 0800 61 62 65 Email: [email protected] Open: Monday to Friday from 8am-6pm, and Saturday 9am-12noon during peak times.

The University of Auckland will be open for enrolment from November 2013 to the end of February 2014. You are welcome to attend at any time during normal office hours to seek academic or enrolment advice or assistance in completing your enrolment.


Postgraduate courses MATHS 703 Theoretical Issues in Mathematics Education (15 points)

An analysis of theoretical perspectives that inform research in mathematics education, with a focus on learning theories, both social and psychological, and their implications for teaching and learning in mathematics.

Recommended preparation: MATHS 302: Teaching and Learning Mathematics is recommended.

MATHS 712 Teaching and Learning in Algebra (15 points)

Recent theoretical perspectives on the teaching and learning of school and university mathematics are linked to the learning of either calculus or algebra. The focus is on the mathematics content, applications, and effective learning at school and university.

Recommended preparation: Students taking this course should normally have studied mathematics or statistics at Stage II.

MATHS 714 Number Theory (15 points)

A broad introduction to various aspects of elementary, algebraic and computational number theory and its applications, including primality testing and cryptography.

Prerequisite: MATHS 320 or B+ in MATHS 328

Teaser: Are 8 and 9 the only consecutive proper powers?

Mathematics postgraduate courses overview*

MATHS 715 Graph Theory and Combinatorics (15 points)

A study of combinatorial graphs (networks), designs and codes illustrating their application and importance in other branches of mathematics and computer science.

Prerequisite: MATHS 320 or B+ pass in MATHS 326 Teaser: Is it true that in any set of people where everyone is friends with at least three others, there is a subset of 2000 people that can join hands in a circle so that each person holds hands only with friends? MATHS 720 Group Theory (15 points)

This course covers the study of groups focusing on basic structural properties, presentations, automorphisms and actions on sets, illustrating their fundamental role in the study of symmetry, for example in crystal structures in chemistry and physics, topological spaces, and manifolds.

Prerequisite: MATHS 320

MATHS 721 Representations and Structure of Algebras and Groups (15 points)

Representation theory studies properties of abstract rings, groups and algebras by representing their elements as linear transformations of vector spaces or matrices, thus reducing many problems about the structures to linear algebra, a well-understood theory. The course is roughly divided into two parts. The first part covers general theory of representations, and the second covers representation theory of rings, groups and algebras.

Prerequisite: MATHS 320

*NB. Many courses are being offered in alternate semesters or years. At the University of Auckland, students can start a degree - and enrol in the respective dissertation or thesis - in either the first or second semester of a given academic year. Students taking Mathematics Education courses can also start a Postgraduate Diploma in Science or a masters research portfolio in the Summer Semester.

Postgraduate courses offered in 2014MATHS Title

Summer Semester

792 Research in Mathematics Ed (MProfStuds)

Semester One

703 Theoretical Issues in Mathematics Education

715 Graph Theory and Combinatorics

720 Group Theory

730 Measure Theory and Integration

740 Complex Analysis

750 Topology

763 Advanced Partial Differential Equations

769 Stochastic Differential and Difference Equations

770 Advanced Numerical Analysis

786 Advanced Topic(s) in Applied Mathematics 1: Mathematical Modelling

Semester Two

712 Teaching and Learning in Algebra

714 Number Theory

721 Representations and Structure of Algebras and Groups

731 Functional Analysis

735 Analysis on Manifolds and Differential Geometry

761 Dynamical Systems

762 Nonlinear Partial Differential Equations

764 Mathematical Biology


MATHS 762 Non-linear Partial Differential Equations (15 points)

A study of exact and numerical methods for non-linear partial differential equations. The focus will be on the kinds of phenomena which only occur for non-linear partial differential equations, such as blow up, shock waves, solitons and special travelling wave solutions.

Prerequisites: B in MATHS 340 and MATHS 361

MATHS 763 Advanced Partial Differential Equations (15 points)

A study of exact and approximate methods of solution for the linear partial differential equations that frequently arise in applications.


MATHS 764 Mathematical Biology (15 points)

A course introducing central concepts in mathematical biology, with emphasis on modelling physiological systems. The course will cover, firstly, a selection of topics in cell physiology, including enzyme kinetics, transport across biological membranes, and action potentials in neurons. Secondly, the course will include a selection of topics in organ physiology, possibly including such topics as muscle physiology, neuroendocrine cells, photoreceptor physiology, and the gastrointestinal system. Usually, the exact selection of topics in the second part of the course will be determined after consultation with the students in the class.

Prerequisites: B- in MATHS 340 and B- in MATHS 361

MATHS 730 Measure Theory and Integration (15 points)

Presenting the modern elegant theory of integration as developed by Riemann and Lebesgue, it includes powerful theorems for the interchange of integrals and limits so allowing very general functions to be integrated, and illustrates how the subject is both an essential tool for analysis and a critical foundation for the theory of probability. Recommended preparation for MATHS 731.

Prerequisite: MATHS 332 Strongly recommended: MATHS 333

MATHS 731 Functional Analysis (15 points)

Provides the mathematical foundations behind some of the techniques used in applied mathematics and mathematical physics; it explores how many phenomena in physics can be described by the solution of a partial differential equation, for example the heat equation, the wave equation and Schrōdinger’s equation.

Prerequisite: MATHS 332 and MATHS 333 Recommended preparation: MATHS 730 and MATHS 750.

MATHS 735 Analysis on Manifolds and Differential Geometry (15 points)

Studies surfaces and their generalisations, smooth manifolds, and the interaction between geometry, analysis and topology, it is a central tool in many areas of mathematics, physics and engineering. Topics include Stokes’ theorem on manifolds and the celebrated Gauss Bonnet theorem.

Prerequisite: MATHS 332 Recommended preparation: MATHS 333 and MATHS 340.

MATHS 740 Complex Analysis (15 points)

An introductory course to functions of one complex variable, including Cauchy’s integral formula, the index formula, Laurent series and the residue theorem. Many applications are given including a three line proof of the fundamental theorem of algebra. Complex analysis is used extensively in engineering, physics and mathematics.

Prerequisite: MATHS 332 Real Analysis

Strongly recommended: MATHS 333 and MATHS 340

MATHS 750 Topology (15 points)

Unlike most geometries, topology models objects that may be stretched. Its ideas have applications in other branches of mathematics as well as physics, chemistry, economics and beyond. Its results give a general picture of what might happen rather than precise details of when and where. The course covers aspects of general and algebraic topology.

Prerequisite: MATHS 332 Real Analysis

Strongly recommended: MATHS 333

MATHS 761 Dynamical Systems (15 points)

Mathematical models of systems that change are frequently written in the form of nonlinear differential equations, but it is usually not possible to write down explicit solutions to these equations. This course covers analytical and numerical techniques that are useful for determining the qualitative properties of solutions to nonlinear differential equations.



Further information

Student support services 24

Financial support for students 25

Mathematics department staff 26

MATHS 769 Stochastic Differential and Difference Equations (15 points)

Systems taken from a variety of areas such as financial mathematics, fluid mechanics and population dynamics can be modelled with partial differential equations and stochastic differential equations. This course uses such applications as the context to learn about these two important classes of differential equations.

Prerequisites: MATHS 340 and MATHS 361

MATHS 770 Advanced Numerical Analysis (15 points)

The use, implementation and analysis of efficient and reliable numerical algorithms for solving several classes of mathematical problems.

Prerequisites: MATHS 270 and one of MATHS 340, MATHS 361, MATHS 363

MATHS 786 Advanced Topic(s) in Applied Mathematics 1: Mathematical Modelling (15 points)

This course will cover concepts and examples in mathematical modelling. We will begin with the underlying concepts of why we build models, what makes a good model, and what models can teach us. The course will also cover a range of models in practice to demonstrate these ideas; these topics may include models from mathematical biology and physiology, engineering, finance, population dynamics, and more.

Recommended preparation: MATHS 340 and MATHS 361

MATHS 792 Research in Mathematics Education (30 points)

A portfolio of research work that will include a Research Case Study of a mathematics learner or teacher, a literature investigation and a research proposal for a larger study.

Prerequisites: 30 points from Stage II courses in Mathematics or Statistics. MATHS 202 may not be taken as a prerequisite for this course.


Financial support for studentsOur students and staff are strongly encouraged to apply for the appropriate scholarships and make the most of the various funding rounds that take place every year. This means that most of our senior postgraduate students will benefit from some type of funding.

See the Postgraduate scholarships web page for further details www.auckland.ac.nz/pgscholarships.

Within the Department of Mathematics, the main types of paid employment for graduate students are assignment marking and lab demonstrating. In addition, students are employed to run first-year tutorials and to help in the first-year assistance room.

Application forms can be obtained from the Department of Mathematics.

Assignment markingThere is a large amount of assignment marking (for undergraduate courses) each year. The Department pays Stage III and graduate students to do marking, and this employment is open to anybody with good grades in first and second year Mathematics courses.

For further information contact: Wendy Stratton Email: [email protected]

Computer lab demonstrating The department has two undergraduate computer labs it shares with the Department of Statistics. Each year, the department employs a small number of students to work in the labs as demonstrators. Naturally, these students must have a good working knowledge of the computers and software used in the labs.

Temporary tutorships There will be a limited number of opportunities for undergraduate tutoring in the department. The duties vary, but usually involve tutoring in the assistance room or being involved in the tutorials for our large Stage I and Stage II courses.

For further information contact: Wendy Stratton Email: [email protected]

Note: There is a trade-off between studying and (part-time) work. If you work too many hours a week, your studies will suffer.

Student support servicesService Location Contact detailsAccommodation and Conference Services

O’Rorke Hall, 16 Mount Street 0800 61 62 63 [email protected] www.auckland.ac.nz/accommodation

Career Development and Employment Services

Room 126, Ground Floor, The ClockTower

+64 9 373 7599 ext 88727 [email protected] www.auckland.ac.nz/careers

Parenting support (including childcare information)

www.auckland.ac.nz/parenting-support

Spiritual and religious support www.auckland.ac.nz/spiritual-support

Disability Services Room 036, The ClockTower (South Wing)

+64 9 373 7599 ext 82936 [email protected]

Mediator’s Office www.auckland.ac.nz/mediation

Equity Office Level 1, The ClockTower (East Wing)

+64 9 373 7599 ext 88211 (Student Equity) www.eo.auckland.ac.nz

Student Finance Room 108, The ClockTower +64 9 373 7599 ext 84422

Health Services (including counselling)

www.auckland.ac.nz/health-services

International Office Room G23, Old Choral Hall, 7 Symonds Street

+64 9 373 7513 [email protected] www.auckland.ac.nz/international

Recreation Centre Building 314, 17 Symonds Street +64 9 373 7599 ext 84788 www.auckland.ac.nz/recreation

Scholarships Office Room 012, The ClockTower +64 9 373 7599 ext [email protected]/scholarships

AUSA Advocacy Old Choral Hall, 7 Alfred Street +64 9 923 [email protected]

Student Information Centre Room 112, The ClockTower Phone: 0800 61 62 63 Fax: 0800 61 62 64 [email protected]

Student Learning Services (Tā te Ākonga)

Room 320, Level 3, Information Commons, 11 Symonds Street

+64 9 373 7599 ext 88850 [email protected] www.library.auckland.ac.nz/student-learning

Student loans and allowances StudyLink 0800 88 99 00 www.studylink.govt.nz

SciSpace and Science Student Resource Centre

G0402, Building 301 (access via the Science Student Plaza)

www.science.auckland.ac.nz/scispace

Auckland University Students’ Association (AUSA)

www.ausa.auckland.ac.nz

University Book Shop (UBS) Kate Edger Building +64 9 306 2700 www.ubsbooks.co.nz

Campus maps www.auckland.ac.nz/maps


Name Phone Email

Academic staffDr Judy PATERSON (Head Mathematics Education Unit)

923 8605 [email protected]

Dr Claire POSTLETHWAITE 923 8817 [email protected]

Dr Philip SHARP (Deputy Head of Department)


A/Prof Arkadii SLINKO 923 5749 [email protected]

Prof James SNEYD 923 7474 [email protected]

Wendy STRATTON (Markers and Tutors Coordinator)


Dr Stephen TAYLOR 923 6622 [email protected]

A/Prof Tom TER ELST (Head Analysis, Geometry, Topology - Semester 1)


Prof Michael THOMAS 923 8791 [email protected]

Dr Shayne WALDRON (Head Analysis, Geometry, Topology - Semester 2)


Dr Shixiao WANG 923 6629 [email protected]

Dr Caroline YOON 923 8740 [email protected]

Administrative staffAlexandra DUMITRESCU (Departmental Coordinator / PA to HoD)


Min-Ah LEE (Academic Administrator) 923 8777 [email protected]

Olita MOALA (Financial Administrator) 923 8743 [email protected]

Lynda PITCAITHLY (Department Manager) 923 8063 [email protected]

Subject librarianMichael PARKINSON (Librarian) 923 5858 [email protected]

Student Resource CentreDebbie HAEFELE (SRC Coordinator) 923 9378 [email protected]

Jaya VENUGOPALAN (Manager) 923 5510 [email protected]

Mathematics department staffName Phone EmailAcademic StaffMaryam ALAVI (International & Exchange Student Adviser)


A/Prof Jianbei AN 923 8773 [email protected]

Prof Bill BARTON 923 8779 [email protected]

Dr Robert CHAN 923 5212 [email protected]

Prof Marston CONDER (Honours and PGDipSci Coordinator)


Dr Julie DE SAEDELEER 923 2121 [email protected]

Dr Graham DONOVAN 923 4771 [email protected]

Dr Tanya EVANS (Undergraduate Coordinator) 923 8783 [email protected]

A/Prof Steven GALBRAITH 923 8778 [email protected]

Prof David GAULD 923 8697 [email protected]

Prof A. Rod GOVER (PhD Adviser) 923 8792 [email protected]

Dr Sina GREENWOOD (Tuākana Programme Coordinator)


Prof Jari KAIPIO 923 8818 [email protected]

A/Prof Vivien KIRK 923 8812 [email protected]

Dr Igor KLEP 923 8495 [email protected]

Prof Bernd KRAUSKOPF 923 5704 [email protected]

A/Prof Dimitri LEEMANS 923 8819 [email protected]

A/Prof Ben MARTIN (Head Algebra and Combinatorics)


Dr Sione MA’U 923 5865 [email protected]

A/Prof Warren MOORS (Masters & International Students Coordinator)


Garry NATHAN 923 4931 [email protected]

Dr Julia NOVAK (Undergraduate Coordinator) 923 4747 [email protected]

Dr Greg OATES 923 8605 [email protected]

Prof Eamonn O’BRIEN (Head of Department) 923 8819 [email protected]

Prof Hinke OSINGA (Head Applied Mathematics Unit)


mailto:[email protected]


































2014 - University of Auckland

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