School of Mathematical &

Information Sciences


July 1998





This news bulletin concerns the activities of staff, students and visitors in the Mathematics Department at the University of Auckland. Copies of this and earlier bulletins are available from the Department Office (Maths/Physics building, 38 Princes St, Auckland, Tel. (09) 373-7599 ext. 8743, FAX (09) 373-7457).

Bulletins can also be read from the Department’s WWW home page, at:



About the Department

The Department of Mathematics is one of three departments in the School of Mathematical & Information Sciences. It is based on two sites (City and Tamaki campuses) and comprises about 50 academic staff and well over 900 equivalent full-time students – making it one of the largest at the University of Auckland.

Within the Department there are two semi-autonomous units: the Applied & Computational Mathematics Unit (ACMU) and the Mathematics Education Unit (MEU). Some staff are involved in the Centre for Discrete Mathematics & Theoretical Computer Science (a joint venture between the Computer Science and Mathematics Departments). Also, an inter-Faculty Centre for the Applications of Mathematics and Statistics is in the process of being established.

The Department has particular research strengths in algebra, combinatorics, complex analysis, differential equations and mathematical modelling, functional analysis and operator theory, history of mathematics, mathematics education, numerical analysis, and topology.





Research Highlights

Teaching News


Appointments & Promotions

PhD Students & Graduands



Seminars & Conferences

Other Staff Activities

Recent Journal Publications





Retirement of Professor Peter Lorimer

On the 20th November 1997 the Department celebrated the achievements of Prof. Peter Lorimer with a special symposium focussing on his work. Peter received the Research Award of the NZ Mathematical Society in 1997 preceding his retirement in January 1998, so the symposium (held in conjunction with the annual Departmental Dinner) was well-timed. See further details later in this Bulletin.

Peter Lorimer was a student here at Auckland before obtaining his PhD under a Commonwealth Scholarship at McGill University (Montreal), and held positions at McGill and the University of Canterbury before taking up a Senior Lectureship in Mathematics at the University of Auckland in 1966. He was promoted to Associate Professor in 1973, elected as a Fellow of the Royal Society of NZ in 1988, and awarded a personal chair in 1991.

A summary of Prof. Lorimer’s research achievements was given by John Butcher in a centrefold article in the August 1988 issue of the NZ Mathematical Society Newsletter. The citation for the NZ Mathematical Society's Research Award reads "for a lifetime of achievements in mathematical research, especially for his contributions to the application of group theory in geometry and combinatorics, and to the structure and classification of finite projective planes".

Over the years Peter has lectured courses at all levels and supervised a good number of graduate students, many of whom have gone on to academic careers in the mathematical sciences. He has greatly contributed to the life and work of the Department, especially making us think about important issues such as equity and the quality of our courses.

The Department welcomes Peter Lorimer’s continued contributions as an Emeritus Professor.


Retirement of Mr Garry Tee

Garry Tee retired at the end of January after 30 years in this Department (and the Department of Computer Science). Garry’s contribution at Auckland was the subject of part of Prof. Butcher’s speech to LOGOS #3 published in Bulletin #4 - indeed that speech was dedicated to Garry.

After Garry Tee graduated from Auckland University College, his first job was to be a Computer (i.e. someone who computed) with an oil exploration team in northwest Australia. In 1958 he went to England to get into computing - quite literally, since on cold English winter days, he and 2 others used to huddle together inside the central processor of a DEUCE computer, basking in the radiation from 3500 glowing thermionic valves. He became a mathematician with English Electric Company, and in 1964 he became a foundation member of the Department of Mathematics at Lancaster University. In 1968 he returned to NZ as a Senior Lecturer in this Department. He worked mostly in numerical analysis, and translated many Russian papers and 5 books on numerical analysis.

However it is important to further note some of Garry’s notable achievements during this time. His unending ability to turn up snippets of mathematical history in New Zealand is a source of delight to this Department. He found very many relics of Charles Babbage, including one of the largest of the 7 fragments of Charles Babbage's Difference Engine No.1 (1822-1833). His uncovering of a Meccano analogue computer buried at the Museum of Transport and Technology, and his shaming of the Conservator into restoring it, is just one of many examples.

In the last two years, Garry has enlivened his lectures in the history of computing by producing, in 1996, the operator of the first computer, COLOSSUS, and in 1997, one of the people who tested many thousands of the valves required to build it. Both people he discovered in New Zealand, and he persuaded them to talk despite still being covered by the British Official Secrets Act.

At the 1998 NZ Mathematics Colloquium, Garry was awarded Life Membership of the NZ Mathematical Society. Garry is continuing to teach courses on the History of Computing and on the History of Mathematics.

Departmental Review

The School of Mathematical & Information Sciences and each of its three Departments were reviewed during the period 11-14 May, 1998. The Review Committee was convened by Dame Prof. Pat Bergquist, and included Prof. Hyam Rubinstein (University of Melbourne) and Prof. Alberto Grumbaum (University of California at Berkeley) as external reviewers for the Department of Mathematics. A comprehensive set of information, and numerous submissions and interviews were considered. The report of the Review is expected in August, 1998


Research Highlights

Fellows of NZMS & RSNZ

Prof. Marston Conder, Prof. David Gauld and Assoc-Prof. M. K. Vamanamurthy were admitted to Fellowship of the NZ Mathematical Society in July 1997, in recognition of their contributions to mathematics and of their professional standing in the NZ mathematical community.

Prof. Gaven Martin was elected to a Fellowship of the Royal Society of NZ in November, 1997.

Royal Society Medal

Congratulations to Prof. David Gauld, who has been awarded a New Zealand Science & Technology Medal by the Royal Society of New Zealand. These medals were instituted by the NZ Government in 1990 to recognise outstanding contributions to the advancement of science and technology, and they bear a likeness of Earnest Lord Rutherford on one side and the emblem of the RSNZ on the other.


Prof. Graeme Wake was awarded a DSc by Victoria University of Wellington in December, 1997 for his outstanding work in Applied Mathematics.


NZ Mathematics Society Research Award

At the 1998 NZ Mathematics Colloquium, Dr Jianbei An was awarded the 1998 NZMS Research Award "for his contributions to the study of modular representations of groups, in which he has established his leading expertise through a combination of deep understanding, ingenuity and technical skill". Dr An is the 11th recipient of this award, and the 6th from our Department.

Marsden Fund Grants

Marsden Fund grants for 1997-1998 included one more for the Department of Mathematics: Prof. John Butcher and Dr Robert Chan received a grant for their project on "Theoretical and practical investigations in numerical analysis".

AURC Research Grants

The following staff were successful in the October 1997 round of AURC staff

research grants (in alphabetic order):

Bill Barton $ 1500 travel/subsistence

Britta Basse $ 1000 travel/subsistence

Colin Fox $ 2500 computer

Margaret Morton $ 3800 travel/subsistence

Mike Thomas $ 4000 travel & computer

Shinji Yamamoto $ 600 research expenses

The following staff were successful in the April 1998 round of AURC staff

research grants (in alphabetic order):

Marston Conder $ 4000 computer

Norm Levenberg $ 3400 travel/subsistence

Barbara Miller-Reilly $ 1000 travel/subsistence

Eamonn O'Brien $ 6000 computer & travel

Ivan Reilly $ 1000 travel/subsistence

MK Vamanamurthy $ 4000 computer

Shayne Waldron $10000 grant-in-aid.

Paul Bonnington received (on behalf of the Department and others based at the Tamakai Campus) $30 000 from the Infrastructure fund for computer equipment.

In May 1998, the PhD students Sina Greenwood, Kerry Richardson, and Sanja Todorovic-Vasiljevic won grants from the University's Graduate Research Fund for conference travel.

Postdoctoral Fellows

Dr Mark Nelson took up a Royal Society of London Postdoctoral Fellowship at Tamaki Campus from the end of 1997 until June 1998. Mark is from from the University of Leeds, Dept of Fuel and Energy and the Centre for Nonlinear Studies. His research is in theory of thermal ignition and applied differential equations and dynamical systems. He has been working with Prof. Graeme Wake and Dr Doug Chen of Chemical and Materials Engineering.

Dr John McKenzie has taken up a position as postdoctoral research fellow working with Prof. Gaven Martin on his Marsden Fund project.

Ministry of Education & NZQA Grants

Dr Bill Barton and Ms Judy Paterson have received a $9000 Ministry of Education Research Grant to investigate the components of effective teacher education. This research is possible because of a new scheme which places experienced teachers (of other subjects) alongside graduate mathematicians as they train together to become secondary mathematics teachers.

Dr Mike Thomas has received a $5000 grant from the NZ Qualifications Authority to investigate the impact of graphics calculators on assessment practices.


NZMS Grants

Dr Margaret Morton and Prof. Gillian Thornley received a $500 grant from the NZ Mathematical Society for their investigation of factors affecting doctoral studies in mathematics. Dr Bill Barton also received a $500 grant to attend the MAA/AMS conference in Baltimore in January.

1998 Napier Summer Research Workshop

The 4th summer research workshop on "Analysis and Geometry" was held in Napier, during the week 3-10 January 1998. This workshop was run under the auspices of the NZ Mathematics Research Institute, and supported financially by the Marsden Fund, the University of Auckland's Mathematics Department, the School of Mathematical and Information Sciences at Auckland, and the US National Science Foundation (through Prof. Vaughan Jones).

Six principal speakers each gave three 90-minute lectures covering quite a spectrum of mathematics within the broad theme of analysis and geometry. The topics and speakers were as follows:

Bruce Palka, University of Texas at Austin (USA): Quasiconformal mappings

Pekka Koskela, Jyväskylä University (Finland): Local to global problems

Kari Astala, Jyväskylä University (Finland): Holomorphic motions

Klaus Schmidt, University of Vienna (Austria): Algebra and geometry of combinatorial tilings

John Hutchinson, Australian National University: Random fractals

Tadeusz Iwaniec, Syracuse University (USA): Nonlinear elasticity.

Among just over 40 conference participants attending the lectures, there were about 20 graduate students from around NZ and also a few from Australia, plus other partipants from universities in Australia, NZ, USA and Sweden. Many participants came with their families. Some notes from the lectures are available to those interested (on request by email to <>).

Also during the workshop a meeting was held to formally establish the NZ Mathematics Research Institute (NZMRI), which now has a growing list of members in NZ and overseas, and the Directors would welcome suggestions for future workshops. That Institute was initially known as the NZ Institute of Mathematics, as reported in the April 1997 issue of the NZMS Newsletter, but it got renamed during the workshop. Proposals may be conveyed to any one of the 5 Directors: Profs. Vaughan Jones, David Gauld, Marston Conder, Rod Downey and Gaven Martin.

The conference venue was the Napier Conference Centre, adjacent to the Masonic Hotel, a short stroll to the beach and other facilities (including the Napier Soundshell, where entertainment in the form of singing by Vaughan Jones and some students could be heard some evenings!). Napier proved to be an attractive venue, with good weather and lots to see and do. Most of the local attractions (including Cape Kidnappers) were enjoyed by all, with the emphatic exception of the downstairs disco at the Masonic Hotel blasting into the early hours of Saturdays and Sundays. The conference wound up with a dinner at Clearview Estate, one of the local wineries.

Honorary Research Fellows

In 1997 five new Honorary Research Fellows joined the Department: Dr Kim Myung Ho (topology), Dr Ali Jabballah (interests in algebra), Dr Majid Ali (algebra), Dr Kuo-Jye Chen (partitions & q-series), and Dr Manoj Kantroo (fuzzy sets).

Teaching Fellows

Andrew Stafford, head of the Mathematics Department at Manurewa High School, has a Royal Society of New Zealand Science and Technology Teacher Fellowship, and he is spending 1998 in the Department. He is joined by Julia Horring (Kelston Girls High School) and Christine Kiernan (Lynfield College), who both have Teacher Study Awards from the Ministry of Education.

Summer Scholarships

Twenty-seven students received Summer Scholarships of up to $3000 each to undertake 6-week research projects in January and February this year. These scholarships targetted at honours students and promising students from under-represented groups.


Teaching News

Web pages

Over 1995-98 a significant activity in the Department has been the development of its web pages. These are now being used for information about the Department and its offerings, for internal administration and record-keeping, and, in some cases, for assisting the delivery of particular courses and the submission of research papers.

Summer School

The paper 445.108 was offered in the university’s Summer School for the first time in January 1998. Over 80 students enrolled in this 6-week intensive course taught by David Thomson, and convened by Chris King as part of the summer school programmes offered by the Arts and Commerce Faculties. The paper will be offered again in Summer School 1999.

New Papers & Streams

The papers 445.350 Topology and 445.355 Geometry (which were offered in alternate years) have now been replaced (for 1999 onwards) with a single paper, 445.353 Geometry and Topology, to be offered each year.

Several streams of the paper 445.102 are now being offered at Manukau Institute of Technology (MIT) under a cooperation scheme initiated this year. The paper is being taught by Engineering staff at MIT as part of their Engineering Mathematics 2 programme. Students successfully passing this paper will be able to gain credit for it when, in the future, they enrol at The University of Auckland.

Cyclic Review

The review of core papers is now complete with new syllabi for papers 445.151, 152, 251 and 252 being phased in over the 2-year period 1999-2000. The normal track has been altered so that it is possible to branch out after 251 instead of having to complete four papers, and paper 445.252 will become a key paper for those majoring in mathematics or planning to proceed to a Masters degree.

In 1998 a review of all other 100- and 200-level papers is being carried out. This review is broken into several mini-reviews, including the 445.107/108, 109, 207/208 track, and the foundation papers 445.101, 102 and 202.

Mathematics Olympiad

The second Auckland Mathematical Olympiad was held at The University of Auckland on May 24th when over one hundred secondary school students competed for prizes provided by the ASB Community Trust. Sixteen fifth, sixth & seventh formers gained senior awards and six third & fourth formers shared the junior awards. A follow-up seminar and workshop was held on July 6th and hopefully some of these students will gain places in future IMO teams.

The 39th International Mathematical Olympiad was held in Taiwan from July 10 to July 21 this year. Dr Arkadii Slinko visited Taiwan to assist with the organisation and was appointed leader of the New Zealand team. There are three Auckland students in the team of six: Robin Christian of St Kentigern College, and Lily Wang & Sarah Young of Epsom Girls’ Grammar School.

Undergraduate Mathematics Education

Drs Paul Hafner, David McIntyre and Margaret Morton attended the Symposium in Undergraduate Mathematics in Brisbane in early December, 1997, giving a seminar on their return about key aspects of the conference.

This year tutorials for Maori, and for Pacific Island students have been initiated as part of the Department’s EEdO policy.





Profile: Prof. Gaven Martin

Gaven Martin is a Professor in Mathematics on the city campus. His major research interests lie in the areas of analysis and geometry. In analysis his work is centered around the nonlinear partial differential equations of quasiconformal mapping theory and nonlinear elasticity (deformations of elastic bodies), as well as complex dynamical systems (iteration theory, Julia sets and the like) and their higher dimensional analogues. In geometry his work is centred around discrete groups, hyperbolic geometry and applications to low-dimensional topology.

This work involves collaborations with mathematicians in many different countries and Gaven has received significant international recognition with grants from the Marsden Fund (NZ), SERC (UK), ARC (Australia), CSNZ (Italy), NSF (USA) and the Finnish Academy over the last few years.

Gaven has recently taken over from John Butcher as Editor of the NZ Journal of Mathematics (and he invites quality manuscripts for submission!)

Profile: Dr Ganesh Dixit

Dr Ganesh Dixit is a Senior Lecturer in Mathematics at the city campus. His research interests are mainly in summability theory and its applications to Fourier series. He has published in excess of forty research papers in different mathematics journals all over the world.

The different aspects of the summability theory that Ganesh has worked on include absolute summability factors, inclusion relations between different methods, "limitation theorems" and 'ineffectiveness' of certain methods, etc. He has studied different aspects of the absolute summability of Fourier series by several methods of summation such as the methods of Cesàro, Riesz, Nørlund, Euler, Bore and Nevanlinna. His work on inclusion relations has not only exhibited the mutual strength, or lack of it, between different methods of summation, it has also enabled him to resolve some standing problems in the absolute summability of Fourier series.

Ganesh is a Founder Member of the Allahabad Mathematical Society which was established in 1958 and which publishes the Indian Journal of Mathematics. He has held different editorial responsibilities for the Journal over a long period of time, including its Editorship over 1991-1994.

Profile: Dr Arkadii Slinko

Dr. Arkadii Slinko is a Senior Lecturer based at the city campus. He started in Mathematics investigating Lie and Jordan algebras, wrote his PhD and co-authored a monograph "Rings that are close to associative", which is often referred to as a classical book in this area. He is a member of the Scientific Committee of the III and the IV International Conference on Nonassociative Algebra and its Applications (July 1993 in Spain, and July 1998 in Brazil).

Arkadii went on to work in topological algebras and co-algebras, wrote another thesis and gained his second degree of DSc from Institute of Mathematics in Novosibirsk (Russia). During the period 1980-1992 he worked for an applied Institute for System Studies in Moscow where he was interested in search problems, experimental designs and pattern recognition. Lately he has been interested in computable algebraic structures and algebraic information theory, in cooperation with Dr. Khoussainov from the Department of Computer Science.

In teaching Arkadii advocates a greater emphasis on applications of algebra, especially in relation to modern information technologies.

Another area of his interest is the mathematics education of gifted students and mathematical competitions. He acted as the Coordinator-in-Chief of the 33d International Mathematics Olympiad in Moscow in 1992, and chaired the Problem Selection Committee of the 38th IMO in Argentina in 1998. He is a member of International Advisory Board of the Masters Program in Mathematics Education of the University Antonio Narino (Colombia), and a consultant to the Organizing Committee of the 39th IMO in Taiwan. For the last five years he has trained the NZ MO Team, writing two books and numerous materials for students participating in mathematical competitions.


Appointments & Promotions

Dr Shayne Waldron was appointed to a Lectureship in October, 1997, following a 2-year post-doctoral position at the Technion in Israel. His interests are in approximation theory.

Prof. Graeme Wake accepted an appointment as Professor of Applied Mathematics at the University of Canterbury from 1st June 1998.

Dr Mohan Chinnappan, from Curtin University and Queensland Institute of Technology, was appointed as Lecturer in the Mathematics Education Unit in June, 1998. His interests are in the psychology of cognition and technology in mathematics learning.

Prof John Butcher has been appointed Head of the Applied and Computational Mathematics Unit until January 1999, when he retires. In December this year, a 2-day symposium and Departmental dinner are planned to celebrate John’s achievements and contributions.

Dr Bill Barton and Dr Mike Thomas are joint Heads of the Mathematics Education Unit until December 2001. Bill Barton for 1998 and 2000, and Mike Thomas in 1999 and 2001.

Dr Mike Meylan is continuing to work in the Department this year as a Temporary Lecturer and Research Fellow, working with Dr Colin Fox and Prof. Boris Pavlov, following completion of his NZS&T Post-doctoral Fellowship.

Wendy Stratton (who worked in our Assistance Room last year) has taken a joint part-time appointment as a tutor in Engineering Science and in Mathematics.

In 1998 the Department farewelled Dr Mark Wilson and Dr Warren Moors, who have both worked in the Department over the last 3 to 4 years as post-doctoral fellows and temporary lecturers (and seminar coordinators and webmaster to boot).

Jean Tahitahi (now Jean Martin) joined the Department as a new secretary in 1997. Sabrina Young resigned in April this year to take up a position in the private sector. She was been replaced in June by Min-Young Lee. Min-Young has a degree in statistics from Yonsei University in Korea.

In June, 1998, Ray Maharaj was appointed full-time Computer Services Manager for the Departments of Mathematics and Statistics. Ray has come to us from a position as Manager of Information Technology at Mercy Hospital.

In the 1997 promotion round the following Departmental applications were successful:

• Dr Norm Levenberg Over the bar in Senior Lecturer Scale

• Dr Jianbei An To Senior Lecturer

• Dr Colin Fox To Senior Lecturer

• Dr Margaret Morton To Senior Lecturer



Please note the following corrections to Bulletin #4


PhD Students & Graduands

Completed PhD's

At the May 1998 Graduation Ceremony John Pearson was awarded his doctorate for a thesis on Computational Aspects of Topological Graph Theory. John is the first PhD graduate from the Tamaki Campus in any subject. John was supervised by Dr Paul Bonnington (main supervisor), Prof. Marston Conder and Prof. Peter Lorimer.

Also in May 1998, Cameron Walker completed his PhD with a thesis on "Symmetric graphs with large vertex-stabilisers". Cameron was supervised by Prof. Marston Conder.

In July 1998 Tina Chan completed her PhD with a thesis on "Algebraic structures for the analysis of numerical methods". Tina was supervised by Prof. John Butcher (main supervisor), Dr Robert Chan and Dr Philip Sharp.

New PhD Students

Alona Ben-Tal has been awarded a University of Auckland Doctoral Scholarship from 1998.

Former PhD students Sina Greenwood and Peter Johnston are re-activating their PhD registrations this year, under the supervision of Prof. David Gauld and Prof. John Butcher respectively. Both plan to complete in the near future.

Tamsin Roberts arrived in January to begin a PhD with Dr Bill Barton in mathematics education for indigenous cultures. Tamsin has a Masters degree in linguistics from Macquarie University (Australia), and most recently has been working as a mathematics teacher at the Aboriginal settlement of Maningrida (NT, Australia).

In July 1998 Tang Yun-Ming (Peter) started on his Ph.D. in functional analysis supervised by Dr Bruce Calvert and Warren Moors. Peter has a thesis on sequence spaces and two years of doctoral studies to his credit, as well as a career in teaching and administration.


John MacCormick completed a Masters degree with Distinction in Mathematics at the University of Auckland, before going to Oxford to study for a doctorate in computer imaging towards the end of 1996. He has recently been awarded a Jowett Senior Scholarship at Balliol College in Oxford, carrying a stipend, dining rights and guaranteed accommodation.

The first four graduates in the Bachelor of Technology Honours option in Industrial Mathematics were capped during the May graduation programme. This programme, which began in 1994, has a problem-solving focus involving quantitative methods in mathematics, operations research, and statistics, and is strongly driven by applications. It is supported across two Faculties (Science and Engineering) and includes contributions from three Departments (Engineering Science, Mathematics and Statistics). It is principally based at the University’s Tamaki campus. All four students graduated with honours (one with first class honours, the other three with second class honours), and are all now in the workplace, one in NZ and 3 overseas.

The last year also saw the graduation of three women in MSc in Mathematics – all with first class honours, all gained prizes, and all have accepted places for PhD studies in top universities overseas.

Louise Parsons’ degree is in Applied Mathematics, with a thesis titled "Optimal Foraging models for Dairy Cows". This consisted of finding a mathematical model to describe the feeding behaviour of dairy cows in a paddock, and analysing the amount of food each cow consumed. This project was carried out for AgResearch, Ruakura. Louise is taking up a Fellowship to do a PhD at Cornell University in USA in the Aerospace Engineering Department. She will work on a project for the US Air Force to look at the way air flows around an aircraft and how a coating might be used to reduce the turbulence and drag on its wall. Louise received several scholarships from the Department of Mathematics and Science Faculty during her Masters studies, and at the 1997 NZ Mathematics Colloquium she won the Aitken prize for best student talk (jointly with Robyn Curtis). She has been selected to participate in the Royal Society of NZ student presentation series.

Robyn Curtis was also one of our first students to take up one of the Department’s Summer Scholarships for study over the summer months. She graduated with first class honours for her work in algebra and combinatorics. She won the NZ Mathematical Society's Aitken Prize (jointly with Louise) at the 1997 NZ Mathematics Colloquium in July 1997 for her talk on "Subgraphs of hypercubes with no small cycles". Robyn also won a Dean of Science Prize for best academic performance in Masters or BSc(Hons) in the last academic year. She won a scholarship to study at the University of Geneva, where she is now undertaking her doctorate in mathematics.

Emily Lane’s Masters thesis was on heteroclinic networks, under the supervision of Dr Vivien Kirk. This work stems from the mathematical modelling of processes such as thermal convection and turbulence. A certain kind of cyclical behaviour – known as a heteroclinic cycle – was observed in these processes. Emily's work looked at different properties of these cycles and showed that they may display chaotic behaviour under certain circumstances. Emily received several scholarships from the Department of Mathematics and the Faculty of Science including a Masters scholarship. She also won a Vacation Scholarship to do research at ANU in Canberra over the summer 1995-96. Earlier this year, Emily won the Fowlds Prize for the best academic performance for students completing a BSc(Hons) or Masters degree in the Faculty of Science. Emily is travelling to Tucson Arizona to take up a fellowship for a PhD at the University of Arizona.

Louise Parsons, Robyn Curtis and Emily Lane represent the best of our recent graduates and their success demonstrates that mathematics is a subject for women.

[Editor’s note: In compiling this Robyn wrote to me: "I guess the only interesting part I would add to any story about Emily and me is the list of universities that we’ve chosen not to go to. Emily has just recently turned down excellent scholarships at Cambridge and Princeton to go somewhere where the rockclimbing's better; I said no to Berkeley because they don’t speak French..."]



Professor Reinhard Laue (Professor of Applied Computer Science in the Mathematics Department of the University of Bayreuth) visited the School for 3 weeks in 1997. His visit was being sponsored by the Centre for Discrete Mathematics and Theoretical Computer Science. During his time here Prof. Laue presented five seminars, the first three on the topic "Construction of Combinatorial Objects".

Dr Rodney Weber (Senior Lecturer In Mathematics at The Australian Defence Forces Academy in Canberra) visited the Department from mid-October to mid-September 1997. Dr Weber is probably best known for his work in combustion. While here he gave a seminar on "Bifurcation Behaviour".

Professor Vadim Adamjan (Department of Theoretical Physics at Odessa University) visited the Department for 3 months to work with Boris Pavlov and others. While here he gave a series of lectures on financial mathematics.

Prof. Kevin Burrage (now Professor of Applied Mathematics at the University of Queensland) visited Prof. John Butcher, Dr Robert Chan and others in the ACMU in January 1998.

Prof. Tony Bracken, also of the University of Queensland, visited for three months from May 1998 as a Visiting Professor with Dr Alex McNabb and Prof. Graeme Wake. Prof. Bracken is a well-known mathematical biologist with a strong interest in partial differential equations.

Prof. Satya Deo, from Jabalpur, visited for the first half of 1998, for joint work with David Gauld.

Prof. Geoff Robinson, from University of Leicester, arrived in July 1998 to work with Dr Jianbei An, Dr Eamonn O’Brien and Prof. Marston Conder. Prof. Robinson has a very high international reputation for his research in algebra, particularly in (modular) representations of groups.

Other visitors included:

Prof. Herb Wilf, University of Pennsylvania

Prof. Aner Shalev, Hebrew University of Jerusalem

Prof. Cheryl Praeger, University of Western Australia

Prof. Anne Street, University of Queensland

Prof. Reinhard Mennicken, University of Regensburg

Prof. John Hearne from Natal (Ecological Modelling).

Professor Alan Camina, University of East Anglia

Professor Herb Freedman, Mathematical Biologist from University of Alberta


Seminars & Conferences


Regular seminar series & convenors:

Algebra/Combinatorics/Geometry Eamonn O’Brien

Analysis Norm Levenberg

Applied/Computational/Industrial Maths Robert Chan

Mathematics Education Judy Paterson

Mini Seminar Series John Butcher

Tamaki Mathematics Steve Taylor

Topology David McIntyre

Symposium on Algebra and Combinatorics

A Symposium on Algebra and Combinatorics was held honour of Prof. Peter Lorimer in November, 1997. Prof. Marston Conder gave an introduction to "The scientific work of Professor Peter Lorimer", Prof. Anne Street (University of Queensland) gave a lecture on "Ramsey theory and the contributions of Peter Lorimer", and Prof. Cheryl Praeger (University of Western Australia) gave a lecture on "Symmetric graphs and Lorimer's theorem". At the Departmental dinner that evening, to honour Peter on his retirement, many people made tributes to him, and letters with tributes from numerous mathematicians were read out. Peter was much gratified by his farewell gift from the Department, of a blown glass artefact by Gary Nash.

LOGOS #3: Mathematics Teacher Pre-Service Education

The third Mathematics Education Unit 1-day seminar in the LOGOS series was held in December, 1997. This seminar made use of the opportunity of simultaneous visits of two Professors of Mathematics Education from our Universitas 21 partners: Prof Susan Pirie from the University of British Columbia, and Prof Kaye Stacey from the University of Melbourne.

The seminar had four presentations: Professor Pirie spke on the innovative teacher education programme at UBC; Prof. Stacey discussed the role of research in teacher education; Judy Paterson from our own teacher education programme discussed the role of associate teachers; and Megan Clark from Victoria University reminded the audience of four critical factors in teacher education in this country, in particular the mathematical knowledge and the need for action in the area of Maori and Pacific Island mathematics education. Each presentor was followed by a commentator. They were: Kay Irwin (School of Education), Greg Lomas (Auckland College of Education), Graeme Aitken (School of Education) and Bronwen Cowie (Waikato University).

Each presentation was followed by an equal time for discussion, and the 30 participants engaged in vociferous debate on a variety of issues. This was a strength of the seminar. The other factor contributing to the success of the day was the geographical and ideological diversity of participants. Visitors from Dunedin, Christchurch, Wellington and Hamilton were attracted to this seminar. Graduate students, teachers, College of Education and University lecturers, and private educational contractors were represented.

Symposium on ODE’s and Stochastic ODE’s

In January 1998 there was a symposium featuring lectures by Prof. Kevin Burrage and Mrs Pamela Burrage on the subject "The Numerical Solution of Stochastic Ordinary Differential Equations". Presentations were also made by: Dr Robert Chan, Dr Wiremu Solomon, Prof. John Butcher, Dr Robert McLachlan, Dr Igor Boglaev (Massey University), Dr Margot Gerritsen (Department of Engineering Science), Prof. Graeme Wake and Dr Nicolas Roubidoux (Massey University).

String Seminar

A 1-day "String Seminar" was held at the university marae on March 11. Six members of the Department spent the day with 6 experts in whai (string games), sharing ideas and experiences. This joining of experts from mathematics and from Maori culture was filmed by the Audiovisual Unit, to produce a videotape for schools.


Auckland Numerical Ordinary Differential Equation (ANODE) Workshop

An international workshop entitled: Numerical ordinary differential equations in theory and practice was held from 29 June to 10 July in the Department. Organised by Prof. John Butcher, Dr Robert Chan, Nicolette Goodwin, Bev Grove and Dr Allison Heard, this workshop was one of the biggest NZ conferences in the area of theoretical applied mathematics. It featured two main series of lectures by prominent numerical analysts, scheduled lectures by other participants, and provision for impromptu presentations on work, as it develops, arising from discussions amongst people taking part.

After a welcome by the Deputy Vice-Chancellor, invited and local speakers began a programme of 50 presentations. Among the international visitors were:

Prof. J. M. Sanz-Serna, University of Valladolid, Spain

Prof. Marc Spijker, Mrs Natalia Borovykh & Mr. Guido van den Heuvel, Rijksuniversteit Leiden, The Netherlands

Prof. Masaharu Nakashima, Kagoshima University, Japan

Prof. Manfred Trummer, Simon Fraser University, Canada

Dr. Amal Al-Amleh, University of Rhode Island, USA

Dr. Anne Aubry & Dr Philippe Chartier, IRISA, Campus de Beaulieu, Rennes, France

Mr. Othmar Koch & Mr. Peter Kofler, University of Technology, Vienna, Austria

Prof Hermann Brunner, Memorial University of Newfoundland

Prof. Yoshiaki Muroya, Waseda University, Tokyo, Japan

Dr. Reinout Quispel & Dr. Barbara Zubik-Kowal, Katholieke Universiteit, Leuven, Belgium

Dr. Adrian Hill, University of Bath, England

Mr David Goeken & Prof. Olin Johnson, University of Houston, USA

Prof. Z Jackiewicz, Arizona State University, USA

Prof. Robert Corless, University of Western Ontario, London, Canada

Dr. Arthur Norman, Cambridge University, England

Prof. Ray Zahar, Université de Montréal, Canada

Dr Barbara Zubik-Kowal, Leuven Catholic University, Belgium.


Departmental Seminars

• Elizabeth Sneyd (Visiting academic) Pseudo-Interval Graphs

• Prof. Ren Potts (University of Adelaide) Traffic Lights

• Dr David Budgett (Department of Engineering Science) Fast computation of Fourier transforms

• Mamokgethi Setati (Centre for Cognitive Development, Vista University, South Africa) To Switch or Not to Switch: A Black Teacher's Dilemma

• Prof. Aner Shalev (Hebrew University of Jerusalem) Groups and Probability

• Prof. Aner Shalev (Hebrew University, Jerusalem) Fractals, subgroup structure, and Kac-Moody algebras

• A-Prof. Paul Austin (School of Engineering, University of Auckland) Singular Optimal Quadratic Gaussian Controls: Some New Results and Insights Using Wiener-Hopf Methods

• Prof. David Ragozin (University of Washington) Non-smooth Wavelets: Graphing functions unbounded on every interval

• Prof. David Ragozin (University of Washington) Rotation invariant kernels on spheres: a geometric introduction to harmonic analysis without spherical harmonics

• Anjana D. Singh (Department of Mathematics) General linear methods with variable stepsize and variable order

• Majid Ali (Auckland) Multiplication modules and ideals

• Kerry Richardson (Department of Mathematics) A report on the recent Summer Topology Conference

• Chris King (Department of Mathematics) Topological Dynamics - An Introduction

• Prof. Boris Pavlov (Department of Mathematics) Spectral Problems in the Theory of Quantum Gates

• Prof. Alan Stamp (Department of Physics) Scattering theory: Potentials of infinite range and the boundary element method

• Dr Rodney Weber (Australian Defence Forces Academy, Canberra) Bifurcating Combustion Behaviour

• Prof. Reinhard Laue (University of Bayreuth) Homomorphisms and orderly generation

• Prof. Reinhard Laue (University of Bayreuth) Double cosets, prescribed automorphism groups

• Prof. Reinhard Laue (University of Bayreuth) Graphical designs

• Prof. Reinhard Laue (University of Bayreuth) Isomers, Groups, t-Designs - a constructive approach to group actions

• Prof. Reinhard Laue (University of Bayreuth) Construction of Combinatorial Objects II: double cosets, prescribed automorphism groups

• Dr. Ali Jaballah (Department of Mathematics) The number of intermediary rings in some ring extensions

• Prof. Boris Pavlov (Department of Mathematics) Spectral Problems in the Theory of Quantum Gates, II

• Dr Michael Roberts (AgResearch, Wallaceville) The Convolution Strikes Back

• Prof. V. E. Cazanescu (University of Bucharest, Romania) Semantic equations and Birkhoff's theorem

• Alexander Kraegeloh (Department of Mathematics) Random Evolutions

• Dr. Mike Meylan (University of Auckland) Spectral Analysis of the Boltzmann Equation

• Prof. M. J. D. Powell (University of Cambridge) Radial Basis Function Methods for Global Optimisation

• Dr Bill Barton (Department of Mathematics) TIMSS: What It Tells Us and What It Doesn’t

• Prof. John Butcher (Department of Mathematics) Stability Barriers for Numerical Methods for Ordinary Differential Equations

• Jiling Cao (Department of Mathematics) The Theory of Quasi-uniform Function Spaces

• Prof. Maximilian Ganster (Technische Universitat, Graz) Resolvability with respect to an ideal

• Dr. Mark Nelson (Royal Society of London Research Fellow, Department of Mathematics) A Mathematical insight into the design of fire resistant materials

• Abdul Mohamad (University of Auckland) Autohomeomorphism Groups of Manifolds

• Prof. John Hearne (University of Natal) Optimal management of multispecies herbivories

• Prof. David Gauld (Department of Mathematics) When is a manifold metrisable if chunks of it are?

• Dr David McIntyre & Dr Margaret Morton (Department of Mathematics) Report on the Brisbane Conference on Undergraduate Mathematics Education

• Prof. John Dempsey (Clarkson University) Scale Effects in Sea-Ice Fracture

• Dr James Lawry (Oxford Centre for Industrial and Applied Mathematics, UK) Exponential Asymptotics

• Prof. Vaughan Jones (University of Auckland / University of California Berkeley) On the Poincaré series of a planar algebra

• Prof. Alan Camina (University of East Anglia) Sizes of conjugacy classes in finite groups

• Prof. Alan Camina (University of East Anglia) Some infinite Designs

• S. Adi Purnomo and Angela Tsai (University of Auckland) Epidemiology of Measles

• Professor Tao Qiu, (University of New England, Armidale) Fourier Analysis on starlike Lipshitz Surface in the Quaternion and Euclidean Space

• Dr Murray Muraskin (Queensland) Mathematical Aesthetic Principles/Nonintegrable Systems

• Prof. John Butcher (University of Auckland) Almost Runge-Kutta Methods

• Prof. Al Taylor (University of Michigan) Which linear partial differential equations can be solved by a formula?

• Prof. Al Taylor (University of Michigan) Teaching Undergraduate Mathematics: A View from the Chair

• Cameron Walker (University of Auckland) The infinitude of 7-arc-transitive graphs

• Prof. Boris Pavlov (University of Auckland) Quantum and acoustic waveguides, resonators and networks

• Dr. Sergei Fedorov (University of Auckland) On one recent result on the intersection of weighted Hardy spaces

• Dr Paul Gartside (University of Galway) Near Metric Properties of Hyperspaces

• Dr. Sing K. Nguang (Department of Electrical and Electronic Engineering, University of Auckland) Robust control of a class of continuous fermentation processes

• Prof. David Gauld (University of Auckland) Matveev's property (a) and related properties

• Dr Paul Bonnington (University of Auckland) Non-isomorphic triangulations of complete graphs

• Dr Paul Gartside (University of Galway) Ubiquity of Free Subgroups

• Assoc. Prof. Gordon Mallinson & Dr. Andrew Reztsov (Dept of Mechanical Engineering, University of Auckland) Structural Surfaces in Three Dimensional Vector Fields

• Dr Norm Levenberg (University of Auckland) Hulls and envelopes

• Prof. Satya Deo (R.D. University, Jabalpur) Discrete Groups and Discontinuous Actions

• Dr. Shayne Waldron (The University of Auckland) Multivariate polynomial interpolation

• Prof. Gaven Martin (The University of Auckland) Analytic continuation, transformation groups and the Hilbert-Smith conjecture

• Dr Stephan K. Matthai (Visiting Australian National University Mathematics from Germany) A Characteristics-Based Mixed Finite-Element /Finite-Difference Method for Chemical Advection in Fractured Rock

• Dr Paul Gartside (University of Galway) The Space of Subgroups of a Compact Group

• Dr Stephan K. Matthai (Visiting Australian National University Mathematics from Germany) A Characteristics-Based Mixed Finite-Element /Finite-Difference Method for Chemical Advection in Fractured Rock

• Prof. Herb Freedman (University of Alberta) Single Species Models of Diffusion in a Patchy Environment

• Dr Shayne Waldron (The University of Auckland) The eigenstructure of the Bernstein operator

• Dr Mark Wilson (The University of Auckland) Algebras of my acquaintance

• Emily Lane (The University of Auckland) Heteroclinic Cycles, Networks and Switching

• Dr John McKenzie (University of Auckland) Metrics, Curvature and modifying 4-Manifolds

• Dr Warren Moors (The University of Auckland) On the Choquet-Dolecki Theorem

• Dr Wiremu Solomon (The University of Auckland) Models of Measles

• Dr Stephen McDowall (University of Washington, Seattle) An Electromagnetic Inverse Problem in Chiral Media

• Prof. Satya Deo (R D University, Jabalpur) On Hopfian and Co-Hopfian Spaces which are Compact Zero-Dimensional

• Dr Colin Bailey (Victoria University of Wellington) Bounding Exponentials in Cardinal Arithmetic

• Dr John McKenzie (University of Auckland) A family of hyperbolic 4-manifolds (2 seminars)

• Prof. Tony Bracken (University of Queensland) Modelling of Drug Uptake by the Liver

• Kerry Richardson (University of Auckland) A new window on the consistency of the NMSC

• Prof. Shamil U. Galiev (Mechanical Engineering, University of Auckland) Nonlinearities, singularities and local resonant wave phenomena in nature

• Tsukasa Yashiro (University of Auckland) An invariant of immersed 3-manifolds

• Abdul Mohamad (University of Auckland) Cleavability over Manifolds

• Assoc. Prof. Don Nield (Department of Engineering Science, The University of Auckland) Mathematical modelling of fluid flow in porous media

• Louise Parsons (University of Auckland) Mathematical Models for the Foraging Strategies of Dairy Cows

• Dr. John Pearson (University of Auckland) Three problems involving graphs and surfaces

• Sina Greenwood (University of Auckland) Type I manifolds

• Prof. Satya Deo (R. D. University, Jabalpur) Alexander-Spanier cohomology of powers of the long line

• Dr. Cai Heng Li (University of Western Australia) On Automorphism Groups and Isomorphisms of Finite Vertex-Transitive Graphs

• Niels Hendriksen (Denmark) Should A Mathematics Teacher Know Something About the History of Mathematics ?

• Sanja Todorovic-Vasiljevic (University of Auckland) Bounds on the number of automorphisms of a non-orientable surface of given genus

• Prof. David Gauld (The University of Auckland) Some highlights of the Topology Conference in Mexico

• Prof. Geoff R. Robinson (University of Leicester ) Minimizing a quadratic form -- with applications to Character Theory

• Dr Amal Al-Amleh (University of Rhode Island) A Difference Equation with Strong Negative Feedback

• Dr. Stuart Scott (The University of Auckland) Primary N-groups

• Dr Amal Al-Amleh (University of Rhode Island, New York) Boundedness of Solutions of a Plant-Herbivore System

• Dr Dane Flannery (National University of Ireland, Galway) Hadamard matrices and cocycles

• A-Prof. M. K. Vamanamurthy (The University of Auckland) Generalised Elliptic Integrals

• Sina Greenwood, and Jiling Cao (The University of Auckland) Constructing type-I manifolds with given Upsilon-trees, and Topological games and multifunctions

• Dr Dane Flannery (National University of Ireland, Galway) Hadamard matrices and cocycles


Other Staff News


Vivien Kirk’s baby Joshua arrived on January 16 in the early evening, and he weighed 3.11 kg at birth. Both Vivien and Joshua are doing very well (Marc too!).

Warren Moors is taking up a two and a half year Fellowship at Victoria University under Vladimir Pestov’s Marsden Fund grant, starting in 1998.

David Smith had to undergo surgery on his back, but has successfully recovered and is back in the Department.

Norm Levenberg has returned from leave at Indiana University and the University of Toronto. Michael Thomas has returned from short leave at the Open University and Warwick University. Boris Pavlov, Jianbei An and Joel Schiff are on long leave this year.

Jiling Cao and his wife, Yan Ling Liu’s new baby Eugenia arrived on 3rd May. Everyone is delighted.

On Tuesday March 31, John Butcher was ambushed by a group of graduate students, who heartily sang "Happy birthday to you" for John’s 65th birthday.


Recent Journal Publications


An, Jianbei. The Alperin and Dade conjectures for Ree groups 2F4(q2) in non-defining characteristics. J. Algebra 203 (1998), 30--49.

Anderson, G. D., Qiu, S.-L. & Vamanamurthy, M. K. Inequalities for distortion functions and plane quasiconformal mappings, NZ J. Maths, 26, (1997), 1-19.

Anderson, G. D., Vamanamurthy, M. K. & Vuorinen, M. Conformal Invariants, Inequalities and Quasiconformal Maps, Canadian Math. Soc. Series of Monographs and Advanced Texts, John Wiley & Sons, Inc., (1997)

Anderson, G. D.; Qiu, S.-L.; Vamanamurthy, M. K. Elliptic integral inequalities,with applications. Constr. Approx. 14 (1998), no. 2, 195-207.

Archdeacon, D., Bonnington, C.P., Siran, J. A Nebesky-type characterization for relative maximum genus. J. Combin. Theory Ser. B 73 (1998), 77--98.

Barton, B., Fairhall, U. & Trinick, T. Tikanga Reo Tatai: Issues in the Development of a Maori Mathematics Register. For The Learning of Mathematics (1998), 18(1), 3-9.

Blocki, Z., Kolodziej, S. & Levenberg, N. Extremal functions and equilibrium measures for Borel sets. Bull. Polish Acad. Sci. Math. 45 (1997), no. 3, 291-296.

Boglaev, Igor P. Iterative algorithms of domain decomposition for the solution of a quasilinear elliptic problem. J. Comput. Appl. Math. 80 (1997), no. 2, 299-316.

Borwein, J. M.; Moors, W. B. Essentially smooth Lipschitz functions. J Funct. Anal. 149 (1997), no. 2, 305-351.

Borwein, J.M., Moors, W.B. A chain rule for essentially smooth Lipschitz functions. SIAM J. Optim. 8 (1998), 300--308.

Borwein, J.M., Moors, W.B. Null sets and essentially smooth Lipschitz functions. SIAM J. Optim. 8 (1998), 309--323.

Brand, N. & Morton, M. A note on the growth rate of planar graphs, Combinatorics, Complexity, Logic (Proceedings of DMTCS ), Springer Verlag, Singapore, (1996), 147-157.

Burns-Wilson, B. E., & Thomas, M. O. J. Computers in primary schools: strategies for overcoming barriers in mathematics, SAME papers, Waikato University, New Zealand, 1997.

Butcher, J. C.; Tracogna, S. Order conditions for two-step Runge-Kutta methods. Volterra centennial (Tempe, AZ, 1996). Appl. Numer. Math. 24 (1997), no. 2-3, 351--364.

Butcher, J. C.; Chartier, P. A generalization of singly-implicit Runge-Kutta methods. Volterra centennial (Tempe, AZ, 1996). Appl. Numer. Math. 24 (1997), no. 2-3, 343--350.

Butcher, J. C. An introduction to "almost Runge-Kutta" methods. Volterra centennial (Tempe, AZ, 1996). Appl. Numer. Math. 24 (1997), no. 2-3, 331--342

Butcher, J. C. Numerical methods for differential equations and applications. Sci. Eng. Sect. C Theme Issues 22 (1997), no. 2, 17-29.

Butcher, J. C.; Jackiewicz, Z. Implementation of diagonally implicit multistage integration methods for ordinary differential equations. SIAM J. Numer. Anal. 34 (1997), no.6, 2119-214

Butcher, J. C. B., Jackiewicz, Z. & Mittlemann, H. D. A nonlinear optimization approach to the construction of general linear methods of high order, J. Comput. Appl. Math, 81 (1997), 181-196.

Butcher, J.C., Chan, R.P.K. Efficient Runge-Kutta integrators for index-2 differential algebraic equations. Math. Comp. 67 (1998), 1001--1021.

Calvert, B. The Downs-Thomson Effect in a Markov Process, Prob. in the Eng. and Informational Sciences, 11, (1997), 327-340.

Calvert, B. Unicursal Resistive Networks, Circuits Systems Signal Processing, 16(3), (1997), 307-24.

Calvetti, D.; Levenberg, N.; Reichel, L. Iterative methods for X-AXB=3DC. Special issue dedicated toWilliam B. Gragg (Monterey, CA, 1996). J. Comput. Appl. Math. 86 (1997), no. 1 73-101.

Conder, M., Morton, M. & Praeger, C. Partition graphs for finite symmetric groups, J. Graph Theory, 25 (1997), 107-117.

Calvert, B., Solomon, W. and Ziedins, I. Braess' Paradox in a Queueing Network with State Dependent Routing, J. App. Probability, 34, (1997), 134-154.

Cao, J., Dontchev, J. On some weaker forms of continuity for multifunctions. Real Anal. Exchange 22 (1996/97), no. 2, 842-852.

Cao, J.; Gehring, F. W.; Martin, G. J. Lattice constants and a lemma of Zagier. Lipa's legacy (New York, 1995),107-120, Contemp. Math., 211, Amer. Math. Soc., Providence, RI, 1997.

Cao, Jiling; Reilly, I.L., Romaguera, S. Some properties of quasiuniform multifunction spaces. J. Austral. Math. Soc. Ser. A 64 (1998), 169--177.

Cuartero, B., Galé, José E.; Slinko, Arkadii M. Linearly compact algebraic Lie algebras and coalgebraic Lie coalgebras. Proc. Amer. Math. Soc. 125 (1997), no. 7, 1945-1952.

Cullen R. M. & Walker W. J. Predicting and preventing the next measles epidemic, NZ Family Physician, 24(4), (1997), 43-48.

Cullen R. M. & Walker W. J. Pertussis hospitalisations and mass vaccination in New Zealand 1948-1996, NZ Family Physician 24(6), (1997), 45-48.

Dikshit, G. D. Absolute Euler summability of Fourier series. J. Math. Anal. Appl. 220 (1998), no. 1, 268-282

Duval, J.; Levenberg, N. Large polynomial hulls with no analytic structure. Complex analysis and geometry (Trento, 1995), 119-122, Pitman Res. Notes Math. Ser., 366, Longman,Harlow (1997).

Fedorov, S. I. On harmonic analysis in a multiply connected domain and character-automorphic Hardy spaces. (Russian) Algebra i Analiz 9 (1997), no. 2, 192-240.

Gehring, F. W.; Maclachlan, C.; Martin, G. J. Two-generator arithmetic Kleinian groups II. Bull. London Math. Soc. 30 (1998), no. 3, 258-266.

Gehring, F. W.; Maclachlan, C.; Martin, G. J.; Reid, A. W. Arithmeticity, discreteness and volume. Trans. Amer.Math. Soc. 349 (1997), no. 9, 3611-3643.

Gehring, F. W.; Martin, G. J. Geodesics in hyperbolic 3-folds. Michigan Math. J (1997), no. 2, 331-343.

Hong, Y. Y. & Thomas, M. O. J. Student Misconceptions in Integration: Procedures and Concepts. Proc. 1997 Int. Conf. on Sci., Maths & Tech. Ed., (1997), 346-354.

Hu, Z., Moors, W. B.; Smith, M. A. On a Banach space without a weak mid-point locally uniformly rotund norm. Bull. Austral. Math. Soc. 56 (1997), no. 2, 193-196.

Kenderov, P. S.; Moors, W. B.; Sciffer, S. Norm attaining functionals on C(T). Proc. Amer. Math. Soc. 126 (1998), no. 1, 153-157.

Kirk, V. & Stone, S. Effect of a refractory period on the entrainment of pulse-coupled integrate-and-fire oscillators, Physics Letters A 232, (1997), 70-76.

Kota, S. & Thomas, M. O. J. Students' Arithmetic Preferences: Effect on Problem Solving Ability, Hiroshima J. Maths Ed., (1998), 6, 33-48.

Kota, S. & Thomas, M. O. J. (1998). Affective Factors and the Improvement of Algebraic Problem Solving, Proc. 21st MERGA Conf., (1998), 303-310.

Leedham-Green, C. R.; O'Brien, E. A. Recognising tensor products of matrix groups. J. Algebra Comput. 7 (1997), no. 5, 541-559.

McIntyre, D. W.; Watson, W. S. Basic intervals in the partial order of metrizable topologies. Topology Appl. 83 (1998), no. 3, 213-230.

Marshall, T. H. Geometry of pseudospheres. I. New Zealand J. Math. 26 (1997), (2) 213-228.

Marshall, T. H. Geometry of pseudospheres. II. New Zealand J. Math. 26 (1998), (1) 81-95.

Marshall, T. H. Volume formulae for regular hyperbolic cubes. Conform. Geom. Dyn. 2 (1998), 25-28.

Marshall, T. H. Truncated tetrahedra and their reflection groups. J.Austral. Math Soc. Ser. A 64 (1998), no. 1, 54-72.

Martin, G. J. Branch sets of uniformly quasiregular maps. Conform. Geom. Dyn. 1(1997), 24-27.

Moors, W. B.; Giles, J. R. Generic continuity of minimal set-valued mappings. J Austral. Math. Soc. Ser. A 63 (1997), no. 2, 238-262.

Moors, Warren B. A characterisation of weak compactness in Banach spaces. Bull Austral. Math. Soc. 55 (1997), no. 3, 497-501.

Morton, M. A note on arc-transitive circulants. Bull. Inst. Combin. Appl. 23 (1998), 63--68.

O'Brien, E. A. & Leedham-Green, C. R. Tensor Products are Projective Geometries, J. Algebra, (189), 1997, 514-28.

O'Brien, E. A. & Leedham-Green, C. R. Recognising tensor products of matrix groups, Int. J. Algebra Comput., (7), 1997, 541-59.

Pritchard, G., Wilson, M. C. & Wood, D. H. Bell's primeness criterion for W(2n+1), Experiment. Math. 6 (1997), 77-85.

Qiu, S.-L.; Vamanamurthy, M. K. Extremal rings and quasiconformal mappings Hokkaido Math. J. 26 (1997), no. 3, 493-508.

Tee, G. J. Characteristic functions for primes, Mathematics Today, 33 (3), (1997).

Tee, G. J., Diverting asteroids, METEORITE! 3 (4), (1997), 19.

Tee, G. J. Relics of Davy and Faraday in New Zealand, Notes Rec. R. Soc. Lond. 52(1), (1998), 93-102.

Tee, G. J. Andrew Cheyne, Father of Sir William Watson Cheyne, Auckland-Waikato Historical Journal, 71, (1998), 25-26

Thomas, M. O. J. & Hall, D. A Computer Environment to Encourage Versatile Understanding of Algebraic Equations, Proc. 21st MERGA Conf., (1998), 605-612.

Waldron, S. Lp error bounds for Hermite interpolation and the associated Wirtinger inequalities. Constr. Approx. 13 (1997), no. 4, 461-479.

Waldron, S. The error in linear interpolation at the vertices of a simplex. SIAM J. Numer. Anal. 35 (1998), 1191--1200.

Waldron, S. L. Integral error formulae for the scale of mean value interpolations which includes Kergin and Hakopian interpolation. Numer. Math. 77 (1997), no. 1, 105-122.

Waldron, S. L. A multivariate form of Hardy's inequality and Lp error bounds for multivariate Lagrange interpolation schemes. SIAM J. Math. Anal. 28 (1997), no. 1, 233-258

Wilson, M. C. Primeness of the enveloping algebra of Hamiltonian superalgebras Bull. Austral. Math. Soc. 56 (1997), no. 3, 483-488.

Wilson, M. C.; Pritchard, G.; Wood, D. H. Bell's primeness criterion for W(2n+1). Experiment. Math. 6 (1997), no. 1, 77-85.

Wilson, M. C.; Pritchard, G. Primeness of the enveloping algebra of the special Lie superalgebras. Arch. Math. (Basel) 70 (1998), no. 3, 187-196.

Yaldwin, J. C., Tee, G. J. & Mason, A. P. The status of Gideon Mantell's "first" Iguanodon tooth in the Museum of New Zealand Te Papa Tongarewa, Archives of Nat. Hist., 24, (1997), 17-41.


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