NOTICES


MATHEMATICA CONTINUES TO DEVELOP

Ray Hoare, owner of Hoare Research Software, recently attended the Mathematica Developers conference in Champaign, Illinois. About 200 users, developers and resellers heard Stephen Wolfram, founder of the company that makes Mathematica, describe the recent activities of his 200 staff.

A notable development in recent time has been the production of applications packs, that make it easy to put the immense but sometimes daunting power of Mathematica to work on the user's problems. The packs contain pre-programmed documents that get you started quickly, or which add functionality. For instance (there are many more functions than these in the packs mentioned) the Mechanical Systems pack contains tools to model the motion of multibody mechanical systems. The Finance pack contains finance calendar functions and sensitivity measures for Options.

There are now more than 20 of these packs, many of them designed to facilitate teaching of mathematical concepts.

A link with Microsoft Word 6 is about to be released, which will allow you to create a document with all the layout power and flexibility of Word, that incorporates the mathematical and graphics capability of Mathematica.

These additions, and major developments of the user interface, are designed to expand Mathematica's user base. In future, many more people will find that Mathematica provides an accessible as well as a powerful and accurate tool for their needs for computation in many areas of education, industry and finance.

Ray also caught up with developments in Matlab, SPSS and several other programs while he was away - email him if you want details.

Ray Hoare, Hoare Research Software

Email Ray_Hoare@hrs.co.nz


PETER DSCHENFFZIG FOUND

In the NZMS Newsletter No.64, I reported that Hans Lausch (of Monash University) is doing research into refugee mathematicians during World War 2. Many refugees in the U.K. were interned, and thousands of them were deported to internment camps in Australia. Many were killed by Nazi submarines, on their way back to England - but some stayed in Australia. Felix Behrend was released from detention and appointed to the Department of Mathematics at Melbourne University, He had organized mathematics courses for other refugees in internment camps. Peter Dschenffzig took those courses, and Hans Lausch had evidence that he had later lectured in mathematics at universities in England, South Africa and New Zealand. I had never heard of Peter Dschenffzig, and Hans Lausch appealed for information about him.

Three weeks after my report was published in Newsletter No.64 (for August 1995), I received a letter from a poet friend:

"Dear Garry,

Bera MacClement sent me your query about Peter Dschenffzig. I know him well: he happens to be myself"

I have been a friend of the poet for many years, when he was a Senior Lecturer in the Department of English at the University of Auckland (now retired). Never had he mentioned to me that he used to lecture in mathematics, under another name!

I had placed a photocopy of pages 16 & 17 of the Newsletter No.64, with my note about "Sculptures by Leigh Christensen", in our Department of Physics Common Room. Dr Bera MacClement saw that photocopy, with the enquiry about Peter Dschenffzig also appearing on page 16. She knows the poet through Friends of the Earth, and she had chanced upon a mention by him that his name had formerly been Peter Dschenffzig. She knew that the poet had lectured in English at Makerere University College in Uganda (not in South Africa), so she considered that Hans Lausch's enquiry probably related to him, and she posted the photocopy to him.

Hans Lausch is delighted with the fruitful outcome of his appeal for information.

Garry J. Tee, University of Auckland


NEWS ABOUT NZ SCIENCE

Keep up to date with what happens in science and technology around New Zealand with the recently-launched Science Digest - a summarised newsletter published monthly by The Royal Society of New Zealand.

The four-page Digest is packed with short, easy-to-read news items about science and technology.

The Digest's key role is to communicate news from the national Society to branches, constituent societies, and individual members of the Royal Society, and to other organisations such as universities, polytechnics, research institutes, educational organisations and schools.

The Society has a growing and varied range of activities such as in science and technology education; science publishing (including seven science journals); specialised science committees, involvement in awards, fellowships, lecture tours etc; plus liaison with Government science agencies, universities, polytechs and industry. Single copies of Science Digest are distributed to each Royal Society branch, individual scientific societies and affiliated societies, as well as to each CRI, research association, and relevant university and polytechnic departments. Societies may care to insert the Digest with their newsletters or to reprint relevant items. Science Digest has been designed to be easily photocopied for further distribution. Up to 10 copies will be made available free of charge to branches and constituent and affiliated societies. Bulk supplies (over 10 copies) are available at cost to any organisation.

If you want a free copy of Science Digest mailed each month to your address, become a member of the Royal Society. The individual membership fee is $40 a year which goes to support the many aspects of the Society's work.

News from constituent societies, and branches can be sent to the Communication Editor, The Royal Society of New Zealand, Box 598, Wellington Fax (04)473-1841 or E-mail: science.digest@rsnz.govt.nz


"SILVER MEDAL AT THE 36TH INTERNATIONAL MATHEMATICAL OLYMPIAD"

New Zealand was represented at the 36th International Mathematical Olympiad by the following team : James McGowan, Burnside High School; Clare and Tim McLennan,Riccarton High School; Jasper Morrow, Onslow College; Russell Neilson, Rotorua Boys' High School; Kevin Ross, Burnside High School. Ivan Reilly of The University of Auckland was team leader; David Wallace of Wellington (NZ's first IMO silver medalist -1988) was deputy leader and Arkadii Slinko, also of Auckland University, was team coach. The IMO was held in Toronto from July 16-25 and the questions proved harder than usual.

Thus it was most encouraging that James McGowan achieved a silver medal - only the second to be won by a NZ student since our first participation. It is harder now to reach that standard as the fragmentation of the old USSR has meant many more top level students from that area. Tim McLennan gained a bronze medal and Russell Neilson just missed one but obtained an `honourable mention'. The team and the NZ Mathematical Olympiad Committee are most grateful for financial support from the NZMS.

Gordon A. Hookings

e-mail hookings@mat.auckland.ac.nz


Questions from the First Day, July 19, 1995

1 Let A, B, C and D be four distinct points on a line, in that order. The circles with diameters AC and BD intersect at the points X and Y. The line XY meets BC at the point Z. Let P be a point on the line XY different from Z. The line CP intersects the circle with diameter AC at the points C and M, and the line BP intersects the circle with diameter BD at the points B and N. Prove that the lines AM, DN and XY are concurrent.

2 Let a, b and c be positive real numbers such that abc = 1. Prove that

3 Determine all integers n > 3 for which there exist n points

in the plane, and real numbers

satisfying the following two conditions:

(i) no three of the points

lie on a line;

(ii) for each triple

the triangle

has area equal to

.

Time allowed: - 41/2 hours.

Each problem is worth 7 points.

Questions from the Second Day, July 20, 1995

4 Find the maximum value of for which there exists a sequence of positive real numbers satisfying the two conditions:

(i) .

(ii) for each i = 1, 2,..., 1995.

5 Let ABCDEF be a convex hexagon with

AB = BC = CD,
DE = EF = FA,
and
.

Let G and H be two points in the interior of the hexagon such that . Prove that

.

6 Let p be an odd prime number. Find the number of subsets A of the set {1,2,...,2p} such that

(i) A has exactly p elements, and

(ii) the sum of all the elements in A is divisible by p.

Time allowed: - 41/2 hours.

Each problem is worth 7 points.