DEPARTMENT OF MATHEMATICS

ANNUAL REPORT 1999

PREAMBLE

For this year the Department of Mathematics was one of three departments in the School of Mathematical and Information Sciences, together with Computer Science and Statistics, offering courses at all levels for students in several Faculties. The Department comprises over 70 established and temporary academic staff, based on two sites (the City campus and Tamaki campus), and with the number of its equivalent full-time students totaling approximately 980 in 1999 the Department is one of the largest at the University of Auckland. During the year the School was disestablished and from 2000 the Department will be line managed directly through the Dean of Science.

The Department has a subunit which operates with a minor degree of autonomy: the Mathematics Education Unit. Also staff have been actively involved in the Acoustics Research Centre, the Centre for Discrete Mathematics and Theoretical Computer Science, and the Mathematical Biology Research Unit. The Department has particular research strengths in algebra, combinatorics, complex analysis (one and several variables), differential equations and mathematical modelling, functional analysis and operator theory, history of mathematics, mathematics education, numerical analysis, topology and geometry.

Highlights for the Department in 1999 include the award to Professor Marston Conder of a DSc from Oxford University and his subsequent promotion to the position of Deputy VC (Research) and the election of Prof V.F.R. Jones to the National Academy of Sciences (US). There were invitations to many of our staff to present plenary addresses at major international conferences. We successfully organized and ran no fewer than 4 international conferences. At the May graduation the Department had 6 new PhD recipients: Cao, Greenwood, Hong, Mohamad, Singh and Yashiro. At the NZ Math. Soc. annual meetings two of our former masters students won the Aitken prize for the best student talk, and one, Sneddon, has since enrolled for a PhD here.

A major concern of the Department is the current level of resourcing. Although recent budgetary measures have forced some reduction in the excessive cross-subsidisation of other parts of the University using the income generated by the students we teach, the Department has a cash contribution rate of approximately 46% (after occupancy, depreciation, salary and running costs). This is about twice the Science Faculty average. This forces us to endure a high student:staff ratio coupled with a severe shortage of space for postgraduate students, tutorial and computer laboratory facilities for undergraduate students, and office accommodation for staff and visiting researchers. Many of these issues were addressed in a comprehensive and very positive external review of the Department in 1998. The recent allocation of space from Physics to Mathematics will go some way to alleviate these problems, however, the lack of resources (largely space and staff) to run tutorials is a very worrying problem, which inhibits the Department from providing the quality teaching that it might otherwise offer. This may be one reason why student pass rates in our department are among the lowest in the university.

I. DEVELOPMENTS IN TEACHING

The Department of Mathematics provides teaching in papers for students in several faculties, traditionally Arts, Engineering and Science, but now also a very large number of students in Commerce.

For the 1999 academic year, student numbers totalled approximately 980 effective full-time students (EFTS), including 925 undergraduate EFTS (800 on the City campus and 125 at Tamaki), and just over 55 postgraduate EFTS. These numbers have stabilised to some extent in the last two years, following considerable increases in earlier years, and it is particularly pleasing that the significant growth in our postgraduate enrolments over recent years has been maintained. We anticipate approximately 1000 EFTS in 2000. Numbers at Tamaki have stabilised despite a significant drop in 1998. Until a clear plan for the future development of Tamaki is presented, the Department remains unsure of how to proceed there, and we must live with potential volatility in student numbers.

Because of resourcing issues, we find that we are unable to meet the learning needs of a large number of students (in terms of tutorial assistance and computer laboratories), or to offer scholarships and other support to research students competitive with those offered elsewhere. Our facilities are over-crowded and cannot be made available to all students in need. Urgent improvement is required, to enable the Department to provide a high

quality environment for teaching and learning for both undergraduate and postgraduate students, and to maintain the high profile it has established in research.

Moreover, the fact that the majority of the undergraduate students in the Department receive most of their mathematics learning in large tiered lecture theatres is contrary to the findings of educational research which shows that smaller class size improves educational outcomes. The Department has one of the lowest pass rates in the University. We believe this aspect of our performance is crucially dependent on being given the resources to offer a comprehensive tutorial scheme. This particular problem was specifically addressed in the review in 1998 with the recommendation "The Department of Mathematics give high priority to providing space and staffing resources to support a programme of small group tutorials (of no more than 30 students in each group) for all large enrolment papers (i.e. with 100 students or more) at Stages 1 and 2, and that a Co-ordinator be appointed for the tutorial programme and all aspects of assistance in the large Stage 1 and 2 papers".

The first four graduates from the BTech (Industrial Mathematics) program were capped at the May graduation ceremony, and another eighteen students completed in 1998, however this has dropped away to 6 in 1999. This 4-year program at the Tamaki campus is supported across two Faculties (Science and Engineering) and includes contributions from three Departments (Engineering Science, Mathematics and Statistics). It has a problem-solving focus involving quantitative methods in mathematics, operations research, and statistics, and is strongly driven by applications. Specific papers are included which are case studies and/or project-based, designed to produce graduates with good problem-solving and communication skills. Completing students gave presentations of their project work at the end of the year, and the quality of these presentations and the fact that the majority of the students have found suitable employment is a very good reflection of the value and further potential of the program. However there have been major upheavals in the program due to the resignation of Prof. G. Wake. The Department is currently in discussion with the Statistics Department and the Engineering Faculty trying to map out a future for this program.

Dr David McIntyre developed a very useful and efficient computer-based system for processing examination results (enabling cross-comparisons and monitoring of pass rates and so forth). This system is constantly being refined and is a wonderful assessment tool. The Departments handling and processing of exams is very efficient and we cannot understand why we must be burdened with the University’s archaic centralised examination system. This year the Head of Department had to personally sign off on about 6000 grades. Moreover, considerable time and resources are now spent copying and returning scripts. The Department dealt with nearly 1000 such requests this year, representing approximately $2000 simply in paper charges which must be borne by the Department. This does not count the approximately 100 hours of secretarial time, nor the postage costs.

Paper 445.109 (Further Mathematics) was introduced in 1998, to provide a bridge between papers 445.107/8 and core papers in mathematics at higher levels. This paper was successfully continued at the Tamaki campus in 1999. Other new papers offered in 1998 on a trial basis (under Stage 3 special topics numbers) were 445.381 (Applied Discrete Algebra) and 445.388 (Mathematical Biology). Both papers have proved successful in their own ways in 1999 and will be continued in 2000.

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 reviewed the remaining Stage 1 and 2 papers in 1998. In 1999 the stage 3 courses came up for review. While some progress was made towards consolidating and revitalising these offerings, the review has slowed to a considerable extent in order to consider the effect and success of earlier reviews, particularly of the Stage 2 papers. The papers 445.230 (Advanced Mathematics 2) and 445.231 (Advanced Mathematics 3) will be discontinued from the year 2000. The Department simply does not have the resources to offer small enrolment courses at undergraduate level. We hope to be able to review this situation as our budget permits.

The Mathematics Education Unit (MEU) is continuing to strengthen its involvement in teacher training and mathematics education: During 1999 the MEU hosted #5 in its LOGOS seminar series on Statistics Education with the participation of Prof Mike Shaughnessey from Portland University. Project highlights included the renewal of Asia 2000 funding for our Phillippines link, and launching a Mathematics Enhancement in South Auckland Schools study. Two PhD's were completed during the year, Maxine Pfannkuch and Ye Yoon Hong. Ye Yoon Hong and Mike Thomas won an award for best paper at an international conference on Technology in Mathematics Education in Japan. In the teaching area highlights included a new Masters paper in Statistics Education, and the secondary teacher education programme has been so successful that it has had to form two classes this year. Among the many conferences attended by MEU members of note is the representation by four people at the International Conference on Undergraduate Mathematics Education in Australia. This signals increased participation generally in this area of research. Bill Barton, during his sabbatical travels, took part in a debate at Oxford University on mathematics and culture, and gave a keynote address to the Canadian Maths

Education Study Group conference. Finally The Department is pleased to welcome to the Unit the new Teaching Fellow and three Royal Society Fellows who were appointed during 1999.

The Royal Society Fellows are:Karyn Woodruffe from Pakuranga CollegeRosheen Gray from Senior College of NZKerry Spooner from Northcote College

The Teaching Fellow isMartine McGregor-Reid from St Cuthbert’s

In 1999 the Wellesley Programme had a record 107 students enrolled in the Basic Mathematics paper 445.091, a rise in numbers due to relaxation of entry requirements for students to be two years out of school. Sixty nine students sat the final examination. The students were taught in four streams, each stream had five hours teaching per week, and in addition the tutors were available to help students individually. There is a considerable pastoral care component involved in Wellesley Programme tutoring. In the second semester, the Wellesley Programme as a whole was involved in a review of pre-degree programmes. The issues of semesterisation have prompted the Wellesley Programme Mathematics tutors to consider possible future directions for the courses offered. We continue to review our resources and the recent purchase of a viewscreen will complement our teaching with graphics calculators. Ex-students were again successful, with two graduates in Statistics during 1999, and two in Mathematics from the November examinations. In 1999 there were 26 ex-Wellesley Programme students enrolled in 39 Mathematics papers at the University of Auckland. During the year the Department continued with its initiatives to improve teaching resources, consistency of the standard of core papers, and the interface with students. Information summaries for the majority of papers are posted on Departmental web pages, to facilitate ready access by both staff and students. Folders containing study guides, assignments and solutions, tests and final examinations for each paper are available in the Mathematics Education Unit's library/archive in the Department (and also databanks of lecture notes, past assignments etc. are available for some papers on disc). Recent historical information is particularly helpful to staff members who are unfamiliar with the contents and standard of a paper.

Summer School: The department had an unanticipated and very heavy demand for the new summer school course 445.208. Despite a predicted enrolment of 40 students in this course, the final enrolment was in excess of 220. There continues to be strong demand for 445.108 during summer, with enrolment exceeding 130. It appears that there is further room for growth here and the Department will investigate new initiatives in this area.

Dr. J. Schiff organized the revival of course 475.370 Financial Mathematics (to be taught again in 2000 jointly between maths & stats)

Close scrutiny continues to be given to two of the most important interfaces with students, namely the Department's Assistance Room, and the marking of assignments. Both of these facilities have been reviewed to try to ensure a consistent standard and to provide those tutors and markers involved with the appropriate training and support. During the year three workshops were held for student tutors working in the Assistance Room, and these students were also encouraged to attend workshops offered by the Center for Professional Development and to obtain the CPD Tutoring Certificate.

II. OTHER STUDENT MATTERS

Scholarships and Prizes

Senior Scholarship in Applied Mathematics Andrew DalySenior Scholarship in Mathematics Irine PengAnnual Prize in Applied Mathematics Andrew DalyAnnual Prize in Pure Mathematics Irine PengCollins Prize in Mathematics Edward RosserMathematics Education Prize Michael PrestidgeUniversity of Auckland Masters Scholarships David Robinson, Irine Peng, John Duncan.University of Auckland Doctoral Scholarships William Wright

Summer Scholarships

Some 25 students were engaged in research projects over the summer 1998/99, with scholarship support from the Department. Some took part in the Mathematics summer workshop in Harmonic Analysis in January, while others assisted staff with computational or practical aspects of individual research projects, or in the preparation of papers and other resource materials. This programme of summer scholarships has proved invaluable to both students and staff and we hope to continue to be able to offer it in the future.

Student/Staff Liaison Committee

A Student/Staff Liaison Committee (comprised of staff and student representatives from all levels) met informally four times in the year, providing a successful means of two-way communication between students and staff in the Department on matters of common concern such as course and degree structures, and more general issues such as tutorial facilities and course assessment.

III. EEO & EEdO

The Mathematics Department and its staff are strongly in favour of principles of Equal Employment Opportunity (EEO) and Equal Educational Opportunity (EedO) and have acted accordingly. Over recent decades the actions and decisions made by the Department have been made with concern for the spirit of EEO and EEdO, and often initiatives have been taken specifically to deal with EEO and EEdO issues.

In 1994 an SMIS committee was set up to deal with EEO and EEdO, and immediately achieved two objectives: some improvements were made for students in wheelchairs (in liaison with Works and the University Disability Officer), and a large amount of material was written and distributed on Treaty of Waitangi Issues. Following a lapse in its activity, this committee was set up again in 1998 by the SMIS Administrator with representatives from all three Departments.

Over the years, staff in the Mathematics Department have continued independently to evolve means by which disadvantaged groups can be helped. For example: Dr Bill Barton has organised summer language schools for many students with limited knowledge and skills in English; Drs Bill Barton and Wiremu Solomon have continued to run individual and group tutorials for Maori students (often sent to them by the Student Learning Centre or Nga Tauira Puaho); and Drs Liao Ke-Cheng and Jianbei An have offered Mathematics tutorials in Mandarin (and also Cantonese and Huk Ga) to students of Chinese origin. These tutorials will continue into 2000; Dr. Sina Greenwood organised a similar tutorial for Pacific island students this year, we have moved to strengthen this aspect of our teaching commitment by hiring Dr Greenwood on a 3-year Postdoctoral position.

The Department continues to run courses at foundation levels to meet the needs of students whose background in mathematics is weak. These include the Wellesley Programme and papers 445.101 Mathematics 1 and 445.102 Mathematics 2, complemented by the work of some staff through the Student Learning Centre and the Centre for Continuing Education.

We have attempted to encourage more female students to study mathematics, with some success: the percentages of women in 1998 were 45.1% in the Wellesley programme, 36.6% at Stage 1, 36.5% at Stage 2, 36.3% at stage 3, and 40% at Masters level (cf. percentages in the mid 20s fifteen years ago). These figures are from the Director of Planning. In recent years some members of the Department have made visits to schools to encourage students into mathematics, particularly students from under-represented groups, and offered short courses for the math anxious. Also many EEdO issues have been discussed in our courses in Maths Education.

More recently the Mathematics Department (in conjunction with the Departments of Computer Science, Engineering Science, Statistics and Physics) has supported open days for female high school students, sponsored visiting speakers on the subject of encouraging students to follow careers in the mathematical sciences and computing, and held seminars on multi-cultural mathematics issues. Many of these initiatives have been continued by the Liaison Officer for Women in Physical Sciences and Engineering, whose appointment was strongly supported by our Department. Together with the EQUALS network in Auckland, the Department applied for and received funding for three Fulbright visitors who were based in the Department each for a period of three months in 1990, 1991 and 1994, and held workshops in Auckland and throughout New Zealand.

Some of our intervention programmes have been more successful than others, and the search continues to find a range of helpful interventions. Part of our long-standing attempt to acquire more space involves setting up dedicated space for our Maori students and Pacific Island students. Also a recent suggestion has been made to help deal with students who do not understand English well, by monitoring tests and exams to find if/how they can be understood better.

Efforts are made in the assistance room and computer labs to have a balance of tutors with regard to gender and ethnicity. In addition to running courses for students without much background in mathematics, the Department offers advanced courses for more able or more qualified students, to meet their needs. The principle of giving students every opportunity has shown itself also in concern for individuals as well as groups of people: for example long ago the Department introduced an assessment formula by which a student's final mark for a course can be taken as the better of their exam mark and a combination of their exam and coursework marks. The Department runs assistance rooms, computer labs and some tutorials, and all staff have office hours, to assist those who need help to learn.

The issue of EEO has been faced mainly by trying to appoint female academic staff where possible. This has nearly always been achieved through personal contacts, although positions have all been advertised in the Bulletin of the Association of Women Mathematicians. There have been women on the permanant staff of the Department since the fifties, but not continuously, and very few. We still have only 2.5 FTE women in a total of 37.5 FTE established academic staff. Our women academics are involved in selecting new staff.

Temporary staff are a target group for EEO. Temporary tutors involved in the Wellesley programme say they have been treated very well by the Department, now after face\ing the uncertainty of a 1-year contract (following two successive 3-year contracts) while the programme was under review have accepted 3 year contracts. Another target group is general staff. Our secretary/typists have a copy of the report by general staff on EEO and support its findings, and also endorse the Department's stated need for more programming and technical staff support, for example to provide a consolidated programme of in-service training in the use of computer systems (especially the TeX and LaTeX mathematical typesetting packages).

Many staff with heavy family responsibilities find the support of colleagues and the environment of the department quite helpful, for example in matters of timetabling lectures or parental leave. Staff with illnesses and temporary disabilities have been treated most considerately.

The Department takes the issue of Maori staff seriously. We have one academic staff member who is Maori and one Pasifika. We have PhD students with Maori and Pasifika ancestry. It should be noted that we often take it for granted that staff of the Department form an international group with various religions and ancestry and first languages.

IV. RESEARCH

1. GENERAL/HIGHLIGHTS

The Department of Mathematics has a very strong research programme, with several of its staff among the world leaders in their fields, and attracts a large number of visitors each year as well as an increasing number of postgraduate students and significant research awards and funding. In 1999 no fewer than 28 plenary lectures were given by our staff at international conferences. Twelve staff were involved as principal or associate investigators in successful grant applications to the Marsden Fund — of the 90 or so Marsden Fund grants awarded to the University of Auckland staff so far, 13 have been awarded to members of the Mathematics Department, reflecting the very high international standing it enjoys in research.

Of particular note was the award in 1999 to Professor Marston Conder of a DSc from Oxford University, the election of Professor Vaughan Jones to the National Academy of Sciences (USA). Also Professor Gaven Martin received a prestigious “Research in Pairs” award, to study at Oberwolfach for a month, arranged through a Fellowship from the Volkswagen Corporation.

The Mathematics Education Unit was awarded research grants from both the Ministry of Education and the NZ Qualifications Authority, and continues with a British Council funded research exchange program.

2. PUBLICATIONS

(a) Refereed Journal Articles

AMLEH, A.M., GROVE, E.A., LADAS, and G., GEORGIOU, D.A. 'On the Recursive Sequence $x_{n+1}= +x_{n-1}/x_n$', J. Math. Anal. Appl., 233, no. 2, 790-798, 1999.

AN, J. 'Dade's conjecture for 2-blocks of symmetry groups', Osaka Journal of Mathematics, 35, 417-437, 1998.

AN, J. 'The Alperin and Dade conjectures for the simple Conway's third group', Israel Journal of Mathematics, 112, 109-134, 1999.

ARCHDEACON, D., BONNINGTON, C.P., PEARSON, J., and SIRÁN, J.A., 'The Hadwiger number for the product of two cycles', Combinatorics, complexity, & logic, 113-120, 1997.

BARTON, B. (1999) Ethnomathematics and Philosophy. Zentralblatt für Didaktik der Mathematik, 1999/2, 54-58

BARTON, B. and REILLY, I. (1999). Topological Concepts and Language: A Report of Research in Progress. Notices of the South African Mathematical Society, 30(2), 110-119.

BERGEN, J., and WILSON, M.C. 'X-inner automorphisms of semi-commutative quantum algebras', J. Algebra 220, no. 1, 152-173, 1999.

BLOCKI, Z., KOLODZEJ, S., and LEVENBERG, N. 'Extremal functions and equilibrium measures for Borel sets', Bull. Polish Acad. Sci. Math. 45, no. 3, 291-296, 1997.

BLOOM, T., and LEVENBERG, N. 'Capacity convergence results and applications to a Bernstein-Markov inequality', Trans. Amer. Math. Soc. 351, no. 12, 4753-4767, 1999.

BONNINGTON, C.P. and SIRAN, J.3 'Bipartite Labeling of Trees with Maximum Degree Three', J. Graph Theory, 31, 7-15, 1999.

BOOTH5, R.D.L. and THOMAS, M.O.J. 'Visualisation in Mathematics Learning: Arithmetic problem-solving and student difficulties', Journal of Mathematical Behavior, 18(2), 1-22, 1999.

BOS, L.P., LEVENBERG, N., MILMAN, P.D., and TAYLOR, B.A. 'Tangential Markov inequalities on real algebraic varieties', Indiana Univ. math. J. 47, no. 4, 681-688, 1998.

BORWEIN, J., MOORS, W.B., and SHAO, Y. 'Subgradient representation of multifunctions', J. Austral. Math. Soc. Ser. B 40, no. 3, 301-313, 1999.

BRAND, N., and MORTON, M. 'A note on the growth rate of planar graphs', Combinatorics, complexity, & logic, 147-157, 1997.

BUJALANCE, E. and CONDER, M.D.E. 'On cyclic groups of automorphisms of Riemann surfaces', Journal of the London Math. Society 59, 573-584, 1999.

BUTCHER, J.C. and CHARTIER, P. 'The effective order of singly-implicit Runge-Kutta methods', Numerical Algorithms 20, no. 4, 269-284, 1999.

BUTCHER, J.C, IRWIN, R. J., and HAUTUS., MJ, An area theorem for the same-different experiment., Perception & Psychophysics, 61 (1999), 766-769

CALVERT, B.D. 'Linear systems in a saturated mode and convergence as gain becomes large of asymptotically stable equilibrium points of neural nets', Circuits Systems Signal Process 18, no. 3, 241-267, 1999.

CALVERT, B.D. and ZEMANIAN, A.H. 'Operating points in infinite nonlinear networks approximated by finite networks', Trans. Amer. Math. Soc. 352, no. 2, 753-780, 2000.

CAO, J., GANSTER, M., and REILLY, I. 'Submaximality, extremal disconnectedness and generalized closed sets', Houston J. Math. 24, no 4, 681-688, 1998.

CAO, J., and DONTCHEV, J. 'On a theorem of Popa and Noiri on multifunctions', Math. Slovaca 49, no. 2, 223-224, 1999.

CAO, J., MOORS, W., and REILLY, I. 'On the Choquet-Dolecki theorem', J. Math. Anal. Appl. 234, no. 1, 1-5, 1999.

CAO, J., GANSTER, M., and REILLY, I. 'On sg-closed sets and g-closed sets', Mem. Fac. Sci. Kochi Univ. Ser. A Math. 20, 1-5, 1999.

CEGRELL, U., KOLODZIEJ, S., and LEVENBERG, N. 'Two problems on potential theory for unbounded sets', Math. Scand. 83, no. 2, 265-276, 1998.

CHINNAPPAN, MOHAN. 'Mathematical knowledge search and retrieval effects of instruction in a knowledge-production strategy on the performance of low-achieving students', Journal of Educational Research, 18, 57-74, 1997.

CHINNAPPAN, M., Lawson, M. and Gardner, D.A. ''The use of microcomputers in the analysis mathematical knowledge schemas', International Journal of Mathematical Education in Science and Technology, 29(6), 805-811, 1998.

CONDER, M.D.E., LI, CAI HENG. 'On isomorphism of finite Cayley graphs', European J. Combinatorics 19, 911-919, 1998.

CONDER, M.D.E. 'Explicit definition of the reflected binary Gray codes', Discrete Mathematics 195, 245-249, 1999.

CULLEN, R.M., ELLIS, N.D., WALKER, W.J. 'A model of measles endemicity', Nonlinear Analysis 35, 191-198, 1999.

CULLEN, R.M., WALKER W.J. 'Poliovirus in New Zealand 1915-1997', New Zealand Family Physician 26(3), 48-51, 1999.

CULLEN, R.M., WALKER W.J. 'Predicting the next measles epidemic', New Zealand Family Physician 26(4), 47-51, 1999.

DUVAL, J., and LEVENBERG, N. 'Large polynomial hulls with no analytic structure', Complex analysis and geometry, Pitman Res. Notes Math. Ser., Longman, 336, 119-122, 1997.

EICK, B., and O'BRIEN E.A. 'Enumerating p-groups', J. Australian Math. Society 67, 191-205, 1999.

EICK, B., and O'BRIEN E.A. 'The groups of order 512', Algorithmic algebra and number theory, Springer, Berlin, 379-380, 1999.

GAULD, D., GREENWOOD, S., and REILLY, I. 'On variations of continuity', Topology Atlas, http://at.yorku.ca/t/a/i/c/32.htm, 1999.

GANSTER, M., KANIBIR, A., and REILLY, I. 'Two comments concerning certain topological spaces', Indian J. Pure Appl. Math. 29, no. 9, 965-967, 1998.

GAULD, D., GREENWOOD, S., and Piotrowski, Z. 'On Volterra spaces III', Topology Proceedings 23, 167-182, 1999.

GAULD, D. 'Manifolds at and beyond the limit of metrisability', Geometry and Topology Monographs 2, 125-133, 1999. http://www.maths.warwick.ac.uk/gt/GTMon2/paper7.abs.html

GEHRING, F.W., and MARTIN, G.J. 'Precisely invariant collars and the volume of hyperbolic 3-folds', J. Differential Geom. 49, no. 3, 411-435, 1998.

GEHRING, F.W., and MARTIN, G.J. 'The volume of hyperbolic 3-folds with p-torsion, p ≥ 6', Quart. J. Math. Oxford Ser. (2)50, no. 197, 1-12, 1999.

GOVER, A.R., ZHANG, R.3 'Geometry of Quantum Homogeneous Bundles and Representation Theory of Quantum Groups', Rev. in Math. Phys. 11, 533-552, 1999.

GRAHAM3, A.T. and THOMAS, M.O.J. 'A Graphic Calculator Approach to Algebra', Mathematics Teaching 167, 34-37, 1998.

IWANIEC, T., and MARTIN, G.J. 'The Liouville theorem', Analysis and topology, World Sci., River Edge, NJ, 339-361, 1998.

JOHNSON, D.L., KIM, A.C., and O'BRIEN, E.A. 'Certain cyclically presented groups are isomorphic', Communications in Algebra 27, 3531-3536, 1999.

KIERNAN5, C, OATES5, G., and THOMAS, M.O.J. 'Graphic Calculators and Mathematics Assessment.' Science and Mathematics Education (SAME) papers, Waikato University, New Zealand, 88-106, 1999.

KOROBEINIKOV, A., and WAKE, G.C. 'Global properties of the three-dimensional prey-predator Lotka-Volterra systems', JAMDS, 3(2), 143-150, 1999.

LAIRD, M and TEE, G.J. ‘Identified Flying Objects’ Journal of the Auckland Astronomical Soc. 11-13, 1999

LEVENBERG, N., and YAMAGUCHI, H. 'Robin functions for complex manifolds and applications', CR geometry and isolated singularities, no. 1037, 138-142, 1998.

LEVENBERG, N. 'Normal Polynomial hulls with no analytic structure', CR geometry and isolated singularities, no. 1037, 143-146, 1998.

LEVENBERG, N., and POLETSKY, E.A. 'Pluripolar hulls', Michigan Math. J. 46, no. 1, 151-162, 1999.

MACCORMICK, J.P., and PAVLOV, B.S. 'A geometrical approach to calculating determinants of Wiener-Hopf operators', Lecture Notes in Phys., 504, Springer, Berlin, 333-342, 1998.

MACLACHLAN, C., and MARTIN, G.J. '2-generator arithmetic Kleinian groups', J. Reine Angew. Math. 511, 95-117, 1999.

MARSHALL, T.H. 'Asymptotic volume formulae and hyperbolic ball packing', Ann. Acad. Sci. Fenn. Math. 24, no. 1, 31-43, 1999.

MARTIN, G.J. 'The Hilbert-Smith conjecture for quasiconformal actions', Electron. Res. Announc. Amer. Math. Soc. 5, 66-70, 1999.

MOHAMAD, A.M. 'Some conditions which imply quasi-developability', Bull. Calcutta Math. Soc. 90, no. 5, 325-330, 1998.

MOHAMAD, A.M. 'Metrization and semimetrization theorems with applications to manifolds', Acta Math. Hungar. 83, no. 4, 339-350, 1999.

NEWMAN, M.F., and O'BRIEN, E.A. 'Classifying 2-groups by coclass', Transactions of the American Math. Society 351, 131-169.

PATERSON, J., HORRING3, J., and BARTON, B. A Comparative Case Study of the Effectiveness of Mathematics Teaching by Two Groups of Teachers in Training. In SAMEpapers 99., 162-80

PAVLOV, B., ROACH, G., and YAFYASOV, A. 'Resonance scattering and design of quantum gates', Springer Ser. Discrete Math. Theor. Comput. Sci., Springer, Singapore, 335-351, 1998.

PAVLOV, B. 'Irreversibility, Lax-Phillips Approach to Resonance Scattering and Spectral Analysis of Non-Self-Adjoint Operators in Hilbert Space', International Journal of Theoretical Physics, Vol 38 no. 1, 21-45, 1999.

RILEY, D.M., and WILSON, M.C. 'Group algebras and enveloping algebras with nonmatrix and semigroup identities', Comm. Algebra 27, no. 7, 3545-3556, 1999.

RILEY, D.M., and WILSON, M.C. 'Associative rings satisfying the Engel condition', Proc. Amer. Math. Soc. 127, no. 4, 973-976, 1999. TALL3, D.O., THOMAS, M.O.J., DAVIS3, G., GRAY3, E. and SIMPSON3, A. 'What is the Object of the Encapsulation of a Process?', Journal of Mathematics Behavior 18(1), 1-19, 1999.

TAYLOR, S.W. 'A Smoothing Property of a Hyperbolic System and Boundary Controllability', Journal of Computational and Applied Mathematics, Vol 114-Issue no. 1, 1999.

TEE, G.J. 'Isochrones and brachistochrones', Neural Parallel Sci. Comput. 7, no. 3, 311-341, 1999.

TEE, G.J. ‘The first 25 years of the NZ Mathematical Societry’, NZMS Newsletter, 76, 30-35, 1999.

VINNIKOV, V.L., and FEDOROV, S.I. 'On the Nevanlinna-Pick interpolation in multiply connected domains', Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 254, 5-27, 1998.

WALDRON, S. 'Refinements of the Peano kernel theorem', Numer. Funct. Anal. Optim. 20, no. 1-2, 147-161, 1999.

WILD, C. and PFANNKUCH, M. 'Statistical Thinking in Empirical Enquiry', International Statistical Review 63(3), 1999.

WILSON, M.C. 'Bell's primeness criterion and the simple Lie superalgebras', Ring theory. J. Pure Appl. Algebra 133, no. 1-2, 241-260, 1998.

(b) Sections in Books

BOSS, L., and PAVLOV, B. 'Absolute Continuity of Convolutions of Singular Measures and New Branches of Spectrum of Liouvillians and Few-Body Hamiltonians'. In I. Antoniou and G. Lumer, Generalized Functions, Operator Theory and Dynamical Systems, eds., CHAPMAN\&HALL/CRC, London, New York, Washington, 308-322, 1999.

ELLIS, J., MILLER-REILLY, B., and PFANNKUCH, M. 'Ways in Which Some Auckland Women Came to Influence Mathematics Education in New Zealand Through the Equals Network 1985-1995'. In C. Keitel (ed) Social Justice and Mathematics Education, Freie Universitat Berlin, 220-237, 1998.

KURASOV, P., and PAVLOV, B. 'Generalized perturbations and Operator Relations'. In I. Antoniou and G. Lumer, Generalized Functions, Operator Theory and Dynamical Systems, eds., CHAPMAN\&HALL/CRC, London, New York, Washington, 345-353, 1999.

WALKER, W.J. 'Sampling theory and the arithmetic Fourier transform in Sampling Theory in Fourier and Signal Analysis: Advanced Topics'. Eds. J.R. Higgins and R.L. Stens, Oxford University Press, Oxford, 38-55, 1999.

(c) Books

SCHIFF, J.L. The Laplace transform. Theory and applications. Undergraduate Texts in Mathematics. Springer-Verlag, New York, 233pp, 1999.

SLINKO, A., V. Kuptzov, Ju. Nesterenko, S .Reznichenko Mathematics Olympiads for School Students of 11th form (Russian), Prosveschenie, Moscow, 1999, 254 pp

JONES, V.F.R. Knot theory. Papers from the mini-semester held in Warsaw, July 13--August 17, 1995. Edited by Vaughan F. R. Jones, Joanna Kania-Bartoszy\'nska, Józef H. Przytycki, Pawe\l Traczyk and Vladimir G. Turaev. Banach Center Publications, 42. Polish Academy of Sciences, Institute ofMathematics, Warsaw, 1998. 463 pp. 57-06

(d) Papers in Referred Conference Proceedings

CHINNAPPAN, M. 'Learning to integrate representations of rational numbers', In E.B. Ogena & E,F. Golla (Eds.), Proceedings of the 8th South-East Asian Conference on Mathematics Education, Ateneo de Manila University (Manila, Philippines,1999), 109-118, 1999.

CHINNAPPAN, M. and THOMAS, M.O.J. 'Structured Knowledge and conceptual modelling of functions by an experienced teacher', Proceedings of the 22nd Mathematics Education Research Group of Australasia Conference (Adelaide 1999), 159-166, 1999.

CHINNAPPAN, M., LAWSON, M., and NASON, R. 'The use of concept mapping procedure to characterise teachers' mathematical content knowledge', In J.M. Truan and K.M. Truan (Eds.), Proceedings of the 22nd Conference of the Mathematics Education Research Group of Australasia, Adelaide University Press, 167-176, 1999.

DEMPSEY, J., FOX, C., and PALMER, A.C. 'Ice-slope interaction: Transitions in Failure Mode', in Proceedings of OMAE99, 18th International Conference on Offshore Mechanics and Arctic Engineering, St. Johns, Newfoundland, Canada, 1999.

EICK, B., and O'BRIEN, E.A. 'The groups of order 512', Algorithmic Algebra and Number Theory (Heidelberg, 1997), 379-380, 1999.

FOX, C., PALM, M., and NICHOLLS, G. 'Efficient, exact PDE solutions for MCMC, in Mathematical Modelling, Bayesian Estimation, and Inverse Problems', F. Preteaux, A. Mohammad-Djafari and E.R. Dougherty eds., Proceedings of the SPIE volume 3816, 1999.

GOVER, A.R. 'Aspects of Parabolic Invariant Theory', Supp. Rend. Circ. Matem. Palermo, Ser.II, Suppl. 59, 25-47, 1999.

HONG5, Y.Y. and THOMAS, M.O.J. 'Super-Calculators and Mathematics Examinations', The 7th International Conference on Computers in Education (Chiba, Japan, 1999), 483-490, 1999. Best Paper Award

HOLTON5, D., CLARK5, M., MILLER-REILLY, B.J., REILLY, I., and RENAUD5, P. 'Diversity in New Zealand', In W. Spunde, P. Cretchley, and R. Hubbard (eds), Proceedings of Delta'99 Symposium on Undergraduate mathematics, University of Southern Queensland, Australia, 248-253, 1999.

MCINTYRE, D.W., 'A Web-based System for Examination Processing', WebNet '99: Proceedings of WebNet 99-World Conference on the WWW and Internet, Honolulu, Hawaii, 1999.

MCINTYRE, D. and PFANNKUCH, M. 'Case study: Evaluation of a University Mathematics Programme', In W. Spundle, P. Cretchley and R. Hubbard (Eds) The Challenge of Diversity: Proceedings of the Delta'99 Symposium on Undergraduate Mathematics (Laguna Quays, Queensland), Delta'99 Committee, 126-130, 1999.

MILLER-REILLY, B.J. 'The effect of Gender and Fluency in English on the Mathematical Confidence and Achievement of Adults in a Realistic Mathematics Course', Proceedings of the Fifth Annual Conference of Adults Learning Maths - A Research Forum (ALM5), University of London, UK, 190-197, 1999.

RAHMAN, S5., and SHARP, P.W. 'A numerical study of a traffic flow problem', proceedings of the Fifth Annual Paper Meet, Institute of Engineers (Chittagong, Bangladesh, 1998), 434-442, 1998.

(e) Reviews and Comments

AN, J.: Michael J. Collins, Blocks, normal subgroups, and Brauer's third main theorem, from Journal of Algebra. Review in Mathematical Reviews 99m:20010, 1999.

AN, J.: Masafumim Murai, Blocks of factor groups and heights of characters', from Osaka Journal of Mathematics. Review in Mathematical Reviews 99k:20022, 1999

AN, J.: Robert A. Wilson, The McKay conjecture is true for the sporadic simple groups, from Journal of Algebra. Review in Mathematical Reviews 99h:20016.

BARTON, B. (1999). Ethnomathematics: A Political Plaything For the Learning of Mathematics, 19(1), pp33-36

CONDER, M.D.E.: David Singerman & Paul Watson, Non-maximal cyclic group actions on compact Riemann surfaces. Review in Mathematical Reviews 99a:20050, 1999.

CONDER, M.D.E.: Jean Bevis & Michael Grady, Toroidal maps of modular quotient groups. Review in Mathematical Reviews 99f:20053, 1999.

CONDER, M.D.E.: Benoit Larose, François Laviolette & Claude Tardif, On normal Cayley graphs and hom-idempotent graphs. Review in Mathematical Reviews 99h:05100, 1999.

DIKSHIT, G.D.: X. Li, Integral formulas and inequalities for rational functions, Review in Zentralblatt für Mathematik.

DIKSHIT, G.D.: K. Scherer, Uniqueness of best parametric interpolation by cubic spline curves, Review in Zentralblatt für Mathematik

DIKSHIT, G.D.: Ruth Haas, Bases for splines on a subdivided domain, Review in Zentralblatt für Mathematik

DIKSHIT, G.D.: P. D. Jun Johnson, Continuous functions which change sign without properly crossing the x-axis, Review in Zentralblatt für Mathematik

DIKSHIT, G.D.: R. A. Zalik, Relative differentiation, Descartes' rule of signs, and the Budan-Fourier theorem for Markov systems, Review in Zentralblatt für Mathematik

DIKSHIT, G.D.: E.G. Kwon, Properties of sequence space 1(s,t), Review in Zentralblatt für Mathematik

DIKSHIT, G.D.: R-Q Jia, Stability of the shift of a finite number of functions, Review in Zentralblatt für Mathematik

DIKSHIT, G.D.: T. Lyche, L.L. Schumaker and S. Stanley, Quasi-interpolants based on trigonometric splines, Review in Zentralblatt für Mathematik

DIKSHIT, G.D.: M.S. Floater, Total positivity and convexity preservation, Review in Zentralblatt für Mathematik

DIKSHIT, G.D.: Wu Xiaoqing, A development on approximation by monotone sequences of polynomials, Review in Zentralblatt für Mathematik

DIKSHIT, G.D.: Zhang Peixuan, Characterization of the convergence domains of polynomial series and the minimal convergence domain, Review in Zentralblatt für Mathematik

DIKSHIT, G.D.: Natalia Butkina, An approximation of noisy data by smoothing splines, Review in Zentralblatt für Mathematik

DIKSHIT, G.D.: E.S. Katsoprinakis and M. Papadimitrakis, Extensions of a Theorem of Marcinkiewicz-Zygmund and of Rogosinski's formula and an application to Universal Taylor series, Review in Zentralblatt für Mathematik

DIKSHIT, G.D.: Vittoria Demichelis, Piecewise weighted mean functions and histograms Shepard interpolation formula, Review in Zentralblatt für Mathematik

O'BRIEN, E.A.: Review of Medvedev, Yuri, p-groups, Lie p-rings, and p-automorphisms. Math Reviews, 99m:20035, 1999.

O'BRIEN, E.A.: Review of ORMEROD, E.A, Some p-groups of Wielandt length three. Math Reviews, 99j:20029, 1999.

(f) Technical Reports

Mathematics Department Research Report Series

408 FOX, C., and CHUNG, H. 'Green's function for forcing a thin floating plate', 1999.

415 TAYLOR, S.W. and LITTMAN, W. 'Boundary Feedback Stabilization of a Vibrating String with an Interior Point Mass', 9 pages, 1999.

416 TAYLOR, S.W. and LITTMAN, W. 'On the Interaction between a Group of Unitary Operators and a Projection', 6 pages, 1999.

417 PAVLOV, B., OLEINIK, V. 'Hilbert Theorem on Lemniscate and the Spectrum of the perturbed Shift', 10 pages, 1999.

418 PAVLOV, B., MIKHAILOVA, A., POPOV, I., YAFYASOV, T., and RUDAKOVA, T. 'Scattering on a domain with few wires attached', 17 pages, 1999.

435 ADAMJAN, V., PAVLOV, B. 'Scattering-theory approach in financial Mathematics: options pricing analysis under floating interest rate', 12 pages, 1999.

436 CHOU, Lin-Yi5, SHARP, P.W. 'Order 5 symplectic explicit Runge-Kutta Nystrom methods', 9 pages, 1999.

437 SHARP, P.W. 'High order explicit Runge-Kutta pairs for ephemerides of the solar system and the Moon', 9 pages, 1999.

Other Reports

MOLLER, J. & NICHOLLS, G.K. 'Perfect Simulation for Statistical inference', Chalmers UoT Math. Stats Dept Preprint 33, 1999.

(k) Other Works

BARTON, B. (1999) The Philosophical Background to Ethnomathematics: Where is it taking us? Proceedings of First International Conference on Ethnomathematics (ICEM1), CD Rom, Granada, Spain: Universidad de Granada

BARTON, B. (1999). If you ask no questions, you’ll be told no lies. NZ Mathematics Magazine, 36(2), 28-33

BARTON, B. (1999). The Politics of Mathematics Education. NZ Mathematics Magazine, 36(2), 44-55

FOX, C. and NICHOLLS, G.K., PALM, M. 'Efficient exact PDE Solutions for MCMC', SPIE'99, Colorado, Vol 3816, 23-30, 1999.

GRAHAM3, A.T. & THOMAS, M.O.J. 'A Graphic Calculator Approach to Algebra', New Zealand Mathematics Magazine, 1-7, 1998.

MCNAUGHTON, A.J. 'A New Interior point Algorithm', Proceedings of ORSNZ annual conference, 43-48, 1999.

PFANNKUCH, M. 'Characteristics of Statistical Thinking in Empirical Enquiry', Doctoral Thesis, The University of Auckland, 1999.

THOMAS, M.O.J. 'The Skilled Calculator', NZAMT newsletter, 3(2), 24-35, 1998.

OTHER MATTERS RELATED TO RESEARCH ACTIVITIES

Diploma, Honours and Masters Students

Name Thesis Topic/Title Supervisor(s)

Lilith Braun Normal Families & Bible Code Investigations

Dr J. Schiff

Lin-Yi Chou Efficient symplectic explicit Runge-Kutta methods

Dr Philip Sharp

Nick Davey Modelling of a piezoelectric chip Dr Philip Sharp & Dr P. Nielson (Eng.Sci)

S. D'Souza Project Spreadsheets and Algebra LearningProject Collaborative Learning

Dr Mike Thomas

Adam Duckworth Long Range Planning of Forestry Estates A/Prof. Andy Philpott & Dr Shane Henderson (Eng.Sci.)

Artemiza Filimon Thesis in Financial Mathematics Dr Wiremu SolomonMichael Harre Advanced Course of Study in Numerical

Analysis and Mathematical PhysicsGrant Harris Robust Model Fitting A/Prof. David Scott (Statistics)Bethanna Jackson Thesis in Numerical Analysis Prof. J.C. ButcherMichael Lim Incorporation of Road-line Harvest Dr Alastair McNaughtonHsin-Yee Lin (Statistics) Optimisation of Bread Delivery Dr Alastair McNaughtonSione Ma'u Advanced Course of Study in AnalysisBen McLeod Sampling-Based Algorithms for

Stochastic Linear ProgrammingDr Geoffrey Pritchard (Statistics)

Sanja Milic Mathematics of Finance (Advanced topic) Dr Rod GoverGareth Minshall Analysis of Lobster Catch Data A/Prof. David Scott (Statistics)Sione Mau Complex Potential Theory Dr. N. LevenbergSione Mau Complex Dynamics Dr. N. LevenbergMathias Palm Mathematics, Monte Carlo Methods in

Electrical Conductance ImagingDr Colin Fox & Dr Geoff Nicholls

Ferna Payne Study of the Occurrence of mathematics in Science and Technology Classrooms

Dr Maxine Pfannkuch

Michael Prestidge Halin's theorem for the Mobius Band Dr Paul BonningtonDianne Ritchie Project Teachers and Student Learning Dr Mike Thomas

Adults' Understanding of Fractions Dr Maxine PfannkuchAmanda Rubick The Statistical Thinking of Year 7 and 8

StudentsDr Maxine Pfannkuch

Sepideh Stewart Graceful tree labelingsAdvanced course of study in Algebra and Mathematics Education

Dr Paul Bonnington

Yi-Jing Tsai Thesis in Numerical Analysis Dr Robert ChanSepideh Stewart Verification of Riemann Hypothesis Dr J. SchiffChung Biu Yau Thesis in Applied Mathematics Dr Philip Stephen Yau Boundary Control of a Rotating Beam Dr Stephen Taylor

PhD Students

Name Thesis Topic/Title Supervisor(s)Alona Ben-Tal Dynamical systems Dr Vivien Kirk

& Dr Geoff NichollsYee Hoe (Connie) Cheng Group Representation Theory Dr Jianbei An /

Dr Eamonn O'Brien (advisor)Hyuck Chung Dynamics of Sea-Ice Cover Dr Colin Fox /

Dr Mike Meylan (advisor)

Jianhua Gong Geometry and Analysis Prof. Gaven Martin & Dr Norm Levenberg

Nicolette Goodwin Numerical Methods for Ordinary Differential Equations

Prof. John Butcher& Dr Robert Chan

Mark Harmer Differential Equations Prof. Boris Pavlov / Dr Colin Fox (advisor)

Gareth Hegarty Applied Mathematics: Partial Differential Equations

Dr Stephen Taylor / Prof. Graeme Wake (advisor)

Junying (Shirley) Huang Numerical Methods for the Solution of Stiff O.D.E's

Dr Robert Chan& Prof. John Butcher

Andrei Korobeinikov Spatial Patterns in Population Models: Numerical Investigation

Dr Wayne Walker /Dr Wiremu Solomon (advisor)

Kerry Richardson Topics in Topology Dr McIntyre & Prof. David Gauld

Sasha Rubin Topics in Computational Algebra Dr Eamonn O'Brien, Prof. Marston Conder & Dr Bakhadyr Khoussainov (Computer Science)

Jamie Sneddon Infinite Planar Graphs Dr Margaret Morton& Dr Paul Bonnington

Sanja Todorovic-Vasiljevic Combinational Group Theory Prof. Marston Conder & Dr Eamonn O'Brien

Chung-Ju Tsai Complex analysis and geometry Prof. Gaven Martin& Dr Norm Levenburg

Brian Van Dam Geometry and Topology Prof. David Gauld /A/Prof. M.K. Vamanamurthy (advisor)

Benjamin Warhurst Analytic Function Theory of Infinite Dimensional Teichmuller Spaces

Prof. Gaven Martin /Dr Norm Levenberg (advisor)

William Wright Numerical Methods for Ordinary Differential Equations

Prof. John Butcher & Dr Robert Chan

Saraswathi Kota Problem Solving in Secondary School Algebra

Dr Mike Thomas & Prof. Ivan Reilly

Tamsin Meaney An Ethnographic Case Study of Community-Based Mathematics Curriculum Development

Dr Bill Barton /Dr Kay Irwin (Education)(advisor)

Barbara Miller-Reilly Gender and Mathematics at the Secondary-Tertiary Interface

Dr Margaret Morton& Constance Brown (Statistics), Dr Kay Irwin (Educaiton) /Dr Mike Thomas (advisor)

v. Research Fellows & Visitors

Name Affiliation

Prof. M. Abate University of PisaProf. Dan Archdeacon University of VermontProf. Mike Atkinson University of St AndrewsDr Andy Begg University of WaikatoDr Brian Bolt Exeter University, UKDr. Z. Blocki Jagellonian U.-KrakowProf L. Bos University of CalgaryProf. T. Branson University of IowaDr Caitlin Buck Cardiff UniversityProf. Dominic de Caen Queen's University, OntarioProf. Judith Cederberg St. Olaf College, Minnesota, USAProf. John Conway Princeton UniversityDr C.W. Eaton University of LeicesterDr Bettina Eick University of KasselDr Barrie Galpin Open University, UK

Prof. Bob Gilman Stevens Institute TechnologyProf. Jane Gilman Rutgers UniversityAssoc. Prof. George Havas University of QueenslandProf. Joel Hillel Concordia University, Canada Dr Derek Holt University of WarwickProf. Derek Holton University of OtagoDr. A Isaev Australian National UniversityProf. T. Iwaniec, Syracuse UniversityDr. S. Kolodziej Jagellonian U.-KrakowAssoc. Prof. V. Olejnik St Petersburg University, RussiaProf. Avinoam Mann Hebrew University JerusalemDr Scott Murray University of ChicagoDr Peter Neumann University of OxfordProf. Charles Leedham-Green University of LondonProf. V. Peller Kansas State University, USAProf. Cheryl Praeger UWA, PerthProf. Steven Pride University of GlasgowProf E. Saff University of Florida USADr Alan Delos Santos Ateneo University, Manila, PhilippinesAssoc. Prof. Milo Schield Augsburg College, MinneapolisDr Axel Schneider University of OxfordProf. Michael Shaughnessy Portland State University, OregonProf. J. Siran Slovak Technical UniversityProf. Jim Verner Queen's University, CanadaDr Colin Wright Industry, UK

Seminars by Visitors, Honorary Research Fellows, Staff and Research Students

Assoc. Prof. George Havas (University of Queensland)Exact linear algebra and extended gcds

Dr Georgy Cimel'farb (Computer Science Department, University of Auckland)Gibbs Random Fields in Image Modelling

Dr Andrew Pullan (Department of Engineering Science, University of Auckland)Electrical Imaging of the Heart

Kerry Richardson (Department of Mathematics)Scheduled Relativisation of Instructions

Prof. Avinoam Mann (Jerusalem)Growth conditions for residually finite groups

Dr Tsukasa Yashiro (Department of Mathematics)Liftabilities of low dimensional immersions

Prof. Dan Archdeacon (Vermont)Variations on a theme of Kuratowski

Prof. Stephen Simons (University of California at Santa Barbara)Hahn-Banach minimax theorems

Dr Bettina Eick (University of Kassel)Computing automorphism groups of p-groups

Dr Myung Ho Kim (Rutgers University)A geometric model for information retrieval systems and a set of relevant documents

Prof. Alastair Scott (University of Auckland)Analysing data from case-control studies

Prof. Alastair Scott (University of Auckland)Analysing data from case-control studies

Jozef Siran (Slovak Technical Institute)Triangle group representations and regular maps

Prof. Marco Abate (University of Rome II)Dynamics of holomorphic maps tangent to the identity

Dr Abdul Mohamad (Department of Mathematics)Diagonal conditions which imply metrizability in topological spaces with application to manifolds

Prof. Tadeusz Iwaniec (Syracuse University) Quasiharmonic Fields (Part I of II)

Prof. David Gauld (Department of Mathematics)Weak Conditions Implying Metrisability of a Manifold

Sasha Rubin (Department of Mathematics)Algebraic Structures and Finite Automata

Alona Ben-Tal (Department of Mathematics)Symmetry breaking and symmetry restoration in nonlinear forced oscillators

Brian Van Dam (Department of Mathematics)Highlights of the Belfast Conference

Derek Holt (University of Warwick)Dehn algorithms, combings, and formal language theory

Prof. E.B. Saff (University of South Florida, Tampa)Distributing Many Points on a Sphere

Prof. V. Peller (Kansas State University)Approximation by analytic matrix functions, II

Dr Abdul Mohamad and Prof. Ivan Reilly (Department of Mathematics)Report on the Topology Meeting in Yokohama

Prof. Thomas Branson (University of Iowa)Kato inequalities

Prof. Slawomir Kolodziej (Jagellonian University (Krakow))The Monge-Ampere equation

Dr Tsukasa Yashiro (Department of Mathematics)Constructing immersions from three-manifolds to four-dimensional space

Douglas K. Russell (University of Auckland)The symmetry groups of non-rigid molecules: a Lie algebraic and group contraction approach

Prof. C.J. Goh (University of Auckland)No plane please, support with a cone

Prof. V. Peller (Kansas State University)Approximation by analytic matrix functions

Dr Majid Ali (University of Auckland)GCD and LCM of multiplication ideals

Prof. Jialin Hong (Chinese Academy of Sciences, Beijing)Some schemes preserving the weak invariance for nonautonomous linear Hamiltonian system and an application

Dr Paul Turner (Heriot-Watt University)Loopy geometry and topology

Dr John McKenzie (University of Auckland)Involutions on integral group rings

Dr Geoff Nicholls (Department of Mathematics)Helping Archaeologists Help Themselves

Prof. Jim Verner (Department of Mathematics and Statistics, Queen's University at Kingston, Canada)Some Ramifications of the Derivation of Explicit Runge-Kutta pairs

Dr John McKenzie (Department of Mathematics)Topological Highlights of the Melbourne Meeting, Part II

Dr Sina Greenwood and Prof. David Gauld (Department of Mathematics)Highlights of the Summer Topology Conference in New York

Dr Zbigniew Blocki (Jagellonian University, Krakow, Poland)Regularity of the pluricomplex Green function

Mr Garry J. Tee (Department of Mathematics)Computing with the Riemann Zeta Function

Dr John McKenzie (Department of Mathematics)Topological Highlights of the Melbourne Meeting

Dr Bakhadyr Khoussainov (Computer Science Department)Automata, Algebras and Computations with Algebraic Constraints

Prof. John Conway (Princeton University, 1999 Mahler Lecturer)Mysteries of the Monster

Prof. John Conway (Princeton University, 1999 Mahler Lecturer)Understanding the Symmetries of things

Prof Richard Weiss (Tufts University)Generalised PolynomialsGeneralised Polygons

Prof. Shicheng Wang (Peking University)

Achiral embeddings into 3-spaceProf. Richard Askey (University of Wisconsin-Madison)

An overview of orthogonal polynomialsLouise Parsons (Cornell University)

Dynamical Systems Modelling of Turbulent Wall LayersDr Charles Eaton (University of Leicester, UK)

Modular representation theory - my part in its downfallMr Brian Van Dam and Dr Abdul Mohamad (Department of Mathematics)

Special Resolutions and their Properties & Metrizability of Manifolds by Diagonal PropertiesProf. Bob Gilman (Stevens Institute of Technology, NJ, USA)

Groups and LanguagesProf. Jane Gilman (Rutgers University, NJ, USA)

Discrete Groups with Real ParametersProf. Len Bos (University of Calgary)

Fekete points for radial basis interpolationProf. Ivan Reilly (School of Mathematical and Information Sciences)

On Preclosed sets and their generalisationsProf John Meakin (University of Nebraska, Lincoln)

Equations in groups and monoidsDr Stuart Scott (Department of Mathematics)

Success and FailureGareth Hegarty (Department of Mathematics)

Existence of Solutions for Semilinear Evolution EquaitonsProf Vladimir Pestov (Victoria University of Wellington)

Fixed points, amenability, and measure concentrationProf. Muhittin Mungan (University of Chicago and Bogazici University Istanbul)

Science from Pictures: Determining Pair Interactions from Structural CorrelationsProf. Boris Pavlov (Department of Mathematics)

Another Quantum Device for triadic LogicDr Alastair McNaughton (Department of Mathematics)

A technique for modelling and solving large mixed-integer applicationsDr Amal Al-Amleh (Department of Mathematics)

Global Stability Analysis for Difference EquationsDr Richard Evans (University of Michigan)

Sequences of hyperbolic 3-manifoldsProf. Mike Atkinson (University of St Andrews)

Descent algebrasProf. Charles Leedham-Green (University of London)

Calculation the order of an invertible matrixDr Shayne Waldron (Department of Mathematics)

Degree reducing polynomial interpolationDr Colin Fox (Department of Mathematics)

Efficient, exact PDE solutions for MCMCDr Jilling Cao (Department of Mathematics)

On Some Questions of C_p(X)Dr Philip Sharp (Department of Mathematics)

Efficient Pouzet MethodsAssoc. Prof. M.K. Vamanamurthy (Department of Mathematics)

Similarities between a topological space and its alpha extensionDr Ali Jaballah (University of Waikato)

How to compute the exact number of intermediate rings in some ring extensionsBen Warhurst (University of Auckland)

Teichmüller spaces and the Bers projectionDr Robert Chan (Department of Mathematics)

Extrapolation of symplectic methods in long-term integration of Hamiltonian problemsDr Tsukasa Yashiro (Department of Mathematics)

Deformations of immersed surfaces in the three-spaceDr Paul Bonnington (Department of Mathematics)

Accumulation points in infinite planar graphsDr Norm Levenberg (Department of Mathematics)

An elementary proof of an interesting theorem

Dr Katharina Huber (Massey University)Computing the injective hull of a metric space

Prof. John Howie (University of St Andrews)The concept of rank in semi-group theory

Dr Steve Taylor (Department of Mathematics)On Smoothing Properties of PDEs and Abstract Controllability Results in Hilbert Space with Applications to Boundary Control of Systems governed by PDEs

Prof. John Butcher (Department of Mathematics)Inherent Runge-Kutta stability and practical general linear methods

Prof. Gaven Martin (Department of Mathematics)A proof of the Hilbert-Smith Conjecture for quasiconformal actions

Dr Susan McKay (Queen Mary and Westfield College London)Grigorchuk's celebrated 2-group

Dr Colin Fox (Department of Mathematics)Dynamic loading of a floating ice sheet: theory and measurement

Dr Tsukasa Yashiro (Department of Mathematics)Immersed surfaces and their lifts

Dr Sergei Fedorov (Department of Mathematics)On the boundedness of the weighted Hilbert transform in multiply connected domains

Dr Geoff Nicholls (Department of Mathematics)Perfect Simulation for Bayesian Inference

Abdul Mohamad (Department of Mathematics)When is a countably compact space compact?

Prof. Charles Leedham-Green (University of London)Recognising matrix groups

Prof. Marston Conder (Department of Mathematics)Experimental Algebra--Do computers outperform coffee in producing theorem?

Prof. Vladimir Oleinik (St. Petersburg University)Hibert theorem on lemniscates and spectrum of the perturbed shift

Dr John McKenzie (Department of Mathematics)2 Generator Kleinian Groups

Dr Alexander Isaev (Australian National University )Characterisation of hyperbolic complex manifolds by the dimensions of their automorphism groups

Prof. David Gauld (Department of Mathematics)Torsion in the group of homeomorphisms of powers of the long line

Prof. Dom de Caen (Queen's University, Kingston)Are there any finite projective planes of orders 4k+2?

Prof Nira Dyn (Tel Aviv University, Israel)Subdivision schemes - an overview

Prof Zouwei Shen (National University of Singapore)Affine frames in L_2(R^d)

Prof. Dom de Caen (Queen's University, Kingston)Graphs with few distinct eigenvalues

Prof. Mike Atkinson (University of St Andrews)Permutations and generalised stacksTrees and priority queues

Prof. Vaughan Jones (University of Auckland and California)Loop Groups and Operator Algebras

Dr Barrie Galpin (Open University, UK)Tapping into Mathematics with a Graphics Calculator

Dr Alan Delos Santos (Ateneo University, Manila, Philippines)The use of the T1 92 calculator in pre-calculus and calculus classes at university level

Prof. Mike Shaughnessy (Portland State University, Oregon, USA)Students' Beliefs and Conceptions in Probability and Statistics: Some Clues from Research

Prof. Judith Cederberg (St. Olaf College, Minnesota, USA)Revitalising Geometry Education

Dr David McIntyre (Department of Mathematics)A web-based system for processing examination results

Dr Mohan Chinnappan (Department of Mathematics)Variance between Teacher and Student Schemas

Mr. Greg Oates

Collaborative Learning in Tertiary MathematicsDr Mike Thomas (Department of Mathematics)

The Conceptual modelling of functions by experienced teachersDr Brian Bolt (Exeter University, UK)

Optimum Routes and Stimulating Mathematical ThinkingProf. Derek Holton (University of Otago)

Undergraduate Teaching and PracticeDr Colin Wright (UK)

Juggling Theory and PracticeDr Mohan Chinnappan and Dr Bruce Calvert (Department of Mathematics)

Knowledge and processes underlying proofs and analysisDr Andy Begg (The University of Waikato)

Enactivism: an emerging theoryDr Joel Hillel (Concordia University, Canada)

Current research involving introductory linear algebra and dynamic geometry software

Research Grants

MARSDEN FUND GRANTS

Drs P. Bonnington & M. Morton Planar infinite graphs ($114000)

Prof. J. C. Butcher Innovative numerical methods for ordinary differential equations.($41000 includes GST)

Prof. J. C. Butcher and Dr. R. Chan Theoretical and practical investigations in numerical analysis ($60000 includes GST)

Drs C. Fox and G. Nicholls New statistical methodologies for physics-based inference ($65000 includes GST)

Prof M. Conder, Dr J. An & E. O'BrienEffective computational approaches to questions in group theory and applications ($80000 includes GST)

Prof V. Jones, M. Conder , D. Gauld, G. MartinInteractions between group theory, topology and mathematical physics ($80000 includes GST)

Prof. G. Martin Analysis and Geometry ($112000 includes GST)

OTHER EXTERNAL GRANTSDr M. Thomas Casio: Calculators and Maths Learning ($8000), Casio: Conference funding ($20000),

Asia 2000 (with MEU and School of Education): Exchange with Ataneo University ($4420), Woolf Fisher (with MEU): Mathematics For South Auckland Schools ($8000), The British Council (with MEU): UK visitor for graphic calculator research ($2500)

Prof. G. Martin National Science Foundation (US $ 2000) Volkswagen Stiftung at Oberwolfach (US $ 2000)

Dr J. Nicholls Maphysto (Denmark): Bayesian Inversion ($5000)

Dr Bill Barton Graphics Calculators($3600) The British Council

MEU South Auckland Maths Enhancement Scoping Study. Woolf Fisher Trust ($9000)

AUCKLAND UNIVERSITY STAFF RESEARCH GRANTS

Dr B. Barton. Topological Concepts (1500)Indigenous. Languages & Mathematics (2500)

Dr M. Chinnappan Understanding and developing teachers' mathematical understanding of & Dr M. Thomas algebra ($6000)Dr M. Chinnappan Effect of self-explanation and technology on knowledge activation in school algebra

($9887)Dr C. Fox & Tan Holographic Auralization ($8000)Prof D. Gauld Joint continuity ($1000)Dr R. Gover Differential geometry etcetera ($12269)Dr P. Hafner Investigations on interconnection networks ($4000)Mr. C. King Chaos ($3500)Dr M. Thomas Calculators and Mathematics: A comparative Study ($4700),

Leaning Mathematics with Graphic Calculators ($4000)A. Prof N. Levenberg, Several complex variables ($3000)

AUCKLAND UNIVERSITY GRADUATE RESEARCH GRANTS

Dr A. McNaughton Visit to UK ($1500)

VI Staff leave and ConferencesInvited/plenary lectures marked with an asterisk (*)

Mr David Alcorn NZ Mathematics Colloquium, University of Canterbury (July)Harmonic Analysis, Raglan NZ (Jan)

Dr Jianbei An Australian and American Mathematical Societies Joint Meeting, Melbourne (July)

Dr. B. Barton 1999 Spring Topology Conference, Salt Lake City, USA, 17-20 March, Topological Concepts and LanguageThird Iberio-American Topology & its Applications conference, Gandia, Spain, 5-8 April, Topological Concepts and LanguageIs Mathematics A Cultural Artifact? * A Debate at the Dept. Educational Studies, University of Oxford, England, 18 May, 1999 Ethnomathematics: A New Path or a Byway to a Quagmire.Technology in Mathematics Education Conference, Brock University, St Catharines, Ontario, Canada, 3-5 June, 1999Canadian Mathematics Education Study Group* 23rd Annual Meeting, Brock University, St Catharines, Ontario, Canada, 5-8 June, Une Archéologie des Concepts Mathématiques: Tamiser le langue pour des significations mathématiques (An Archaeology of Mathematical Concepts: Sifting Languages for Mathematical Meanings).Methodology in Mathematics Education, Dept. Education Seminar, University of Bristol, 17 June, Borrowing Methodologies: The Frying Pan and the FireNZ Mathematics Colloquium, Christchurch, 6-9 July, 1999Post-Constructivist Theories in Education, Centre for Science & Mathematics Education, Victoria University, 4-5 November, Cultural Relativity & Mathematics Education

Dr Paul Bonnington Short Leave (June-July)4th Slovene Conference on Graph Theory, Bled, Slovenia (June-July)British Combinatorial Conference, Kent, England (July)

Prof J. C. Butcher MODSIM 99 International Conference on Modelling and Simulation, Hamilton,* (December)"Efficient Integration for Continuous Simulation"SciCADE 99 International Conference on Scientific Computation and Differential Equations*, (August) “A New Family of Numerical Methods for Stiff Problems"

Dr Mohan Chinnappan South-East Asian Conference on Mathematics Education, Atenoe de Manila University, Manila, Philippines

Prof Marston Conder Groups & Computation, Columbus, Ohio (June) “Fast recognition of classical groups over large fields”

Algebraic & Topological Methods in Graph Theory, Bled (June/July) * “Combinatorial group-theoretic methods in graph theory and discrete geometry”

New Zealand Mathematics Colloquium, Christchurch (July)Joint Meeting of Australian and American Math Societies, Melbourne (July)Victoria Algebra Conference, Melbourne (July)BHN 90, Canberra (October)RSNZ Conference on Interactions between universities, CRIs & industry, Auckland (November)Groups & Computation, Sydney (December) Association of Pacific Rim Universities (Auckland, September 1999)

Dr Colin Fox Short Leave (January, June-July)OMAE99 *SPIE Eenver99 *

Prof David Gauld NZ Mathematics Colloquium Summer Conference on Topology and its Applications, New YorkHarmonic Analysis, Raglan NZ (Jan)Vamanamurthy Symposium* (November)

Dr Rod Gover Colloquium of the Société Mathématique de France CIRM, Luminy, France *National Research Symposium on "Partial differential equations and differential geometry" at the University of Melbourne, Australia *Special session on "Partial differential equations and differential geometry" at the combined meeting of the Australian Mathematical Society and the American Mathematical Society University of Melbourne, Australia *

Dr Allison Heard SciCADE (August)ANODE conference, University of Auckland (August)

Dr. N. Levenberg Midwest Several Complex Variables, Toronto, Canada, April, 1999Wallenburg Symposium in Complex Analysis, conf. in honor of C. Kiselman, Stockholm, Sweden (May)Midwest Several Complex Variables* Conf. in honor of B. A. Taylor ( November)

Prof. Gaven Martin Colloquia and Seminars at the University of Michigan* (1) The Hilbert Smith Conjecture, (2) Two generator Arithmetic Kleinian groups, (3) Geometry of discrete GroupsFunction Theory, Oberwolfach (January)* Familes of analytic functions avoiding continuous functionsHarmonic Analysis, Raglan NZ (Jan)Vamanamurthy Symposium* (November)XVI Joint Meeting of the Finnish and Romainian Mathematical Societies*, Yash (June)VC's day symposium on Research: Policy, Management and Performance (October)

Dr David McIntyre New Zealand Mathematics Colloquium, ChristchurchWebNet '99, Honolulu, Hawaii (October) *Delta '99, Laguna Quays, Queensland (November) *

Dr Alastair McNaughton Annual leave (January)TC7, Cambridge, UK (July)Operational Research Society, Hamilton (December)

Ms Barbara Miller-Reilly Delta'99 Symposium on Undergraduate Mathematics, Queensland, Australia (November)Polytech Mathematics Teachers Conference, Auckland (December)

Dr Geoff Nicholls LWOP based in Auckland (1st semester)NZAA conference on Chronometrics in Archaeology

Dr Eamonn O'Brien Ohio Sate University (June) *University of Sydney (November)*

Prof Boris Pavlov Special short leave for conferences in EuropeCongress of Applied and Industrial Mathematics, Edinbourgh, GB (July) *Conference on NanoComputing, Gerhard Mercator University, Dujsburg, Germany (July) *Conference on Time Asymmetric Quantum Mechanics and Rigged Hilbert Space mathematics, Arnold Sommerfeld Institute, Clausthal, Germany (July) *Memorial conference of Professor B. Scökefalvi-Nagy on functional analysis and applications, Szeged, Hungary (August) *Conference on Analysis and Mathematical Physics in honour of Lars Gårding on his 80th birthday, Lund, Sweden (August) *Harmonic Analysis, Raglan NZ (Jan)*

Dr Maxine Pfannkuch LOGOS#5 Research Issues in Statistics Education Seminar Day in Auckland (March)

Dr Stuart Scott Near-Ring Conference, Edinburgh*

Dr Philip Sharp SCICADE conference, Fraser Island, Australia (August) * ANODE conference, University of Auckland (August)

Dr A. Slinko, International Algebraic Seminar in honour of $70$th anniversary of theChair of Higher Algebra of Moscow State University, Moscow XXII Bosphorus Workshop on Economic Design, Istanbul SAET (Society for the Advancement of Economic Theory)Conference, Rhodes, Greece Twelfth World Congress of the International Economic Association, Buenos

Aires, ArgentinaInternational Conference on Mathematical Logic (devoted to $90$-th birthdayof Malcev) Novosibirsk*

Mrs Moira Statham Mathematics Colloquium Education Day (July)New Zealand Statistical Assoc. 50th Anniversary Conference (July)ATEC Annual Conference (July)LOGOS (Statistics) (March)

Dr Stephen Taylor New Zealand Mathematics Colloquium, University of Canterbury, Christchurch (July)

Mr Garry Tee, NZ Mathematics Colloquium, University of Canterbury (July)*NZ Statistical Association, Jubilee Meeting, Wellington (July)*

Dr Michael Thomas 22nd Mathematics Education Research Group of Australasi Conference, AdelaideLogos 5 Research Issues in Statistics Education (March)VC's day symposium on Research: Policy, Management and Performance (October)

Associate-Professor M. K. Vamanamurthy was honoured on his retirement by a symposium on November 19. His colleagues Glen Anderson (Michigan State University) and Matti Vuorinen (University of Helsinki) attended, with support from our Department. The following lectures were presented:

Marston Conder, "Introduction",Gaven Martin, "Conformal geometry",

John Butcher, "Some Diophantine equations related to the Hardy-Ramanujan taxi",Glen Anderson, "A quasi-story of Three Guys",Bruce Calvert, "Local and global extrema for polynomials in several variables",Ivan Reilly, "Vamanamurthy's topological work",Matti Vuorinen, "Conformal invariants and quasiconformmal mappings",Tadeusz Iwaniec, "The failure of lower semi-continuity for linear distortion",David Gauld, "Meticulous Keen Versatile, a mathematical tribute to MKV",M. K. Vamanamurthy, "Quasiconformal distortion".

Vaman was presented with a coffee-table made of teak, and the celebrants then attended dinner at Langford's Restaurant on Mount Eden, where Vaman was given some books to place on that table.

A Masters student John Duncan was awarded a Fulbright Scholarship for study in the USA.

The 1999 Auckland Numerical Ordinary Differential Equations Workshop (ANODE99) was held here in the Department on August 16-20. The workshop, organized by John Butcher, Robert Chan, Nicolette Goodwin and Allison Heard, was one of a series of international workshops in numerical analysis held in Auckland overthe last several years. The workshop was attended by 63 academic participants from over 16 countries. The meeting included three morning sessions consisting of lectures on specific themes, allowing a more in-depth presentation than is usually possible. The themes were: Dynamics of General Linear Methods (Ernst Hairer and Pierre Leone), The Joint Spectral Radius of Families of Matrices, with Applications to Stability Theory (Marino Zennaro and Nicola Guglielmi) and Sensitivity Analysis and Optimal Control for Large-Scale Dynamical Systems (Linda Petzold and Radu Serban). The remaining talks were organized into a minisymposium and covered a wide range of topics in numerical ordinary differential equations, including stochastic differential equations, delay equations, software, waveform relaxation techniques, and differential-algebraic equations. There was much opportunity for discussion, including an interesting panel session on the last day.

1999 Raglan Summer Research Workshop. The annual summer workshop organised by the New Zealand Mathematics Research Institute was held this year in Raglan, from 3-9 January. Initially oriented toHarmonic Analysis on Riemann surfaces, the main topic was gradually transformed and finally covered many wider parts of mathematics. The total number ofparticipants 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 universitiesin Auckland, Christchurch, Wellington and Hamilton. These lectures were also reasonably well attended and most of the attendees came to Raglan. Each lecture inRaglan 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.

A Group Theory Workshop was held on November 22-23, with visitors supported by the Marsden Fund and the Department of Mathematics. The following lectures were presented: Dr Bettina Eick (Kassel), "Algorithms for infinite polycyclic groups".

Prof. Avinoam Mann (Jerusalem), "On the number of groups having a certain number of generators or relations",

Dr Scott Murray (Chicago), "Using subgroup chains in algorithms",Dr Axel Schneider (Oxford), "Classifying p-groups by hyperclass".Peter Dobcsanyi, "A parallel implementation of the Low-Index Subgroups algorithm", andProf. Steve Pride (Glasgow), "The geometry of group extensions".

418 COMMUNITY SERVICES

David Alcorn continued his work as chair of the committee responsible for publishing the NZ Journal of Mathematics, and Prof. Gaven Martin took over as Editor after Prof. John Butcher retired from this position during the year. Also David Alcorn served as Book Reviews Editor for the NZ Mathematical Society Newsletter.

Dr. J. Schiff lectured at St. Cuthberts College on Transfinite Arithmetic. He also announced the discovery of asteroid 1999 SO9, Minor Planet Circular 36835, Nov. ’99, Harvard-Smithsonian Center for Astrophysics

Dr Jianbei An delivered an invited series of seminars at Peking University and conducted a workshop at Beijing Normal University. He also acted as Examiner/Assessor of three PhD and three Masters theses in Mathematics at Peking University, Capital Normal University and Southwest-China Normal University, and was a member of the Scientific Committee of the International Conference on Representation Theory held at Shanghai.

Dr Bill Barton served on the Editorial Board of the journal Educational Studies in Mathematics and as Assistant Editor of the Mathematics Education Research Journal and as Review Editor of the journal For the Learning of Mathematics. He gave an invited address to Graduates at Wellington College of Education: Gaining Perspective: Some thoughts for teachers (especially of mathematics), completed a report for the Dept Mathematics, University of Canterbury on Mathematics Education Issues in the Department. He was also elected to the executive of the NZ Mathematical Society.

Dr Paul Bonnington served (as Vice-President) on the Council of the Combinatorial Mathematics Society of Australasia.

Prof. John Butcher served on the Editorial Boards of five international journals, and for part of the year as Editor of the NZ Journal of Mathematics. He also served as a member of the Mathematical and Information Sciences advisory panel for the Marsden Fund, wrote a series of popular articles for the NZ Mathematical Society Newsletter and the NZ Mathematics Magazine, and together with Dr Robert Chan organised an international workshops in Auckland on the numerical analysis of ordinary differential equations.

Dr Bruce Calvert served on the Editorial Board of the Journal of Abstract and Applied Analysis.

Dr Mohan Chinnappan coordinated the special interest group on Mathematics Cognition/Instruction for the Mathematics Education Research Group of Australasia (MERGA), and contributed to a workshop on "Maths Meets People" for the Wellington Mathematics Association.

Prof. Marston Conder served on the Foundation for Research, Science & Technology’s Advisory Committee for NZ Science & Technology Postdoctoral Fellowships.

Profs Conder, Gauld, Jones and Martin are directors of the NZ Mathematics Research.

Dr Fox acted as Head of the University's Acoustic Research Centre, and served on the Committee of the NZ Acoustical Society.

Prof. David Gauld served as Secretary of the NZ Mathematics Research Institute, and as Examiner for the NZ Educational Scholarships Trust. Also as a member of the Advisory Committee of the Summer TopologyConference

Lynne Gilmore served as coordinator of the Tamaki Science & Technology Staff/Student Consultative Committee, a member of the Auckland branch committee of the Association of University Staff, AUS Status of Women representative, and a member of the AUS Academic Staff Collective Employment Contract negotiation team. She also participated in the University's "Resolve" Harassment Contact Network, and as a Marker for the 1998 Bursary Examination in Mathematics with Statistics.

Dr Paul Hafner served as a member of the Science Faculty's panel for Distingished Teaching Awards.

Dr Vivien Kirk served on the Council of the NZ Mathematical Society.

Dr David McIntyre served as an Editor of the Topology Atlas, and as Publications Convener and Visitors Coordinator for the NZ Mathematical Society.

Dr Alastair McNaughton was an invited participant in a panel for the University's "Top Teachers" seminar (run by the CPD), and was engaged in consultation on forest harvesting and the NZEST scholarships examination for Mathematics with Calculus.

Dr Margaret Morton continued to present courses for the Centre for Continuing Education, and served on the University's Education Committee and on Lecturers' Association.

Dr Eamonn O’Brien served on the Advisory and Editorial Council for the computational algebra system GAP (advising on development of the system and acting as an editorial board for software submitted for the system). He has also been invited as Guest Editor for a special issue of the Journal of the Australian Mathematical Society to appear in 1999.

Maxine Pfannkuch served on the Editorial Board for SAME Papers (University of Waikato).

Prof. Ivan Reilly, Dr Arkadii Slinko and retired Assoc. Prof. Gordon Hookings all continued their important work in the training and selection of NZ participants for the International Mathematical Olympiad, and Dr Slinko was co-Leader of the NZ team for the 1998 International Mathematics Olympiad Also Prof. Reilly carried out the role of Esquire Bedell for numerous official functions and graduation ceremonies the first semester.

Dr Joel Schiff served as Executive Editor of the NZ Journal of Mathematics, and as Editor and Publisher of the journal "Meteorite!".

Dr Wiremu Solomon served as a member of the Executive Committee of the New Zealand Statistical Association, the Science Faculty's Staffing Committee and its Committee for Maori Equity in Science, and the University's Operations Research Committee. He was also a Marker for the 1998 Bursary Examination in Mathematics with Statistics, and continued to offer tutorials for Maori and Pacific Island students in mathematics.

Moira Statham served as Deputy Coordinator of the Wellesley Programme, and together with Pam Hurst was involved in interviewing prospective students for the programme, their subsequent orientation to the University, pastoral care, and giving them advice on options for further study upon completion. Organising Committee for Time 2000 and International conference on Technology in Math. Education.

Dr Steve Taylor assisted with the Coca-Cola Youth Expo, and gave an invited talk on careers and opportunities in mathematics at the Selwyn College Careers. He was on the organizing committee for the ANZIAM 2000 Conference and the McNabb Syposium.

Dr Mike Thomas served as a member of the RSNZ Science & Technology Teacher Fellowship Panel, the Auckland College of Education BEd Advisory Board, and the Executive of the Auckland Mathematics Association and a Thesis Examiner for Canterbury University.

Dr Shayne Waldron is serving on the organising committee for an international conference on Surface Approximation and Visualisation, to be held at Christchurch in February 1999.

Drs Wayne Walker and Rhys Cullen have become involved in serious and ongoing debate over infectious diseases and vaccination issues, with North Health and the Department of Health.

VII. OTHER MATTERS

Staffing

The year started with the recruitment of a new Departmental Administrator Mr. Ross McCallum after the retirement of Mrs Bev Grove. Ross has warmed to the challenge of organizing such a large department and his contributions, along with those of the secretarial staff Olita Moala, Min Young and Jean Martin (who left at the end of the year) have been crucial in the success of the Department in meeting its mission.

A long-standing member of the Department, Associate Professor M.K. Vamanamurthy retired from his position in December (see below). Mr John Pemberton also took early retirement, having been with the Department as a programmer for many years.

We also welcomed Dr Rod Gover who has taken up his lectureship in the department. Also and Adjumct Professorship was accepted by Prof C. J. Goh who was previously at the University of Western Australia

The vacant chairs of Profs. J. Butcher, G Wake and M. Conder, as well as other recently vacated positions have not been filled. These issues will be addressed in the Departments forthcoming strategic plan.

Short-term visiting positions were held by Professors Mike Atkinson (St. Andrews), Prof. Charles Leedham-Green (University of London), Prof L. Bos (University of Calgary), Prof. T. Iwaniec, (Syracuse University), Prof V. Peller, (Kansas State).

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

Dr N. Levenberg to associate ProfessorDr J. An Over Senior Lecturer barDr Bruce Calvert Over Senior Lecturer barDr Bill Barton Special Increment in SL scaleDr Mike Thomas Special Increment in SL scaleDr P. Bonnington to Senior LecturerDr. P. Sharp to Senior LecturerDr M. Chinnappan to Senior LecturerDr M. Pffankuch to Senior LecturerDr. A. McNaughton Over Senior Tutor Bar Dr G. Oates to Senior Tutor

The Department is grateful to the Science Faculty for its support in the promotions round this year which resulted ion unprecedented success.

Department Administration

Many staff members have made substantial contributions to the effective administration of the Department. Thanks are especially due to the Department Assistant (Ross McCallum) and all the general staff, and to the following staff for taking on key responsibilities in the Department:

Deputy Head of Department Mr. David AlcornHead of Department's Advisory Group Prof. Boris Pavlov, Prof. David Gauld, Dr Colin Fox, Prof. J

Butcher, Mr. David AlcornDepartment Staffing Advisory Committee (Academic Promotions)

Prof. John Butcher, Prof. David Gauld, Dr Margaret Morton, Prof. Ivan Reilly

Academic Staff Performance Reviewers Prof. David Gauld, Prof. Boris Pavlov, Prof. Ivan ReillyHead of Mathematics Education Unit Dr Mike ThomasHead of Tamaki Mathematics Group Dr Robert ChanDirector of Graduate Studies Dr. N. Levenberg Research Coordinator Prof. David GauldTeaching Coordinator Dr Margaret MortonComputing Services Dr Paul Bonnington, Dr David McIntyre, Dr Philip Sharp,

Dr Mike ThomasBTech (Industrial Maths) Programme Coordinator

Dr Steve Taylor

Enrolment Coordinator David Alcorn Timetable Administrator Chris KingExaminations Coordinator Chris KingPublicity Officer Dr Bill BartonRegulations/Handbooks Dr David SmithEEO/EEdO Representative Dr Bruce CalvertNZ Mathematical Society Correspondent Garry TeeWebmaster Dr Shayne Waldron Overseas Students & Ad Eundum Admissions Assoc. Prof. M.K. Vamanamurthy

Library Liaison Officer David AlcornConvener of Staff/Student Liaison Committee Greg OatesSafety Officer John Pemberton/Ross McCallumLab Demonstrators Coordinator John Pemberton/Nicolette GoodwinMarkers Coordinator Roy SwensonDepartment Research Report Series Olita MoalaSeminars:

Algebra, Geometry & CombinatoricsAnalysisApplied, Computational & Industrial MathsMathematics EducationTopology

Dr Eamonn O'BrienDr Norm LevenbergDr Robert ChanMs Judy PatersonProf. David Gauld and Sina Greenwood

Faculty Representatives: Arts Commerce Engineering

David AlcornDr Joel SchiffDr Geoff Nicholls

University Committees:

Dr Bonnington: Subprofessorial Rep on Information Technology CommitteeLecturers Association ExecutiveFaculty of Science IT Review

Prof Conder: DVC (Research) Potgrad, Planning and Resources, Education, Budget, Quality Committees

Prof Martin Research committee, Education Committee

Dr Taylor: Faculty advisor Coca-Cola Youth Expo

New Zealand Journal of Mathematics

The New Zealand Journal of Mathematics is jointly produced by the Department and the New Zealand Mathematical Society, with Editorial staff consisting of Prof. John Butcher (outgoing Editor), Prof. Gaven Martin (Editor), Dr Joel Schiff (Executive Editor), Dr Jianbei An (Associate Editor), Sabrina Young and Jean Martin (Editorial Assistants), and Betty Fong (Production Assistant). Two issues of Volume 28 (Numbers 1 and 2) of the NZJM were published during the year. Members of Department who have served on the Editorial Board are Professors Marston Conder, David Gauld, Vaughan Jones, and Gaven Martin, and the Department's representatives on the Management Committee are David Alcorn (who is also convener of the Committee) and Prof. Ivan Reilly.

VIII.

OVERALL COMMENTS ON WORK AND PROGRESS WITHIN THE DEPARTMENT

The Department is actively pursuing the broad aims set out in the University's mission documents, encouraging a high quality environment for teaching and learning, continuing to undertake world class research in several areas, and attracting and supporting an increasing number of postgraduate students. The Department is clearly the strongest department in this country, by any measure, and in virtually every area. Within Australasia we rank within the top few, however, we have grander aspirations. These will be set forth in our coming strategic plan.

Our ability to achieve these aims is hampered by a relatively low level of resourcing, and of considerable worry is the lack of adequate tutorial and computer laboratory facilities for undergraduate students. The Department was externally reviewed in 1998, and received a laudatory report on its research and teaching programs, along with some constructive suggestions for further developments. These have largely been implemented. However, the lack of a properly mounted system of tutorials was highlighted and has not been addressed. Finally, on a personal note, I would like to thank the very many staff whom I have relied on this year for help and advice. I would particularly like to mention Ross McCallum (Admin), David Acorn (Teaching), Paul Bonnington and Phillip Sharp (Technical and Capex) and Mike Thomas and Bill Barton (Math Ed) who have put in a considerable effort to help me in various ways. Also to Marston Conder, who put in place some pretty good systems to make life easier, and has proven a hard act to follow.

Prof. Gaven J. Martin FRSNZHead of Department of Mathematics