Prof. John Butcher formally retires from the University of Auckland on 31 January 1999.

John has served the University for almost 33 years, for most of this time in the Mathematics and Statistics Department. His service included terms as Head of Department as well as various roles on university committees, and he served the Department of Computer Science as its foundation Head. To all of us John is not only a valuable colleague but an inspiration because of his enthusiasm and love for mathematics in all forms.

John's academic achievements have been recognised nationally through Fellowship of the Royal Society (1980) and the award of the Royal Society's Hector Medal (1997). On the international scene he is widely regarded as the premier research worker in the numerical solution of ordinary differential equations. Above all, John is known as a people-person for his genuine warmth, care and encouragement for all those with whom he comes into contact, especially his students.

Several activities will mark the occasion of his retirement. One of these, as an appropriate way to honour his academic achievements and as a fitting tribute to his contributions to mathematics in New Zealand as well as to the international scientific community, is the establishment of a fund for a John Butcher scholarship in Mathematics. The fund will be used to award one or more students in the study of mathematics in the form of an annual grant or scholarship. We are grateful that the University has given its blessings and has agreed to administer the fund when it is established.

His retirement was also marked by an Annual Dinner in conjunction with an ANODE Symposium (see below).

Professor Gaven Martin has been appointed Head of the Department of Mathematics for a 3-year term commencing 1st February 1999, in succession to Professor Marston Conder. Gaven comes to this position in times of increasing financial constraint, but with the support of a positive Departmental Review and far-reaching recommendations.

We are extremely grateful to Marston for the way in which he has lead the Department over the past few years, maintaining its integrity in the face of funding cuts and increasing bureaucracy.

Prof. Marston Conder was elected to a Fellowship of the Royal Society of NZ in November 1998.

Five research teams from the Department were awarded Marsden Fund Research Grants in the 1998/99 round:

• Dr Paul Bonnington and Dr Margaret Morton $ 43 000
• Prof. Marston Conder, Dr Jianbei An, and Dr Eamonn O'Brien $ 80 000
• Dr Colin Fox and Dr Geoff Nicholls $ 65 000
• Prof. Vaughan Jones, Prof. Marston Conder, and Prof. David Gauld $ 80 000
• Prof. Gaven Martin $ 112 000

The following were successful in the October round of grants-in-aid of the AURC:

• Dr Bill Barton and Prof. Ivan Reilly $ 6 500
• Dr Mohan Chinnappan and Dr Mike Thomas $ 6 000
• Dr Margaret Morton $ 4 550

The annual summer workshop organised by the New Zealand Mathematics Research Institute was held this year in Raglan, from 3-9 January. Initially oriented to Harmonic Analysis on Riemann surfaces, the main topic was gradually transformed and finally covered many wider parts of mathematics. The total number of participants was about 60, including approximately 25 students among them: 10 from Auckland, 5 from Christchurch, 6 from Hamilton and others from abroad.

The main lectures were given by:

• L. Carleson (Sweden) on graphs, manifolds and circle packing
• K. Uhlenbeck (USA) on classical mechanics, solitons and integrability
• V. Jones (NZ and USA) on statistical mechanics
• S. Trei (USA) on Harmonic analysis, exponential bases and Bellman function
• B. Williams (USA) on dynamical systems
• H. Short (France) on braid-groups and a topological application
• V. Vinnikov (Israel) on applications of Harmonic Analysis on Riemann surfaces to systems

of commuting operators.

• S. Avdonin (Australia) on applications of Harmonic Analysis to Control Theory
• V. Gershkovich (Australia) on noncommutative geometry and application of it to robotic systems
• S. Naboko (Russia) on analytic operator - functions with positive imaginary part
• L. Bos (Canada) on wavelets
• S. Fedorov & B. Pavlov (Auckland) on applications of Harmonic Analysis on classical and

multiply-connected domains to the spectral theory of differential and difference operators.

Almost all lectures were designed for advanced graduate and postgraduate students, and were very well attended by students. Probably this was the result of our careful preparation for the workshop: Professors Gaven Martin and Boris Pavlov gave about 25 hours of preparatory lectures in total for students of universities in Auckland, Christchurch, Wellington and Hamilton. These lectures were also reasonably well attended and most of the attendees came to Raglan. Each lecture in Raglan was designed to bring students to the latest achievements in the corresponding domain of mathematics, so the total sum of lectures has given a good review of essential parts of modern analysis. The students obviously appreciate these efforts — in particular they suggested that the organising commitee collects and distributes files or hard-copies of lectures, and it is intended to meet this request.

Generally the workshop in Raglan was a success. The weather was beautiful — probably organised by the Director of the School. It was particularly pleasing that there were so many well-prepared young women who challenged students from other cities and countries. It was pleasing to observe the students talking during breaks with L. Carleson, Karen Uhlenbeck, Vaughan Jones and other distinguished lecturers. Vaughan Jones and David Gauld organised exciting sport activities — surfing and hiking — and both provided reasonably good weather for it. One student (Sikimeti) got briefly lost in the mountains, which added to her popularity. At the end, in a marvellous place overlooking Raglan Harbour, the traditional fabulous barbecue organised by Vaughan Jones gave a last perfect touch to the whole event.

Twenty students have received $3200 each for 6-week summer scholarships over the summer 1998/9. This includes ten Hons/Masters students and ten promising undergraduates, and some partially subsidised this year by external research grants.

Bev Grove resigned from her position as Department Assistant in December. This position has been upgraded to one of Department Manager, and was taken up by Ross McCallum in January 1999.

Alastair McNaughton (Senior Tutor) has completed his PhD in Engineering Science on forest harvesting schedules ("Long-term scheduling of harvesting with adjacency and trigger constraints"). Dr Ramankutty left the employment of he University (as a senior lecturer) in September.

The following academic staff were successful in their applications for promotion in 1998:

• Jianbei An Special increment in the Senior Lecturer scale
• Eamonn O'Brien Promotion to Senior Lecturer.

For 1998 the Department of Mathematics had about 950 effective full-time students (EFTS), including 900 undergraduate (120 at Tamaki), and 50 postgraduate. The growth in postgraduate enrolments appears to be continuing.

The papers 445.107 and 445.108 are being offered again in the University's summer school in January 1999, following their successful introduction last year. Over 150 students enrolled, and the papers are being taught again by David Thomson.

In February 1999, a two-week "SuperStart" course is being offered in collaboration with the School of Engineering. This course can be used by students who lack the necessary background to enrol in 445.151 or 445.108 as a way of revising their mathematics skills. In particular it is aimed at students who have less than an A-pass in 445.102, or who have 40 to 60% in Bursary Mathematics with Calculus or 50 to 70% in Bursary Mathematics with Statistics.

At the beginning of 1997 the Department initiated a revolving three-yearly cyclic review of the papers we offer. The first grouping of papers, considered in 1997, were the core Stage 1 and 2 papers 445.151, 445.152, 445.162, 445.251, 445.252 and 445.260, and teams were formed to review the remaining stage 1 and 2 papers in 1998. The following modifications were ratified (among other minor ones) at a Department meeting in December:

• New syllabi for the core papers 445.251 (Mathematics 5) and 445.252 (Mathematics 6) are to be introduced in 2000, with content as previously agreed upon. The resulting new version of 445.251 will be re-numbered as 445.253, and the replacement for 445.252 be re-numbered and re-named as 445.255 Principles of Mathematics. If resources allow then paper 445.255 should be offered every semester from the first semester of 2000 onwards.

• The papers 445.230 (Advanced Mathematics 2) and 445.231 (Advanced Mathematics 3) will be discontinued from the year 2000, due to low numbers of enrolments in these papers and their lack of success in channeling students through to a major or graduate study in Mathematics. It is felt that the new papers 445.253 and 445.255 offer sufficient choice and advantage for students who successfully complete the accelerated Stage 1 paper 445.130, and will provide a better platform for advancing to Stage 3 and 700-level Mathematics.

• Minor changes will be made to papers 445.107/108 and 445.207/208, and the distinction between numbers will be discontinued, with 445.107 and 445.207 being removed and 445.108 and 445.208 re-named as Mathematics for Business and Technology 1 and Mathematics for Business and Technology 2 respectively.

• The limit on enrolment for 445.202 (Tutoring in Mathematics) will be increased to 30 students. (Students in this paper normally assist with tutorials for paper 445.102 (Mathematics 2). In 1998 a few students were engaged as tutors in 445.151 (Mathematics 3) on a trial basis, and it is hoped to increase the number of students with this capability in 1999.)

• The viability of a "Mathematics for Humanities" paper at Stage 1 or 2 will be explored concurrently with the delayed review of paper 445.210 (Contemporary Topics in Mathematics) in 1999.

• The increased emphasis on proof techniques trialled in 445.225 (Discrete Mathematics) in 1998 has proved satisfactory and will be continued, and the prerequisites for this paper will be slightly strengthened.

All Stage 3 papers are to be reviewed in 1999, and the review cycle will start again in 2000.

David Gauld is a Professor of Mathematics at the city campus. His formal education began at a primary school in which he and his two brothers at one stage formed half of the roll. After attending three secondary schools, he was educated at the University of Auckland and the University of California at Los Angeles. His current interests are in the topology of manifolds, especially non-metrisable manifolds and criteria for metrisability. While the main tool used in the study of compact manifolds is Algebraic Topology, for non-metrisable manifolds it is Set Theory. On his own and with others he has developed conditions equivalent to metrisability for a manifold and constructed a strange surface whose existence required the use of the Continuum Hypothesis. Some of this research has been supported by a Marsden Fund award.

David has also served the University of Auckland in numerous administrative roles, including over 10 years as Head of the Department and two and a half years as Assistant Vice-Chancellor (Research). For this and other contributions he was awarded one of the 1997 New Zealand Science and Technology Medals.

He served as the first Editor of the New Zealand Journal of Mathematics after its reincarnation from the Mathematical Chronicle, as President of the New Zealand Mathematical Society, and is the inaugural Secretary of the New Zealand Mathematics Research Institute. In the last role he has actively promoted the annual summer workshops run by the Institute.

Judy Paterson is a half-time lecturer in Mathematics Curriculum on the city campus. She is involved in the Secondary Teaching Diploma course as a lecturer, visiting mentor and tutor. Currently her research interests lie in the assessment and development of secondary mathematics teachers in training. In 1998 she completed a research project for the NZ Ministry of Education in this area.

She also teaches Mathematics with Statistics at The Senior College of New Zealand. In all her teaching she is interested in the factors that influence the student's understanding of mathematics particularly when the student is learning mathematics in a language other than their mother tongue.

Shayne Waldron is a lecturer in Mathematics at the city campus, with principal research interests in approximation theory and numerical analysis. Shayne was an undergraduate at the University of Canterbury before winning a Fulbright scholarship to study for a PhD at the University of Wisconsin-Madison. He completed his PhD in 1995 under the supervision of Prof. Carl de Boor, with a thesis on the topic of error bounds for multivariate polynomial interpolation schemes.

Shayne took up a 2-year postdoctoral fellowship at the Technion in Israel before coming to Auckland in October 1997. He has published nine research articles (all single-author papers) in international journals, and has many more in the pipeline. Also he plays a valuable role as the Department's webmaster, responsible for the Department's home page and related documentation available on the internet, and he is a co-organiser of an international conference "Surface Approximation and Visualisation" being held at the University of Canterbury this February.

In August last year David Chen completed his PhD with a thesis on "The effective order of singly implicit methods for stiff differential equations". David was supervised by Prof. John Butcher (main supervisor), Dr Robert Chan and Dr Philip Sharp.

Charlotte Martindale and Shinji Yamamoto, students of our former colleague Prof. Graeme Wake, have transferred their enrolments to the Universities of Waikato and Canterbury respectively.

Several other PhD students are in the process of completing their theses over the 1998/99 summer.

Four of our recent Masters graduates have commenced PhDs in the Department:

• Hyuck Chung, on Dynamics of Inhomogeneous Sea-Ice, supervised by Dr Colin Fox (along with Dr Mike Meylan as Adviser)

• Jianhua Gong, in Geometry and Analysis, supervised by Prof. Gaven Martin and Dr Norm Levenberg

• Jamie Sneddon, on Infinite Graphs, supervised by Drs Paul Bonnington and Margaret Morton

• Chung-Ju Tsai, in Complex Analysis and Geometry, supervised by Prof. Gaven Martin and Dr Norm Levenberg.

Also we are pleased to welcome Junying (Shirley) Huang into the Department as new PhD student. Junying has a first class Masters degree from the University of Western Ontario, and is commencing a PhD in Numerical Analysis under the supervision of Dr Robert Chan and Prof. John Butcher.

Congratulations to the following students who have been awarded University or Faculty scholarships from February 1999:

Junying (Shirley) Huang University Doctoral Scholarship Edward Rosser University Masters/Honours Scholarship Michael Prestidge Arts Faculty Masters Scholarship.

Professor J.R. Patadia, of M.S. University of Varodara (Baroda), India, was hosted by Ganesh Dixit from July to October. Professor Patadia gave two seminars in the Department.

Professor Chaitan Gupta, of the University of Nevada, Reno, U.S.A., was hosted by Bruce Calvert.

Professor Charles Leedham-Green, of Queen Mary Westfield College, University of London, is visiting the Department on a year's sabbatical, from October 1998 to September 1999. His interests lie in computational algebra, and he is hosted by Dr Eamonn O'Brien and Prof. Marston Conder.

Professor Anant Vyawahare, a Rotary Scholar, and Head of the Mathematics Department, Nagpur University, India, is being hosted by Ganesh Dixit over December/January. His specialities include Graph Theory, Maths Education and History of Indian Mathematics. While here he has given seminars on both Graph Theory and Vedic Mathematics.

Algebra/Combinatorics/Geometry Eamonn O'Brien

Analysis Norm Levenberg & Shayne Waldron

Applied/Computational/Industrial Maths Robert Chan

Mathematics Education Judy Paterson

Topology David Gauld & Sina Greenwood

Building on the opportunity provided by the visiting members of the MEU Review team, a LOGOS seminar on Graduate Supervision in Mathematics Education was held on Saturday 7th November. This attracted participants from Waikato, Massey and Victoria Universities as well as Auckland College of Education. Prof. Gilah Leder (La Trobe), Prof. Kaye Stacey (University of Melbourne), Dr Andy Begg (Waikato University) and Dr Mohan Chinnappan (MEU) all contributed to promote a wide-ranging discussion amongst participants.

On 26th November 1998 the MEU hosted a teachers‚ workshop on using the TI92 calculator for teaching Bursary Mathematics with Calculus. The workshop was held at the University's Conference Centre and was sponsored by Samcor Computers on behalf of Texas Instruments. The 21 teachers participating came from 15 different secondary schools, including Tauranga Girls‚ College, Bay of Islands‚ College and Fairfield College, Hamilton.

The workshop leaders were Ye Yoon Hong and Mike Thomas of the MEU and Christine Kiernan of Lynfield College, who has been in the MEU on a Ministry of Education Study Award during 1998. The workshop concentrated on showing how the symbolic manipulator Derive, which is part of the TI92, can be used to help students solve Bursary Calculus questions. The day went very well and was clearly appreciated by all the teachers.

In December the Department honoured one of its most illustrious members by celebrating the scientific work of Professor John Butcher, with a 3-day international symposium (as part of the ANODE series mentioned in the previous bulletin). Numerous speakers from overseas and other parts of New Zealand and the University as well as the Department presented lectures and speeches in honour of John, including guest lecturers Professor Christopher Baker (Manchester) and Professor Gerhard Wanner (Geneva), and visiting dignatories Sir John Scott, President of the Royal Society of NZ, and Professor Rob Goldblatt, President of the NZ Mathematical Society. Further speeches and congratulatory letters were delivered during a special session one afternoon and the Department Annual Dinner held one evening.

On 25th November the MEU organised the annual SMIS Workshop, this year on Assessment in Undergraduate Mathematics. A series of speakers throughout the day from each Department in the School set up discussions ranging from Dealing with Examinations to Cheating to Collaborative Tutorial Assessment. A School lunch was organised to coincide with this day.

An, J. & O'Brien, E.A.: A Local Strategy to Decide the Alperin and Dade Conjectures, J. Algebra 206, 183-207, 1998.

An, J.: Dade's conjecture for 2-blocks of symmetric groups, Osaka J. Math. 35, 417-437, 1998.

Aseev, V., Vamanamurthy, M.K., & Vuorinen, M.: Quasiadditive properties and Bilipschitz conditions, Aequationes Math. 56, 98-130, 1998.

Balanathan R., Pahalawaththa N.C., Annakkage U.D. & Sharp P.W.: Undervoltage load shedding to avoid voltage instability, IEE Proc.-Gener. Transm. Distrib. 145, 2, 175 - 180, 1998.

Barton, B.: Spinning a language web: limitations and opportunities provided by language in mathematics and science education, SAMEpapers, 15-30, 1997.

Butcher, J.C., Chartier, P., Jackiewicz, Z.: Nordsieck representation of DIMSIMs. Num. Algorithms 16, 209-230, 1997.

Butcher, J.C.: Numerical methods for differential equations and applications. Arabian J. Sci & Eng. 22 #2C 17-29, 1997.

Butcher, J.C.: Jackiewicz, Z.: Construction of high order diagonally implicit multistage integration methods for ordinary differential equations. App. Num. Math. 27, 1-12, 1998.

Butcher, J.C.: Diamantakis, M.T.: DESIRE: diagonally extended singly implicit Runge-Kutta effective order methods. Num. Algorithms 17, 121-145, 1998.

Butcher, J.C.: ARK methods up to order five. Num. Algorithms 17, 193-221, 1998.

Butcher, J.C.: Order and effective order. App. Num. Math.. 28, 179-191, 1998.

Butcher, J.C., Chen, D.J.L.: ESIRK methods and variable stepsize. App. Num. Math. 28, 193-207, 1998.

Cao, J., Künzi, H.P.A., Reilly, I.L. & Romaguera, S.: Quasi-uniform hyperspaces of compact subsets, Topology & Its Applns 87, 117-126, 1998.

Chinnappan, M.: The accessing of geometry schemes by high school students, Maths. Ed. Res. J. 10, 27-45, 1998.

Chinnappan, M.: Schemas and mental models in geometry problem solving, Ed. Stud. in Maths. 36(3), 1998.

Conder, M.D.E. & Walker, C.G.: Vertex-transitive non-Cayley graphs with arbitrarily large vertex-stabilizer, J. Algebraic Combintorics., 8, 29-38, 1998.

Conder, M.D.E. & Walker, C.G.: The infinitude of 7-arc-transitive graphs. J. Algebra, 208, 619-629, 1998.

Cullen, R.M., Ellis, N.D. & Walker, W.J.: A model of measles endemicity, Nonlinear Analysis 35, 191-198, 1999.

Federov, S.I.: Weighted norm inequalities and the Muckenhoupt condition in a multiply connected domain, Indiana Univ. Math. J. 46, 1221-1254, 1997.

Gehring, F.W., Marshall, T.H. & Martin, G.J.: On the spectrum of axial distances in Kleinian groups, Indiana Math. J. 47, 1--10, 1998.

Gehring, F.W., Marshall, T.H. & Martin, G.J.: Collaring theorems and the volumes of symmetric hyperbolic n-manifolds, N. Z. J. Math.ematics 27, 207--226, 1998.

Knight, R.W., Gartside, P. & McIntyre, D.W.: All finite distributive lattices occur as intervals between Hausdorff topologies, Order 14, 259-265, 1998.

McIntyre, D.W. & Watson, W.S.: Basic intervals in the partial order of metrisable topologies, Topology & Its Applns 83, 213-230, 1998.

Martin, G.J.: On the geometry of Kleinian groups, Quasiconformal Mappings and Analysis, Springer--Verlag, 253-274, 1998.

Mohamad, A.M.: Generalisation of G*_∂-diagonals and w∆-spaces, Acta Math. Hungarica 80, 285-291, 1998.

Nicholls, G.K.: Bayesian image analysis with Markov Chain Monte Carlo and colored continuum triangulation models, J. Royal Statistical Soc. B, 60, 643-659, 1998.

Oates, G.: A stab in the dark? Intuition and its use by students in mathematical problem solving. SAMEpapers, 157-186, 1997.

Qiu, S.-L., Vamanamurthy, M.K., & Vuorinen, M.: Some inequalities for the growth of elliptic integrals ", SIAM J . Math. Anal. 29(5), 1224-1237, 1998.

Scott, S.D.: N-solubility and N-nilpotency in tame N-groups, Alg. Colloquium 5, 425-458, 1998.

Sharp P.W. & Parsons, L.: The efficiency of extended explicit Pouzet Volterra Runge-Kutta pairs, NZ J Mathematics, 27, 97-111, 1998.

Sharp P.W. & Verner J.H.: Generation of high-order interpolants for explicit Runge-Kutta pairs, ACM Transactions on Mathematical Software 24, 13-29, 1998.

Tee, G.J.: Professor and Mrs Aldis: mathematics, feminism and astronomy in Victorian Auckland, Southern Stars 38(1), 18-27, 1998.

Tee, G.J.: Sir James Lighthill dies, NZ Math. Soc. Newsletter 74, 1998.

Waldron, S.F.D.: Multipoint Taylor Formulae, Numerische. Mathematik 80, 461-494, 1998.

This Bulletin is published by

The Department of Mathematics, The University of Auckland

Editor: Bill Barton, Rm 313, Ph (09) 373 7599 Extn. 8779