faculty of science mathematics postgraduate …...2013 mathematics postgraduate handbook 3 welcome...

Faculty of ScienceMathematics Postgraduate Handbook

2013

| 2013 Mathematics Postgraduate Handbook 2

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

2013 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, Master of Arts or Master of Education), 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


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

Dr Steve Taylor Phone: +64 9 923 6622 or ext 86622 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

Dr Graham Donovan Phone: +64 9 923 8780 or ext 88780 Email: [email protected]

Head of the Algebra and Combinatorics Group

Associate Professor Steven Galbraith Phone: +64 9 923 8778 or ext 88778 Email: [email protected]

Head of the Analysis, Geometry and Topology Group

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

Second Semester: Associate Professor Tom ter Elst Phone: +64 9 923 6901 or ext 86901 Email: [email protected]

Head of the Applied Mathematics Unit

Associate Professor Vivien Kirk Phone: +64 9 923 8112 or ext 88112 Email: [email protected]

Head of Mathematics Education Unit

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

Head of Department

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

mailto:[email protected]










Important datesSummer School - 2013Lectures begin Friday 4 January

Auckland Anniversary Day Monday 28 January

Waitangi Day Wednesday 6 February

Lectures end Friday 15 February

Study break Saturday 16 February

Exams Monday 18 - Wednesday 20 February

Summer School ends Wednesday 20 February

Semester One - 2013Semester One begins Monday 4 March

Easter Break Friday 29 March - Tuesday 2 April

Mid-semester break Monday 22 - Saturday 27 April

ANZAC Day Thursday 25 April

Graduation Monday 6 May, Wednesday 8 May, Friday 10 May

Queen's Birthday Monday 3 June

Lectures end Friday 7 June

Study break Saturday 8 - Wednesday 12 June

Exams Thursday 13 June - Monday 1 July

Semester One ends Monday 1 July

Inter-semester break Tuesday 2 - Saturday 20 July

Semester Two - 2013Semester Two begins Monday 22 July

Mid-semester break Monday 2 - Friday13 September

Graduation Tuesday 24 September

Lectures end Friday 25 October

Study break Saturday 26 - Wednesday 30 October

Exams Thursday 31 October - Monday 18 November

Labour Day Monday 28 October

Semester Two ends Monday 18 November

Semester One - 2014Summer School begins Monday 6 January

Semester One begins Monday 3 March


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 dimensionReading courses, dissertations 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. Moreover, since 2006, it became a Faculty of Science 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.


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/uoa/home/about/our-research/postgraduate-research-topics/postgraduate-research-topics-in-pure-mathematics

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.

http://www.math.auckland.ac.nz/uoa/home/about/our-research/postgraduate-research-topics/postgraduate-research-topics-in-pure-mathematics


Associate Professor Jianbei An has received his PhD from the University of Illinois. He has been associated with the Mathemat-ics 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 combinato-rial 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.

Algebra and Combinatorics research staff

systems.Eamonn


Analysis, Geometry and Topology 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.

http://www.math.auckland.ac.nz/d.gauld


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, par-ticularly 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.

Over the past 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 would attend international workshops and some of their work has been published in well-quoted international journals.

For a list of postgraduate research topics in applied mathematics, see www.math.auckland.ac.nz/uoa/home/about/our-research/postgraduate-research-topics/postgraduate-research-topics-in-applied-mathematics

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.

http://www.math.auckland.ac.nz/uoa/home/about/our-research/postgraduate-research-topics/postgraduate-research-topics-in-applied-mathematics

http://www.math.auckland.ac.nz/uoa/home/about/our-research/postgraduate-research-topics/postgraduate-research-topics-in-applied-mathematics


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 recently com-pleted his PhD, examining the use of technology in the under-graduate mathematics curriculum. His principal research interests are in the teaching and learning of undergraduate and bridging

mathematics, with a particular focus on peer tutor-ing, 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 develop-ment 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 Auck-land since 1993, and has been engaged in research in mathemat-ics 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, MA or MEd programme.

MEU researchers work closely with academics from the Faculty of Education and are able to

Mathematics Education research staff

For a list of postgraduate research topics in mathematics education, please see www.math.auckland.ac.nz/uoa/home/about/ our-research

offer jointly-supervised projects, dissertations or PhD theses.

Mathematics education papers and research are credited under the Mathematics major offered by the department.

http://www.math.auckland.ac.nz/uoa/home/about/our-research/postgraduate-research-topics/postgraduate-research-topics-in-mathematics-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 16

Research topics for postgraduate studies 17

Applying for a postgraduate degree or diploma 17

Postgraduate courses offered in 2013 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: Dr Steve Taylor Phone: +64 9 923 6622 or ext 86622 Email: [email protected]

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

MSc or MA

PGDipSci

BSc(Hons) orBA(Hons)

Usually at least A- average

Minimum B- average

BSc or BA

GradDipSci

Equivalent degree

PhD

Minimum B average




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 at least B in at least 90 points of courses at Stage III. These courses need not all be in Mathematics.

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.

http://www.auckland.ac.nz/calendar

http://www.auckland.ac.nz/calendar


If you are doing a BSc(Hons) in Applied Mathematics, you must pass MATHS 361 and MATHS 340 with 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, you must either do a 120 point thesis or a 90 point thesis and 30 points of other courses. Depending on your research topic,

you can do an MSc in Mathematics, Applied Mathematics, Bioinformatics or Logic and Computation, an MA in Mathematics or an MEd in a Mathematics Education subject.

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.

You need to pass eight 15-point courses at either 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 2012, 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]

The University of Auckland will be open for enrolment from November 2012 to the end of February 2013. You are welcome to attend at any time during normal office hours to seek academic or enrolment advice or assistance in completing your enrolment.



http://www.math.auckland.ac.nz/postgraduate

http://www.auckland.ac.nz/applynow



Postgraduate coursesPostgraduate courses offered in 2013MATHS Title

Summer Semester

707 Special Topic in Mathematics Education 1: Mathematical Processes

792 Research in Mathematics Ed (MProfStuds)

Semester One

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

706 Technology and Mathematics Education

708 Special Topic in Mathematics Education 2: Analysing Mathematical Thinking

713 Logic and Set Theory

714 Number Theory

725 Lie Groups and Lie Algebras

731 Functional Analysis

761 Dynamical Systems

762 Nonlinear Partial Differential Equations

782 Advanced Topic(s) in Mathematics 2: Discrete Geometry

789 Advanced Topic(s) in Applied Mathematics 4: Inverse Problems

Summer Semester 2014

701 Research Skills in Mathematics Education

792 Research in Mathematics Ed (MProfStuds)


MATHS 701 Research Skills in Mathematics Education (15 points)

Prepares students for postgraduate study in mathematics and statistics education. Its emphasis is on workshops in the key research skills required by students working at this level. It will cover a range of research issues and techniques.

Recommended preparation: MATHS 302: Teaching and Learning Mathematics and one of MATHS 702-709 is recommended.

MATHS 706 Technology and Mathematics Education (15 points)

Practical and theoretical perspectives on the use of technology, including calculators and computers, in the mathematics classroom. A focus on teaching and learning through development of teacher familiarity with technology and identification of obstacles to its use.

MATHS 707 Special Topic in Mathematics Education 1: Mathematical Processes (15 points)

A new course designed to examine mathematical processes such as problem-solving, argumentation and proving, conjecturing, abstracting and generalising, and modelling. The focus will be on senior secondary and undergraduate mathematics.

Mathematics postgraduate courses overview*

MATHS 708 Special Topic in Mathematics Education 2: Analysing Mathematical Thinking (15 points)

Mathematical thinking is an elusive phenomenon for researchers to study. This course addresses three core questions regarding research on mathematical thinking:

1. What kinds of research environments will increase the likelihood of mathematical thinking occurring in forms that can be studied?

2. What research tools can capture, document and describe the mathematical thinking that occurs within these environments?

3. How can this mathematical thinking be analysed so that reliable distinctions can be made between different instances, to characterise for example, the strength, depth and stability of that mathematical thinking?

Students will learn a variety of research approaches for analysing the mathematical thinking of other learners and teachers.

MATHS 713 Logic and Set Theory (15 points) A study of the foundations of pure mathematics, formalising the notions of a “mathematical proof” and “mathematical structure” through predicate calculus and model theory. Explores the limits of these formalisations such as those posed by Gōdel’s Incompleteness theorems, and it includes a study of axiomatic set theory.

Prerequisite: MATHS 315 Mathematical Logic or PHIL 305 Advanced logic

*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.


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?

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)

A 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

Teaser: How much symmetry does a Rubik’s Cube have?

MATHS 725 Lie Groups and Lie Algebras (15 points)

Symmetries and invariants play a fundamental role in mathematics. Especially important in their study are the Lie groups and the related structures called Lie algebras. These structures have played a pivotal role in many areas, from the theory of differential equations to the classification of elementary particles.

Strongly recommended for students advancing in theoretical physics and pure mathematics.

Prerequisite: MATHS 320 Algebraic Structures and MATHS 332 Real Analysis

Strongly recommended: MATHS 340 Real and Complex Calculus and MATHS 333 Analysis in Higher Dimensions

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 Real Analysis

Strongly recommended: MATHS 333 Analysis in Higher Dimensions


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 Real Analysis and MATHS 333 Analysis in Higher Dimensions

Recommended preparation: MATHS 730 and MATHS 750.

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.


Strongly recommended: MATHS 333 Analysis in Higher Dimensions and MATHS 340 Real and Complex Calculus

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.


Strongly recommended: MATHS 333 Analysis in Higher Dimensions

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.

Prerequisites: B in MATHS 340 Real and Complex Calculus and MATHS 361 Partial Differential Equations

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.


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 769 Applied Differential 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 Real and Complex Calculus and MATHS 361 Partial Differential Equations

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 Numerical Computation and one of MATHS 340 Real and Complex Calculus, MATHS 361 Partial Differential Equations, MATHS 363 Advanced Modelling and Computation

MATHS 789 (Formerly PHYSICS 707) Advanced Topic(s) in Applied Mathematics 4: Inverse problems (15 points)

Inverse problems involve making inferences about physical systems from experimental measurements. Topics in this course include the linear inverse problem, regularisation, introduction to multidimensional optimisation, Bayes theorem, prior and posterior probabilities, physically-based likelihoods, inference and parameter estimation, sample based inference, computational Markov chain Monte Carlo and output analysis.

Prerequisite: PHYSICS 701, or MATHS 340 and MATHS 361

MATHS 782 Advanced Topic(s) in Mathematics 2: Discrete Geometry (15 points)

Discrete and combinatorial geometry is a relatively modern area of mathematics with wide-ranging applications in engineering, crystallography, computer-aided design, graphics, and pattern recognition. Topics will be chosen from the following: abstract and convex polytopes, point-line arrangements, symmetries of discrete geometric structures, regular maps, hyperplanes in discrete spaces, Groebner bases, polynomial ideals, algebraic geometry, applications.

Recommended preparation: Good background in at least two of algebra, geometry and combinatorics.

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: Real and Complex Calculus and MATHS 361: Partial Differential Equations


Further information

Student support services 24

Financial support for students 25

Mathematics department staff 26

Heading B


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

Careers Centre Room 001, The ClockTower +64 9 373 7599 ext 88727 [email protected] www.auckland.ac.nz/careers

Parenting Support (including childcare information)

+64 9 373 7599 ext 85894 (childcare information only)www.auckland.ac.nz/parenting-support

Chaplain’s Office 18 Princes Street +64 9 373 7599 ext 87731 or 87732 [email protected]

Disability Services Room 036, The ClockTower (South Wing)

+64 9 373 7599 ext 82936 [email protected]

Mediator’s Office +64 9 373 7599 ext 88905 [email protected] 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 84422Health Services (including counselling)

Level 3, Student Commons + 64 9 373 7599 ext 87681

Dental Services Level 3, Student Commons +64 9 373 7599 ext 83860International Students’ Information Centre

Auckland International Old Choral Hall

+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 Visit the Student Information Centre in the ClockTower

+64 9 373 7599 ext 87494 [email protected] www.auckland.ac.nz/scholarships

Student Advocacy Network (WAVE)

AUSA House 3 Alfred Street

+64 9 309 0789 ext 202 [email protected] www.auckland.ac.nz/wave

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

Student Learning (Tā te Ãkonga)

Level 3 Information Commons +64 9 373 7599 ext 88850 [email protected] www.slc.auckland.ac.nz

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

SciSpace G16, Ground Floor, Building 303 +64 9 373 7599 ext 85510 www.science.auckland.ac.nz/scispace

Students' Association AUSA, 4 Alfred Street +64 9 309 0789 [email protected] www.ausa.auckland.ac.nz

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


http://www.auckland.ac.nz/accommodation


http://www.auckland.ac.nz/careers




http://www.auckland.ac.nz/mediation

http://www.eo.auckland.ac.nz


http://www.auckland.ac.nz/international

http://www.auckland.ac.nz/recreation


http://www.auckland.ac.nz/scholarships


http://www.auckland.ac.nz/wave



http://www.slc.auckland.ac.nz

http://www.studylink.govt.nz

http://www.science.auckland.ac.nz/scispace


http://www.ausa.auckland.ac.nz

http://www.ubsbooks.co.nz

http://www.auckland.ac.nz/parenting-support


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/uoa/cs-postgraduate-scholarships

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. For example, if you are doing an MSc thesis full-time and you work 15 hours a week, your thesis will take several months more to complete than if you had no employment.

http://www.auckland.ac.nz/uoa/cs-postgraduate-scholarships

http://www.auckland.ac.nz/uoa/cs-postgraduate-scholarships




Mathematics department staffName Phone EmailAcademic StaffA/Prof Jianbei AN 923 8773 [email protected]

Prof Bill BARTON 923 8779 [email protected]

Dr Robert CHAN 923 5212 [email protected]

Prof Marston CONDER 923 8879 [email protected]

Dr Graham DONOVAN (PhD Adviser) 923 4771 [email protected]

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

A/Prof Steven GALBRAITH (Head Algebra and Combinatorics)

923 8778 [email protected]

Prof David GAULD 923 8697 [email protected]

Prof A. Rod GOVER (Head Analysis, Geometry, Topology)


Dr Sina GREENWOOD (Tuākana Programme Coordinator)


Dr Allison HEARD (Computer Labs Coordinator) 923 8816 [email protected]

Prof Jari KAIPIO 923 8818 [email protected]

A/Prof Vivien KIRK (Head Applied Mathematics Unit)


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 923 1816 [email protected]

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 923 5056 [email protected]


























Name Phone Email

Academic staffDr Judy PATERSON (Head Mathematics Education Unit)


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 (Honours and PGDipSci Coordinator)


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


Prof Michael THOMAS 923 8791 [email protected]

Dr Shayne WALDRON 923 5877 [email protected]

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 CentreLily LIOW (Coordinator) 923 9378 [email protected]

Jaya VENUGOPALAN (Manager) 923 5510 [email protected]




















www.math.auckland.ac.nz

Contact

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

http://www.math.auckland.ac.nz


http://www.math.auckland.ac.nz

faculty of science mathematics postgraduate …...2013 mathematics postgraduate handbook 3 welcome...

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