Department of Mathematics Publicity Bulletin

DEPARTMENT OF MATHEMATICS School of Mathematical & Information Sciences The

Publicity Bulletin #4 August 1997

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

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 over 70 academic staff and over 950 equivalent full-time students – making it one of the largest at the University of Auckland. With the Department there are two semi-autonomous units: the Applied & Computational Mathematics Unit (ACMU) and the Mathematics Education Unit (MEU). Some staff are members of the Centre for Discrete Mathematics & Theoretical Computer Science (a joint venture between the Computer Science and Mathematics Departments of the Universities of Auckland and Waikato), and some are attached to the Mathematical Biology Research Unit (a joint venture involving AgResearch). 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.

Contents General Research Highlights Teaching News Profiles Appointments, Promotions Postgraduate News Visitors in 1997 Seminars & Conferences Other Staff Activities Recent Publications PhD Students & Masters Students

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General The current EFTS figures for the Department are close to 950, up about 6% on the same time last year. Approximate current figures are as follows: EFTS 1997 EFTS 1996 Change Wellesley 20 22 –2 Stage 1 536 500 +3 Stage 2 242 248 –6 Stage 3 96 79 +17 Stage 4 (BTech projects) 2 0 +2 Total undergraduate 896 849 +47 ( +5.5%) Postgraduate 56 51 +5 (+11.0%) Total 952 900 +52 ( +5.8%) Research Highlights NZMS Fellows Prof. David Gauld, Assoc-Prof M. K. Vamanamurthy and Prof. have been elected Fellows of the NZ Mathematical Society, in the inaugural round of FNZMS awards. NZMS Research Award Professor Peter Lorimer (Mathematics Department) has just been presented with the New Zealand Mathematical Society's Research Award for 1997, with the citation: "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". The Aitken Prize Robyn Curtis and Louise Parsons, two Masters students in the Department, were awarded the New Zealand Mathematical Society's Aitken Prize for 1997. The Aitken Prize was introduced in honour of AC Aitken, one of New Zealand's best-known early mathematicians and a pioneer of computing, is awarded for the best paper(s) presented by students at the annual NZ Mathematics Colloquium. It includes a certificate and a cash prize of $250. Robyn and Louise share the award this year for the talks they gave at the 5th Australasian Mathematics Convention: Robyn for her paper on "Subgraphs of hypercubes containing no small even cycles", and Louise for her paper on "Mathematical models for the foraging strategy of dairy cows". AgResearch Fellowship Dr Tatiana Sobeleva has been awarded a prestigious AgResearch Fellowship to work on genetic/kinetic models of animal growth, and other ecological models of invasive weed ecology using stochastic models. Previous to coming to NZ, Tatiana was a Professor of Physics in the Ukraine. Her interests includes stochastic biological models. Only 5 of these awards are made annually and only rarely outside of existing AgResearch scientists. She will hold the Fellowship as part of the cooperative agreement between The University of Auckland and AgResearch in the recently formed Mathematical Biology Research Unit, and will continue to be based jointly in the Applied Mathematics group based in Tamaki as well as Hamilton. Centre/Institute for the Applications of Mathematics & Statistics Profs Conder, Butcher, Reilly and Wake have been meeting heads of Statistics and Engineering with a view to establishing an interdisciplinary centre. Further meetings are scheduled for September. Research Grants The following staff of the Mathematics Department were successful in obtaining individual grants in the April grant round of the AU Research Committee: Dr Paul Bonnington $3000 for lap-top computer Dr Geoff Nicholls $10000 for CPU time on the High Performance Computer Dr Eamonn O'Brien $3000 for travel Dr Arkadii Slinko $3000 for travel

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Also the Department was awarded an infrastructure grant of $100 000 to upgrade the Department's staff computer system and purchase a number of X-terminals. Most was put into upgrading the Sun Enterprise server ("Aitken") based at Tamaki. Dr Mike Thomas has been awarded assistance from Texas Instruments to the value of $16000 for his research into graphics calculators, and the Mathematics Education Unit has obtained continuation of its British Council funded Link with The Open University with a grant worth $22000. Travel grants from the University's Graduate Research Fund have been won by the following PhD students in the Maths Department this year: Tina Chan David Chen Peter Dobcsanyi Yee Yoon Hong Saraswathi Kota Anjana Singh Cameron Walker Tsukasa Yashiro. Teaching News Web pages Summaries containing general information on Mathematics papers taught by the Mathematics Department are now available on web pages at: http://www.math.auckland.ac.nz/Teaching/Summaries/summaries.html. New papers Four new papers are likely to be introduced by the Mathematics Department in 1998. One is 445.109 Further Mathematics (see the December 1996 issue of the Maths Dept Bulletin). Two others are Stage 3 papers to be trialled under "Special Topics" options: 445.381FC Special Topic: Applied Discrete Algebra (2 points), and 445.388SC Special Topic: Mathematical Biology (2 points). Another is a 4th year paper 445.788FT Advanced Topic: Applied Mathematical Modelling (2 points) principally for BTech students, but also available for Masters students. Consideration is being given to replacing papers 445.350 Topology and 445.355 Geometry (which are offered in alternate years) with a single paper, 445.353 Geometry and Topology, to be offered each year. A committee to consider the matter has been appointed, consisting of David Alcorn and Chris King together with other volunteers. From 1988, the papers 445.101 and 445.202 will be the single-semester papers 445.101SC and 445.202FC, instead of double semester papers. Cyclical Review The review of the core papers 445.151, 152, 162, 251, 252 and 260 is currently underway, chaired by Paul Hafner. It is hoped that a comprehensive proposal will be put before the Department in September, and that the review process will be finished in October. A mini-review of analysis- related 300-level papers is planned for later this year.

Manukau Institute of Technology The paper 445.102 will be taught at MIT in both semesters of 1998, under the auspices of the Department. This is a contribution to an initiative to offer university courses to students at MIT. Teacher Education The secondary teacher education programme is being extended in 1998 to include an intake of students who are already teachers, but of other subjects. These students will study mathematics content in lieu of teaching practice during their pre-service programme. A proposal for a BEd programme for primary teachers in the School of Education contains a compulsory 2-point mathematics content. If accepted, this will be provided by an adaptation of the current paper 445.101.

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Mathematical Olympiad About 100 students from Auckland secondary schools participated in the first Auckland Mathematical Olympiad at the end of May. This initiative, suggested by Arkadii Slinko, had the financial support of the ASB Bank Trust. Teaching Seminar: Using the Computer in Our Teaching On 14th August a seminar addressing some of the issues surrounding the use of the computer in undergraduate mathematics teaching was held. Mike Thomas, Werner Schmidt, John Pemberton, Michelle Wood, Paul Hafner and Geoff Nicholls each made a presentation followed by discussion. Two Coups Last year, in his History of Computers and Computing paper, Garry Tee surprised his class by introducing in person Mrs Catherine Caughey, who operated the first working computer COLOSSUS at Bletchley Park in England during the Second World War. This year he matched that by introducing David Bolam, who helped to build that first computer under secrecy so tight that not all restrictions have yet been lifted by the British Government. Profiles Profile: Dr Jianbei An Dr Jianbei An is a lecturer based at the City campus. His research interests are mainly in group theory, and in particular, the modular representations of finite groups. The representation theory of finite groups is one of the most important and active areas of modern mathematics. A particular focus in recent years is the modular representation theory, and a central topic is the famous Alperin weight conjecture. Jianbei has been working on the modular representation theory for several years, and his work has concentrated on the Alperin weight conjecture and the Dade conjecture, which is a generalization of the Alperin weight conjecture. Last year Jianbei was invited to visit Japan to review a national research project, which is supported by the Ministry of Science and Culture of Japan and organised by Associate Professor Katsuhiro Uno (Osaka University, Japan), and to give talks at the Research Institute for Mathematical Sciences (RIMS) conference at Kyoto and the Algebra conference at Chiba. Profile: Dr Mike Thomas Dr. Mike Thomas is a senior lecturer based at the city campus and is a member of the Mathematics Education Unit. His research interests involve developing a psychological theory of learning mathematics, which includes the promotion of versatile learning (the integration of sequential and holistic modes of mathematical thinking) and proceptual thinking (the ability to see mathematical concepts either as objects or in terms of their inherent processes). This theory has been applied to investigations of how computers and graphic calculators may improve students' conceptual understanding of mathematics through direct experience with mathematical processes. Mike has carried out research in school algebra (particularly on variable, expressions and linear equations), and on the effect of spreadsheets and symbolic manipulators on students' understanding of integration concepts. Mike travelled to UK in 1995, (and will return again in 1988), as part of a graphics calculator research link with The Open University, UK. In 1996 he had the assistance of a Royal Society Teacher Fellow, Bridget Jones, for research into using computers in primary mathematics classrooms. He is currently editing a book, with David Tall, on Intelligence, Learning and Understanding, which looks at the contribution to Mathematics Education of the late Richard Skemp. Mike is also: co-convenor (software) of the Department's Computer Services Committee; a member of the Board of Studies for the Diploma in Mathematics Education; a member of the executive of the Auckland Mathematics Association; and a member of the BEd advisory committee for Auckland College of Education.

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Profile: Dr Philip Sharp Dr Philip Sharp is a lecturer in Mathematics on the city campus, and has been the head of the Applied and Computational Mathematics Unit from February 1995 to August, 1997. His main research interests involve the development of numerical methods for ordinary and delay differential equations, Volterra integral equations, and integro-differential equations. He also has some interest in large-scale computation. Philip believes that an important role for research in Computational Mathematics is to provide reliable and easy to use mathematical software. He is currently involved with the RK99 project, the aim of which is to produce software based on Runge-Kutta methods for different sub-classes of differential, integral and integro-differential equations. The research is being done in collaboration with a colleague in the Department of Mathematics and Statistics at Queens University (Canada), and with several colleagues in the Department of Computer Science at the University of Toronto. In the first semester of this year, Philip used the Internet to aid the teaching of a Stage 2 paper on Computational Mathematics. He found it time-consuming to put the lecture notes, assignments, tests and handouts on the internet, but he believes that the Internet can be used to significantly enhance the learning environment for students. Outside his professional life, Philip is deeply involved in the promotion and administration of billiards, and he has a growing interest in sports psychology.

Appointments, Promotions The Vice-Chancellor has awarded Professor John Butcher a promotion within the Professor range, for his contributions "not only to Mathematics but to the reputation of the University". Dr Eamonn O'Brien and Judy Paterson have both taken up their new appointments in the Department (see previous Bulletin). A new lectureship in Mathematics Education has been advertised, arising from the retirement of Garry Tee in January 1998 (see the Departmental Internet homepage for details). Drs Paul Bonnington, Robert Chan, David McIntyre and Steve Taylor have all had continuation of their initial appointments confirmed. Prof. Graeme Wake has been appointed Deputy Head of the Division of Science and Technology at the Tamaki campus. Prof. John Butcher has been appointed Acting Head of the Applied and Computational Mathematics Unit. Dr Patty McKenna has been appointed as a Post Doctoral Fellow to the Department for two years, working with Dr Paul Bonnington, Dr Margaret Morton and Prof. Marston Conder, on an UARC funded project on topological and combinatorial properties of graphs and tournaments. Patty has a PhD in Applied Mathematics (Graph Theory) from the University of Colorado at Denver, and will be helping teach the Discrete Maths paper 445.225 this semester. There have been three new part-time support staff appointments in the Mathematics group at Tamaki in 1997: Dr Easwaran Balakrishnan (computer software support/programming), Axel Stegner (Scitec unix system support), and Scott Wackrow (Head Demonstrator). The latter positions are shared with Computer Science and Statistics. Jean TahiTahi has been appointed as a new secretary to replace Esther McCondach, who resigned to take up further studies.

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Postgraduate News This year we have a record number of 27 PhD students in Mathematics or Mathematics Education (see below). University of Auckland Doctoral Scholarships were awarded this year to the following Mathematics students who completed their previous degrees with Honours/Distinction: Tina Chan Elliot Lawes Stephen Taylor Matthew Tearle Sanja Todorovic-Vasiljevic Charlotte Martindale has been awarded an AgResearch Scholarship for her PhD work on Modelling Soil Sulphur Dynamics. University of Auckland Masters Scholarships were awarded to Shih-chang Huang and Alexander Kraegeloh, and Mathematics Department Masters Scholarships to Robyn Curtis and Louise Parsons. Alexander Kraegeloh was awarded a Dean of Science Prize for 1996. Gregory Ball (winner of the Senior Scholarship in Applied Mathematics in 1996) has been awarded the Sir George Grey Scholarship for 1997. One of the Master of Science graduates in Applied Mathematics this year has successfully completed a thesis in Mathematical Biology, which is an area of Applied Mathematics developing at the University of Auckland. Shinji Yamamoto, who comes from Tokyo, has completed a thesis on age- structured models of the transmission of diseases such as tuberculosis and HIV. He investigated successfully the stability of various steady age distributions, with a view to establishing the likely long-term incidence of various diseases. Visitors in 1997 Prof. Fred Gehring (), geometric function theory, visited Gaven Martin Dr David Johnson (University of Nottingham), group theory, visited Marston Conder & Eamonn O'Brien Prof. Richard Wilson (Universidad Autonoma Metropolitana, Mexico), topology, visiting David Gauld. Dr Andy Macintosh (Department of Fuel & Energy, University of Leeds), visited Prof. Graeme Wake, to further collaboration on the theory of combustion as part of his Marsden Fund Project in February.

Dr Michalis Diamantakis and his wife Dr Monica Perez de Diamantakis (both with degrees from Imperial College) visited for four months. Michalis worked with John Butcher on his Marsden Fund projects on Runge-Kutta methods, and Monica taught part of the paper 445.310 on History of Mathematics. They have left to take up Research Associate positions at Imperial College. Dr George Gheverghese Joseph (University of Manchester), the eminent historian of non-European mathematics, came as a British Council Visitor for the first semester. He gave the 1997 Aldis Lecture on "Calculating Peoples", and he gave lectures at the other universities in NZ. With Dr Ramankutty we had two Malayalam-speaking mathematicians in offices on the same floor – there are very few universities outside southwest India where that happens. Professor David Tall, the Professor of Mathematics Education at Warwick University, came for June as an Auckland Foundation Visitor. His visit was also supported by The British Council, as part of their 1997 Link programme. He gave lectures at Auckland, Waikato, Victoria, Canterbury and Otago universities; and he was an Invited Speaker at the MERGA Conference.

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Dr Jagdish Prakash, from the University of Botswana (Department of Mechanical Engineering) is visiting Tamaki Campus as an Honorary Research Fellow in Mathematics. He has worked extensively in Medical Fluid Dynamics, including blood flows and human body dynamics. In April, three PhD. students of Prof. Urban Cegrell from Umeå University (visiting him at the University of Canterbury) visited our Department, and they gave general talks on certain areas in analysis. Frank Wikstrom spoke on "Representing measures for the ball algebra", Ewa Berqvist spoke on "Different types of convexity", and Magnus Carlehed spoke on "Comparison of different Green functions". Prof. A. Hinkkanen (University of Illinois, Urbana-Champaign), visited Prof. Gaven Martin. Prof. Herb Wilf (University of Pennsylvania), visited Profs. Marston Conder & Gaven Martin. Prof. Lev Nikitin (Lomonossov State University, Moscow) visited Prof Boris Pavlov. Prof. Jen-Paul Calvi (Universite Paul Sabatier, Toulouse) visited Dr Norm Levenberg. Prof. Len Bos (University of Calgary), approximation theory, visited Dr Norm Levenberg Prof. Christer Kiselman (Uppsala University), several complex variables; convexity theory, visited Dr Norm Levenberg Dr Ron Gribben (Mathematics Department, University of Brunei, Darussalam), is visiting Graeme Wake and helping teach the Advanced Applied & Computational Mathematics paper 445.367. Prof. Reinhard Mennicken (University of Regensburg, Germany). Prof. Mennicken is a senior figure in Applied Mathematics and has published extensively in operator theory, spectral analysis, and partial differential equations. He was Director of the latest International Congress on Industrial and Applied Mathematics held in Germany in 1995, and has been involved in the negotiations for ANZIAM's successful bid to host ICIAM in 2003. Dr Rod Weber (Australian Defence Forces Academy, UNSW), will be visiting for October, working with Prof. Graeme Wake on ignition problems as part of his Marsden Fund project. Dr Mark Nelson (University of Leeds) has been awarded a Royal Society of London postdoctoral fellowship to come to New Zealand and The University of Auckland, to pursue work on the mathematical theory of ignition. Seminars & Conferences Regular seminar series & convenors: Algebra/Combinatorics/Geometry Mark Wilson Analysis Norm Levenberg Applied/Computational/Industrial Maths Vivien Kirk & Graeme Wake Informal Seminar Series Arkadii Slinko Mathematics Education Bill Barton Mini Seminar Series John Butcher PhD Students Seminar Sina Greenwood Tamaki Mathematics Steve Taylor Topology David McIntyre Conferences & Special Seminars Mathematics Summer Workshop At Tolaga Bay Following successful workshops at Huia in December 1994 and at Tolaga Bay in January 1996, a third Mathematics summer workshop was held at Tolaga Bay from 3 to 11 January 1997.

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The theme of this summer's workshop was "Discrete groups and hyperbolic manifolds". Courses of lectures were given by Colin MacLachlan (Aberdeen), Martin Bridson (Oxford), David Singerman (Southampton), Andre Haefliger (Geneva), Linda Keen (CUNY, New York), and Walter Neumann (Melbourne), and individual lectures by Milagros Izquierdo (Malardalen, Sweden), Fred Gehring (Michigan), and Jonathan Hillman (Sydney). The workshop was attended by 45 mathematicians including 15 from overseas and 15 students, and together with family members the number of participants totalled 80. Lectures were held in the mornings and evenings, with afternoons free for recreation and discussion. All participants were accommodated in motels and homestays, and meals were provided by a local catering group. On free afternoons and a day off in the middle of the workshop, participants enjoyed exploring the locality, and some took part in a bus tour of sites near Tolaga Bay of cultural and historical interest. The workshop was run under the auspices of the NZ Institute of Mathematics (Directors Marston Conder, David Gauld, Vaughan Jones and Gaven Martin), with financial support from Marsden Fund grants and the Mathematics Department. LOGOS #1 A 2-day Symposium on "Mathematics, Language & Culture" was held in March to take advantage of the visits of Dr George Joseph (Manchester University) and Dr David Pimm (Open University). Also present were Prof. Alan Bishop (Monash University) and Tamsin Roberts (Maningrida, Northern Territory), Uenuku Fairhall (Western Heights High School) and Sala Bakalevu (Fiji). These last four are all teachers of mathematics in indigenous languages. LOGOS #2 A Symposium on "History and Historians of Mathematics" was held at the University of Auckland Conference Centre on May 27, as the second LOGOS Seminar. Dr George Joseph (visiting from the University of Manchester) spoke on "Confessions of an Unfinished Maths Historian", Monica Perez (visiting from Imperial College) spoke on "A Mathematician's Quest for Truth", and Garry Tee spoke on "Mathematics Outside the Greek Tradition". George Joseph was a British Council Visitor to NZ, and the Symposium was supported by the British Council. Prof. John Butcher rounded off the seminar with an historical look at the Department of Mathematics (see Insert). Mini-Conference on Banach Spaces As a prelude to the 5th Australasian Mathematics Convention, 12 analysts attended a mini- conference in our Department on "Analysis of Banach spaces: Geometry, Differentiability theory, etc.", from Thursday July 3 to Saturday July 5. Invited speakers included: Robert Deville (Bourdeaux), Jon Vanderwerff (Seattle), John Giles (Newcastle), Brailey Sims (Newcastle), Ian Doust (Sydney), Vladimir Pestov (Wellington), Jerry Koliha (Melbourne). The conference organiser was Dr. Warren Moors. Fifth Australasian Mathematics Convention The 5th Australasian Mathematics Convention was held at the University of Auckland Conference Centre, from July 7 to July 11. It incorporated the Annual Meetings of the Australian Mathematical Society, the Australia-New Zealand Industrial Applied Mathematics Group (NZ division) and the New Zealand Mathematical Society. It was attended by 160 mathematicians from NZ, Australia and elsewhere. The conference was directed by Gaven Martin on behalf of the N.Z. Mathematical Society and our Department of Mathematics, with assistance from David McIntyre, and with much of the administration being handled by the University's Centre for Continuing Education. Invited Addresses were given by: Prof. John C. Butcher (Univ. of Auckland) NZMS Lecturer, "Traditional and non-traditional numerical methods for ordinary differential equations''; Prof. Urban Cegrell (Univ. of Canterbury), "Pluripotential theory"; Dr Robert DeVille (Univ. of Bordeaux), "Smooth variational principles and non-smooth analysis in Banach spaces''; Dr Peter Hall (ANU) "Estimating a boundary in an image"; Prof. Peter J. Hilton (SUNY Binghamton) Mahler Lecturer, "The legacy of Henry Whitehead'';

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Prof. A. Hinkkanen (Univ. of Illinois, Urbana-Champaign), "Dynamics and zeros of meromorphic functions''; Prof. Kathy Horadam (RMIT, Melbourne), "Cocyclic matrices and their codes''; Dr Arun Ram (Princeton Univ.), "Combinatorics and representation theory: recent results for Hecke theory''; Prof. Hyam Rubinstein (Univ. of Melbourne), "Extending 3-dimensional topology to dimension n''; Dr Rodney Weber (Australian Defence Forces Academy), ANZIAM speaker, "Combustion waves''; Prof. G. Weiss (Washington Univ., St Louis), "Some basic properties of wavelets and their connectivity properties''; Prof. Herbert S. Wilf (Univ. of Pennsylvania), "Computer proofs of identities: the state of the art''; Prof. Keith J. Worsley (McGill Univ.), "The geometry of random images''. Members of the Department of Mathematics at the University of Auckland gave the following Contributed Talks: Dr Jianbei An, "Dade's conjecture for the Chevally Groups G2(q)''; Britta Basse, "Population dynamics of endangered species''; Dr Bruce Calvert, "An o.d.e. on a closed cube and equilibrium points of neural nets''; Jiling Cao, "On the completeness of hyperspaces" David Chen, "ESIRK methods and variable stepsize''; Tina Ming-hua Chan, "Graph-theoretic structures for Runge-Kutta and other methods"; Prof. Marston Conder, "Inner reflectors and non-orientable regular maps''; Robyn Curtis, "Subgraphs of hypercubes containing no small even cycles''; Dr Michalis T. Diamantakis, "An extension of singly-implicit methods for solving stiff initial value problems''; Sina Greenwood, "Microbundles, manifolds and metrisability''; Dr Vivien Kirk, "Noise and heteroclinic cycles''; Emily Lane, "Chaos near structurally stable heteroclinic cycles''; Dr Tim H. Marshall, "Sphere packing in Euclidean and hyperbolic space''; Dr Warren Moors, "Topological games and semi-topological groups''; Dr Margaret Morton, "Growth of infinite planar graphs''; Louise Parsons, "Mathematical models for the foraging strategy of dairy cows''; John Pearson, "Some minimal obstructions to planar embeddings with three face vertex covers"; Filip Saidak, "New analytical methods in number theory''; Garry J. Tee, "Modelling cometary impact with planetary atmospheres''; A-Prof. M. K. Vamanamurthy, "Distortion functions and quasiconformal maps''; Prof. Graeme Wake, "Industrial Mathematics Clinic: a model for applied mathematics teaching''; Dr Mark Wilson, "Associative rings satisfying the Engel condition''; Shinji Yamamoto, "Epidemic modelling for gender class". Education in Mathematics for Undergraduates Taking advantage of the presence of delegates to both the 5th Australasian Mathematics Convention and the Mathematics Education Research Group Australasia conference, a 1-day seminar was held in the Department on the theme of mathematics education for undergraduates. Twenty people debated four topics in round-table discussions: Course organisation and assessment; Content issues; Social, cultural and affective issues; and the forthcoming ICMI Study Group. The day was organised by Dr Bill Barton. 7th Australasian Bridging Mathematics Network Conference The 7th Annual Australasian Bridging Maths Network Conference was held in Auckland from July 12-14. This was the first time the conference had been held in New Zealand. The conference committee, chaired by Barbara Miller-Reilly, were drawn from a variety of tertiary institutions in Auckland, a reflection of the variety of settings in which Bridging Maths Educators work. Of the 65 participants, about 20 were Australian, the rest New Zealanders. This compares favourably with the 5-10 New Zealanders who normally attend the conference when it is held in Australia. There were about 40 workshop and paper presentations.

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1997 seminars by visitors and local staff and students • Prof. Vaughan Jones FRS FRSNZ (Auckland and Berkeley) Planar Algebras • Dr Norman Wildberger (University of New South Wales) An introduction to hypergroups • Dr Andrew McIntosh (University of Leeds) Ignition of Hazardous Materials • Sanja Todorovic-Vasiljevic (MSc student) Residually finite groups and infinite simple groups • Prof. Ian Stewart (University of Warwick) Does God Play Dice? • Prof. Ian Stewart (University of Warwick) Hidden Symmetries in Partial Differential Equations • Dr Fridrich Sloboda (Bratislava-Slovakia Academy of Sciences) On Piecewise Linear Approximation of Planar Jordan Curves and Arcs • Dr David McIntyre (Department of Mathematics) Finite intervals between Hausdorff topologies • Dr Andrea Peter (University of Münster, Germany) The life and work of Johann Amos Comenius in the light of his impact on current issues in Mathematics Education • Dr Michael Meylan (Department of Mathematics) Waves and the Marginal Ice Zone • Prof. Boris Pavlov (Department of Mathematics) A remark on Wiener-Hopf operators with rational symbols • Prof. Ferencz Moricz (University of Szeged, Hungary) The Cesàro and Copton operators on some Lebesgue spaces • Prof. Richard Wilson (Universidad Autonoma Metropolitana, Mexico) In quest of Tychonoff maximal connected spaces • Assoc. Prof. Peter Hunter (Department of Engineering Science) Soft tissue mechanics • Dr Sergei Federov (Department of Mathematics) On the angle between certain function subspaces of a weighted L2 space on the unit circle • Sina Greenwood (Research Fellow) Microbundles, manifolds and metrisability • Prof. Graeme Wake (Department of Mathematics) Critical Initial Conditions for Thermal Ignition • Robyn Curtis (MSc student) Subgraphs of a hypercube containing no small cycles • Prof. John Butcher (Department of Mathematics) SIRK methods for numerical ordinary differential equations • Dr Eamonn O'Brien (Department of Mathematics) Investigating group representations • Prof. Uri Srebro (Technion-Haifa, Israel) Uniformization of Maps with Folds • Dr Douglas Rogers (East-West Center, Honolulu) From radio telescopes to pool-ball triangles • Dr Margot Gerritsen (Department of Engineering Science) Designing an efficient solution strategy for fluid flows: local grid adaptation and error estimation • Dr Mark Wilson (Department of Mathematics) Associative rings satisfying the Engel condition • Dr Norm Levenberg (Department of Mathematics) Polynomial hulls • Prof. Cris Calude (Department of Computer Science) Some applications of automata to Physics • Dr Monica Perez Diamantakis (Imperial College London) Mathematics and the Unity of Knowledge: Scientific & Philosophical Influences in 16th Century Architecture - El Escorial • Prof. Richard Wilson (Universidad Autonoma Metropolitana, Mexico) Dense subspaces satisfying stronger separation axioms • Prof. J.J.H. Miller (Trinity College, Dublin) On the importance of Shishkin meshes for the accurate numerical solution of flow problems • Bob Valkenburg (Industrial Research Limited) Mathematical Modelling in Videometrics • Prof. Richard Wilson (Universidad Autonoma Metropolitana, Mexico) A review of some recent results on submaximal spaces • Prof. Kevin McLeod (University of Wisconsin-Milwaukee) Sobolev Regularity of Solutions of Parabolic Equations • Dr Brent Everitt (University of Warwick) Automorphisms of Hyperbolic Manifolds • Prof. L.V. Nikitin (Moscow Lomonossov State University) Differential equations changing type: well-posed boundary problems • Dr David Yost (Université de Lyon) Reducible Convex Sets • Assoc. Prof. Mike O'Sullivan (Department of Engineering Science) Current problems in computer modelling of geothermal fields • Dr Arkadii Slinko (Department of Mathematics) Coding and Design of Experiments: two faces of the same problem • Prof. Henrik Bresinsky (University of Maine) Generating sets for polynomial ideals and their radicals • Frank Wikstrom (Umeå University, Sweden) Representing measures for the ball algebra • Ewa Berqvist (Umea University, Sweden) Different types of convexity

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• Magnus Carlehed (Umeå University, Sweden) Comparison of different Green functions • Dr Vincent Moulton () Motions of points in two dimensional complex space • Britta Basse (PhD student) The analysis of a simple predator prey system when one of the terms is replaced by a delay • Dr Vincent Moulton (Massey University) T-theory: the mathematics of similarity • Dr Norm Levenberg (Department of Mathematics) Orthogonal Polynomials in CN • Dr George Gheverghese Joseph (University of Manchester) Multicultural Mathematics, Anti- racist Mathematics: What Can That Be? • Dr Richard Wilson (Universidad Autonoma Metropolitan, Mexico) Dimensions of Digital Spaces • Dr Philip Smith (Osaka University School, Japan) Cybernetic drift and the evolution of pleiotropy • Dr D.L. Johnson (University of Nottingham) Embedding some recursively presented groups • Dr Bruce Calvert (Department of Mathematics) Asymptotically stable equilibrium points of neural nets for ultrahigh gain • Dr George Gheverghese Joseph (University of Manchester) Infinite Series Across Cultures: Background and Motivation • Ulf Backlund (Umeå University, Sweden) The Gleason Property for Reinhardt Domains • Prof. Peter Nyikos (University of South Carolina) Some consistency results in topology • Prof. Peter Nyikos (University of South Carolina) Higher cardinality analogues of the Cantor set • Dr Fridrich Sloboda (Bratislava-Slovakia Academy of Sciences) On Approximation of Jordan Surfaces: A Topological Approach • Assoc. Prof. Brian Mace (Department of Mechanical Engineering) Wave Transmission and Energy Flow in Structures: Modelling and Control • Prof. Bryan Cain (Iowa State University) How Sylvester's Theorem and Lyapunov's Theorem grew together • Prof. Stan Gudder (University of Denver) Sharp and unsharp quantum effects • Peter Nyikos (University of South Carolina) The role of trees in topology • Peter Nyikos (University of South Carolina) Trees, manifolds and special axioms • Professor Naixing Chen (Chinese Academy of Sciences) An inverse method for 2 and 3 dimensional aerodynamic design of turbomachinery • Dr. David McIntyre (Department of Mathematics) Countable metric spaces • Alain Vandal (Department of Statistics) Minimal covers of maximal antichains for interval orders • Dr. Stuart Scott (Department of Mathematics) An unexpected occurrence of the reals • Professor John Butcher and Mr David Chen (Department of Mathematics) The effective order of singly implicit methods for ordinary differential equations • Professor Kevin McLeod (University of Wisconsin, Milwaukee) Mathematical Quantum Field Theory • David Riley (University of Alabama) Burnside-type problems for groups, rings and Lie rings • Carlo Laing (Dept Applied Maths & Theoretical Physics, University of Cambridge) Coupled oscillator networks and their symmetries • Prof David Tall (Warwick University) Visual Aspects of Formal Analytic Concepts • Prof David Tall (Warwick University) Symbolic & Visual Thinking in the Calculus • Dr. Ian Coope (University of Canterbury) Spherical Objects: The Least Circle, Best Sphere and GPS Navigation Problems • Dr. Ian Coope (University of Canterbury) Exact Penalty Function Methods for Nonlinear Semi- infinite Programming • Brian van Dam (PhD Student) Resolutions Revisited • Dr. Mike Hirschhorn (University of New South Wales) The magic of Ramanujan • Dr Michalis Diamantakis (Visiting Research Fellow, Department of Mathematics) Stiff Initial Value Problems and their numerical solution using Diagonally Extended Singly Implicit Runge-Kutta Methods • Prof Len Bos (University of Calgary) Bivariate Kergin Interpolation • Sina Greenwood (Research Fellow) Type I manifolds and their skeletons • Alona Ben-Tal (PhD Student) Domains of Ferroresonance Occurrence By Bifurcation Diagrams • Professor Christer Kiselman (Uppsala University) Lineal Convexity

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• Prof. Aimo Hinkkanen (University of Illinois at Urbana-Champaign) Functions of bounded type • Dr. Colin Fox (Department of Mathematics) Using Markov Chain Monte Carlo to Perform Conductivity Imaging • Dr. Patty McKenna (Post-Doctoral Fellow) Competition Graphs and their Generalisations • Prof Reinhard Mennicken (University of Regensburg, Germany) Spectral Theory for Systems of Differential Operators of Mixed Order and Applications • Dale Winter (University of Michigan) Complete Solutions to Einstein's Equations • Dr. Alex McNabb (Research Fellow) Extensions of Ussing's flux ratio theorem • Dale Winter (University of Michigan) Calculus and Pre-Calculus at the University of Michigan • Prof Reinhard Mennicken (University of Regensburg) Spectral decomposition of symmetric 2X2 block operator matrices • Dr. Ron Gribben (University of Brunei Darussalam) On the heat impulse methods for deducing sap velocity • Tsukasa Yashiro (PhD Student) Immersions from 3-manifolds into R^4 • Dr. Colin Please (University of Southampton) Some mathematical models of cell motion in tumours • Dr. Bruce Calvert (Department of Mathematics) Existence and bounds for a resistive network Other Staff Activities - Prof. Marston Conder and Dr Eamonn O'Brien were invited participants at the meeting on computational group theory, held at the Mathematical Research Institute at Oberwolfach (Germany) in June. Marston Conder went on to give lectures at the universities of Tübingen (Germany), Oxford and Warwick. - Marston Conder was an invited speaker at the 3rd International Conference on Combinatorial Mathematics and Combinatorial Computing held at the University of Melbourne in July. - Prof. Vaughan Jones was honoured when the leading French magazine of science, La Recherche, devoted its issue for July/August 1997 to 300 Years of Science, including a large poster which displays 300 of the most important scientific advances during the past 300 years. The top left entry announces (in French): "1985: Vaughan Jones publishes an important contribution to the theory of knots, and identifies a new invariant polynomial associated with those objects." - Prof. Boris Pavlov has given lectures at the following conferences: "Calculation of Szegö-Kac determinant via fractional model" (with John MacCormick), contributed talk at Steklov Institute, St Petersburg; "Functional model methods for determinants of Wiener-Hopf operators", Invited Address at Moshe Lifschic Conference at Rehovot, Israel; "Functional model of dissipative operators and some practical problems of spectral theory", Invited Address at conference on "Mathematical questions of quantum mechanics and theory of complex systems", Solvay Institute (Brussels); "Dynamics of complex systems and invertibility", Invited cycle of lectures at the conference on "Modern progress in Lax-Phillips scattering theory", Peiresc (France); "Dynamics on Markov background and Demidov stabilization", poster display at University of Queensland; "Symposium on fractional analysis", at the conference on "Lax-Phillips scattering theory after Lax-Phillips", UNSW. - Dr Arkadii Slinko spent three months in Argentina, chairing the Problem Selection Committee of the 38th International Mathematical Olympiad. - A-Prof. M. K. Vamanamurthy has been visiting Lansing, Helsinki, Bangalore, Hangzhou and Adelaide. He was also guest speaker at a Special Analysis Symposium at the University of Michigan in July. - Prof. David Gauld is on leave, at the University of York and at Youngstown State University, Ohio. - Dr Paul Bonnington is on leave, at Bratislava, Ottawa and Burlington, Vermont. - Dr Philip Sharp has gone on leave to Queen's University (Ontario)

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- Maxine Pfannkuch visited Dr Rolf Biehler at the Institut für Didaktik der Mathematik (Bielefeld University) and Prof. Heinz Steinbring at the Institut für Didaktik der Mathematik (Dortmund University). - Prof David Gauld, Sina Greenwood, Abdul Mohamad, and Kerry Richardson attended the 12th international conference on General Topology and its Applications at Nipissing in Canada. Prof Gauld appeared on television and in the press in respect of this conference. - Three School of Mathematical and Information Sciences Professors were invited speakers at a meeting at the International Solvay Institutes for Physics and Chemistry on "Integrability and Chaos in Discrete Systems" in Brussels in early July: Profs Chris Calude (Computer Science), Boris Pavlov (Mathematics), and Graeme Wake (Mathematics). The conference was held at the Solvay Conference Hall of the University Libre de Bruxelles. The reknowned Solvay Institute is directed by Nobel Prizewinner I. Prigogine. Themes for the conference were aspects of nonlinear dynamics and complexity, including integrable and chaotic discrete systems, information processing and computational mathematics. - The conference on ``Women As An Influence In Mathematics Education'', which was held in the Department of Mathematics on 1996 November 29 in honour of Jill Ellis, was reported in the previous Bulletin. The Proceedings of that Conference were published on 1997 August 21, at a Departmental function. Copies of that book (134 pages, plus Supplement) are available from the SMIS. - Three members of the Mathematics Education Unit have been in public media on topical issues. Dr Mike Thomas appeared in a NZ Herald article on Calculators in Schools, and was interviewed on Varsity Hour on Access Community Radio. Dr Bill Barton was interviewed on National Radio on the Brian Edwards Show, and appeared in The Press in Christchurch in an article on ethnomathematics. Prof. Ivan Reilly also appeared in The NZ Herald speaking about the Third International Mathematics and Science Study, and he was interviewed on Asia Dynamic in ETV. Recent Publications An, J. The Alperin and Dade conjectures for the simple Held group, J. Algebra, 189, (1997), 34-57 An, J. The Alperin and Dade conjectures for some finite groups, Proceedings of RIMS Conference on Groups and Combinatorics, 991, (1997), 28-35 An, J. The weights for some finite groups, Proceedings of Conference on Representations of Algebras, Chiba, 6, (1997), 1-7 Bagby, T., Bos, L. & Levenberg, N. Quantitative approximation theorems for elliptic operators, J. Approximation Theory, 85, (1996), 69-87 Bagby, T. & Levenberg, N. Bernstein regions for elliptic operators in two dimensions, Complex analysis, harmonic analysis and applications, Pitman Research Notes in Mathematical Sciences, 347, (1996), 143-156 Balakrishnan, E., Swift, A. & Wake, G. C. Critical values for some non-class A geometrics in thermal ignition theory, Mathematical and Computer Modelling, 24, (1996, 1-10 Barton, B. Anthropological Perspectives on Mathematics and Mathematics Education. In A. Bishop et al (eds) International Handbook of Mathematics Education, Dordrecht: Kluwer Academic Publishers, (1996), 1035-53 Barton, B. Ethnomathematics: A Mathematical View of Culture. In L. Wood & G Perrett (eds) Advanced Mathematical Discourse, University of Technology, Sydney, (1997), 117-123 Barton, B. Cultural Issues in NZ Mathematics Education. In Neyland, J. (ed), Mathematics Education, Vol 2, Reston, VA: National Council of Teachers of Mathematics, (1997), 150-64 Barton, B. The Politics of Mathematics Education. In Neyland, J. (ed), Mathematics Education, Vol 2, Reston, VA: National Council of Teachers of Mathematics, (1997), 165-74 Butcher, J. C. B. Order and stability of parallel methods for stiff problems, Advances in Comp. Math., 7, (1997), 79-96 Butcher, J. C. B. & Chartier, P. A generalization of singly-implicit Runge-Kutta methods, App. Num. Math., 24, (1997), 343-350 Butcher, J. C. B. & Tracogna, S. Order conditions for two-step Runge-Kutta methods, App. Num. Math., 24, (1997), 351-364

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Butcher, J. C. B. An introduction to ``Almost Runge-Kutta" methods, App. Num. Math., 24, (1997), 331-342. Cao, J. & Reilly, I. L., Alpha-continuous and alpha-irresolute multifunctions, Math. Bohem. 121 (1996), no. 4, 415--424 Cao, J. & Reilly, I. L., Almost quasiuniform convergence for multifunctions, Comment. Math. Prace Mat. 36 (1996), 57--68 Cao, J., Reilly, I. L. & Vamanamurthy, M. K. Comparison of convergences for multifunctions, Demonstratio Mathematica, 30, (1977), 171-82 Chan, R. P. K. A-stability of implicit Runge-Kutta extrapolations, Applications Numerical Math., 22, (1996), 179-203 Conder, M. & McKay, J. Markings of the Golay code, NZ J. Mathematics, 25 (1996), 133-139. Conder, M., Morton, M. & Praeger, C. Partition graphs for symmetric groups, J. Graph Theory, 25 (1997), 107-117 Cools R. & Reztsov, A. V. The Different Quality Indexes of Lattice Rules, J. Complexity, 13(2), (1997) Davis, G., Tall, D. O. & Thomas, M. O. J. What is the Object of the Encapsulation of a Process? Proceedings of the 20th MERGA Conference, Rotorua, New Zealand, (1997), 132-139 Ellis, J., Miller-Reilly, B. & Pfannkuch, M. Ways in Which Some Auckland Women Came to Influence Mathematics Education in New Zealand Through the Equals Network 1985-1995. In J. Horring (ed) Celebrating Constructive Change: Women as an Influence in Mathematics Education, Auckland: Mathematics Education Unit, The University of Auckland, (1997), 21-44 Graham, A. T. & Thomas, M.O.J. Tapping into Algebraic Variables Through the Graphic Calculator, Proc. of the 21st PME Conference, Lahti, Finland, 3, (1997), 9-16 Hood, M. J. & Wake, G. C. Gel'fond's equation in spherical domains: II further results and the spherical annulus revisited, Mathematical and Computer Modelling, 24, (1996), 47-54 Hong, Y. Y. & Thomas, M.O.J. Using the Computer to Improve Conceptual Thinking in Integration, Proc.21st PME Conference, Lahti, Finland, 3, (1997), 81-88 Jones, V. F. R. Fusion en Algebres de von Neumann et groupes de lacets (d'apres A. Wassermann), Seminaire Bourbaki no. 800, Asterisque (1996), 251-273 Kota, S. & Thomas, M.O.J. Gender Differences in Algebraic Problem Solving: The Role of Affective Factors, Proc.21st PME Conference, Lahti, Finland, 3, (1997), 152-159 Lee, A. M., Taylor, S. W., Dombroski, J. P. & Gill, P. M. W. Optimal Partition of the Coulomb Operator, Physical Review A 55 (1997) 3233-3235 Leedham-Green, C. R. & O'Brien, E. A. Tensor Products are Projective Geometries, J. Algebra, 189 (1997), 514-28 McIntosh, A. C., Gray. B. F. & Wake, G. C. Analysis of the bifurcation behaviour of a simple model of vapour ignition in porous material, Proc. Royal Society London A, 453, (1997), 281-301 Miller-Reilly, B. J. Gender and Realistic Investigative Mathematics. In J. Horring (ed) Celebrating Constructive Change: Women as an Influence in Mathematics Education, Auckland: Dept. Mathematics, The University of Auckland, (1997) Morton, M. Mathematics - Grad Students and Faculty. In J. Horring (ed) Celebrating Constructive Change: Women as an Influence in Mathematics Education, Auckland: Dept. Mathematics, The University of Auckland, (1997) Morton M. & Thornley G, Mathematics Departments in NZ Universities, NZMS Newsletter, August (1997) Mrsevic, M. & Reilly, I. L. Covering and connectedness properties of a topological space and its associated topology of alpha-subsets, Indian J. Pure and App. Maths., 27, (1996), 995-1004 Pfannkuch, M. Is the Gambling of Men Still Influencing the Teaching of Statistics Today? In J. Horring (ed) Celebrating Constructive Change: Women as an Influence in Mathematics Education, Auckland: Mathematics Education Unit, The University of Auckland, (1997), 109-114 Pfannkuch, M. Statistical Thinking: One Statistician's Perspective. In F. Biddulph and K. Carr (eds) MERGA 20 Aotearoa Conference Proc., Vol 2, Waikato: The Mathematics Education Research Group of Australasia Incorporated, (1997), 406-13 Pleasants, A. B., Wake, G. C. & Rae, A. L. The allometric hypothesis when the size variable is uncertain: Issues in the study of carcass composition by serial slaughter, J. Australian Math. Soc., 38, (1997), 477-88 Pleasants, A. B., Wake, G. C., McCall, D. G. & Watt, S. D. Modelling pasture mass through time in a managed grazing system subject to perturbations resulting from complexity in natural biological process, Agriculture Systems, 53, (1997), 191-208

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S.- L. Qiu, M. K., Vamanamurthy & Vuorinen, M. Bounds for quasiconformal distortion functions, J. Mathematical Analysis and Applications, 205(1), (1997), 43- 64 Reztsov A.V. & Sloan, I. H. On 2D packings of cubes in the torus, Proc. Amer. Math. Soc., 125, (1997), 17-26. Reztsov A.V. & Wake, G. C. Theory and use of functionals on the class of nonnegative polynomials and quadrature formulae, Mathematical and Computer Modelling, 25(6), (1997), 45--55 Rivers, C. M., Wake, G. C. & Chen, X. D. The role of drying in the spontaneous ignition of moist milk powder, Math. Engineering Ind., 6, (1997), 1-14 Scott, S. Transformation Near-rings Generated by a Unit of Order Three, Algebra Colloquium 4(4), (1997), 371-392) Slinko, A. Local structure of linearly compact algebras and local finiteness of coalgebras. First International Tainan-Moscow Algebra Workshop (Tainan, 1994), Berlin: de Gruyter, (1996), 307- 316 Slinko, A., Gale, J. & Cuartero, B. Linearly compact algebraic Lie algebras and Coalgebraic Lie coalgebras., Proc. Amer. Math. Soc., 125(7), (1997), 1945-1952 Slinko, A. USSR Mathematics Olympiads, 1989-1992, Australian Mathematical Trust, (1997), 140pp Slinko, A., Agahanov, N., Reznichenko, S. & Kuptzov, V. All-Union Mathematics Olympiads (9th form) (Russian), Pedagogika, Moscow, (1997), 320pp Tee, G. J., Alexander Craig Aitken: 1895-1967. In L. Kavalieris., F. C. Lam, L. A. Roberts & J. A. Shanks (editors), Proc. of the A. C. Aitken Centenary Conference, Dunedin, University of Otago Press, (1996), 11-19 Tee, G. J., Mark, K. Meteorite craters. Review in Meteorite!, 3, (1997), 37-38 Tee, G. J. John Herschel's Analysis of an Iron Meteorite from Southwest Africa, Meteorite!,4, 1997, 36-7 Tee, G. J., Comments on "Calculating before the chip: an Australian perspective'', Australian & New Zealand Physicist, 34, (1/2), (1997), 5-7 Tee, G. J., Patently first, New Scientist, 29 March (1997) Tee, G. J., Boscovich's parallel, New Scientist, 24 May (1997) Thomas, M.O.J. Computers in the Mathematics Classroom: A survey. In Proc.19th MERGA Conference, Melbourne, Australia, (1996), 556-563 Thomas, M.O.J. & Kota, S. Problem Solving in Algebra: The Role of Arithmetic Thinking and Affective factors, Proc.19th MERGA Conference, Melbourne, Australia, (1996), 564-571 Thomas, M.O.J. & Hong, Y. Y. The Riemann Integral in Calculus: Students' Processes and Concepts, Proc.19th MERGA Conference, Melbourne, Australia, (1996), 572-579 Wake, G. C. Hi-tech Angles: Mathematics at Work, NZ Science Review, 54(1-2), (1997), 5-9 Wild, C., Triggs, C. & Pfannkuch, M. Assessment on a Budget: Using Traditional Methods Imaginatively. In I. Gal and J. Garfield (eds) The Assessment Challenge in Statistics Education , Netherlands: IOS Press, (1997), 205-20 Wilson, M. C. Primeness of the enveloping algebra of a Cartan type Lie superalgebra, Proc. Amer. Math. Soc., 124, (1996), 383-387 Wilson, M. C. Crossed products of restricted enveloping algebras, Comm. Algebra, 25(2), (1997), 487-496

PhD Students in Mathematics or Mathematics Education 1997 Britta Basse Population dynamics of endangered species Supervisor: Graeme Wake Alona Ben-Tal Dynamical Systems Supervisors: Vivien Kirk & Graeme Wake Jiling Cao Quasiuniformities, hyper-quasiuniformities & quasiuniform function spaces Supervisors: Ivan Reilly & Mavina Vamanamurthy Tina Chan Numerical analysis Supervisor: John Butcher Advisers: Philip Sharp & Robert Chan David Chen Numerical analysis Supervisor: John Butcher Advisers: Philip Sharp & Robert Chan Peter Dobcsanyi Combinatorial computation using distributed processing Supervisors: Marston Conder & Peter Gibbons [Computer Science]

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Grant Emms Active control of periodic noise Supervisor: Colin Fox Rose Gong Combustion of wet materials Supervisor: Graeme Wake Adviser: John Burnell [IRL] Mark Harmer Differential equations Supervisor: Boris Pavlov Adviser: Colin Fox Gareth Hegarty Control theory and partial differential equations Supervisor: Stephen Taylor Adviser: Graeme Wake Ye Yoon Hong Promoting conceptual understanding of Integration using spreadsheet and symbolic manipulations Supervisors: Mike Thomas & Ivan Reilly Suzanne Kopetschny Dynamical systems models of soil biological processes Supervisor: Graeme Wake Advisers: AgResearch [Palm Nth] Andrei Korobeinikov Spatial patterns in population models: numerical investigation Supervisors: Graeme Wake & Robert Chan Saraswathi Kota Problem solving in secondary school algebra Supervisors: Mike Thomas & Ivan Reilly Elliot Lawes Group representation theory Supervisor: Jianbei An Adviser: Eamonn O’Brien Charlotte Martindale Soil sulphur dynamics modelling Supervisors: Graeme Wake & Bruce Thorrold [AgResearch] Barbara Miller-Reilly Affective change in adult students returning to mathematics Supervisors: Margaret Morton & Constance Brown [Statistics] Abdul Mohamad Topology Supervisors: David Gauld & David McIntyre John Pearson Studies in combinatorics & group theory Supervisors: Paul Bonnington, Marston Conder & Peter Lorimer Kerry Richardson Topics in Topology Supervisors: David Gauld & David McIntyre Anjana Singh Numerical analysis Supervisor: John Butcher Adviser: Robert Chan Matthew Tearle Dynamical systems Supervisor: Vivien Kirk Adviser: Philip Sharp Sanja Todoriovic- Combinatorial Group Theory Vasiljevic Supervisors: Marston Conder & Eamonn O’Brien Brian van Dam Geometry & Topology Supervisor: David Gauld Adviser: Mavina Vamanamurthy Cameron Walker Compact presentations for the symmetric groups Supervisor: Marston Conder Shinji Yamamoto Mathematical models of population involving disease with age structure Supervisors: Graeme Wake & Mick Roberts [AgResearch] Tsukasa Yashiro Immersions in Manifolds Supervisor: Gaven Martin Adviser: Tim Marshall

Final-year Masters Students in Mathematics or Applied Mathematics 1997 Chung Hyuck, Edward Clark, Robyn Curtis, Alexander Krageloh, Lin O'Driscoll, Louise Parsons, M. D. Saidur Rahman, Jamie Sneddon, Benjamin So, Ieuan Wickham, Rawlinson Yu. Recent Results: Robyn Curtis MSc Hons, First Class Filip Saidak BSc Hons, Second Class Div I Rawlinson, YuMSc Hons, Second Class Div II

This Bulletin is published by: The Department of Mathematics, The University of Auckland Editor: Bill Barton, Rm 313, Ph (09) 373 7599 Extn. 8779

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