My Automathography.

Thirty years at UWA.

After two delightful years at Missoula, in 1970 Beth and I packed up and set out for the University of Western Australia, accompanied by Jonathan aged 3 and Rosalie, 6 months. In 1970, the staff here numbered about 15, and I was the first of a large influx which saw the size of the Department double in 10 years. The old hands included Phil Silberstein, Malcolm Hood, John Mahoney, Beryl Hume, Dave Hurley, Peter Chapman, Ray Storer, Frank Gamblen, Des Fearnley-Sander, Ron List, Frank Yeomans, Peter Wynter and Neville Fowkes, as well of course as Larry Blakers, who had been the sole Head since the death of Weatherburn. Tsoi Ma, Mike Fisher and Bob Sullivan started in the same year as me and Rick McFeat shortly thereafter.

In those days the structure and content of the first two years of mathematics courses was similar to what it is today, although the names of the courses have changed. Hence it is not misleading to call them low and high Calculus I and II, Linear Algebra I and II and Probability and Statistics I and II. At different times I have taught all of these courses except high Probability and Statistics, and made some horrendous errors. One that sticks in my mind is trying to prove the properties of the Wronskian in high Calculus I, instead of just stating them. Even worse occurred one year when I thought it would be helpful in low Calculus I to put all the lectures onto transparencies. I must have believed that the students could copy all this out and at the same time listen to me explaining it. My student evaluations that semester are an all-time record low.

Upper undergraduate students in Mathematics present a different set of problems. I feel privileged to have been in contact with some fine young minds, who have gone on to spectacular success in Universities and private life around the world. Some people complain, as Socrates probably did, about falling standards. I have found that as far as the upper échelon of mathematics students are concerned, their motivation and preparation equals or surpasses those I have encountered in the past.

Incidentally, during several study leaves I have taught essentially the same material at the same level at UWA, Hawaii, New Mexico, and Germany. I have found no real difference in average quality of students or exam performance. The students even dressed the same!

Right from the beginning of my sojourn in WA I have been involved in enrichment of gifted and talented high school students. For several years I ran a mentor programme aimed at attracting Year 10 girls into mathematics, one of the success stories being Jane Perkins. When Australia first entered the International Mathematical Olympiad in the early 1980s I became the WA Director of Olympiad Training, and have been privileged to introduce to mathematical problem solving some exceptional high school students, including Andrew Kepert, Andrew Hassell, Jeremy Liew, Kin Yan Chung, Chris Barber, Akshay Venkatesh and Peter McNamara.

Along similar lines, for several years I ran a 'Problem of the Week' Competition for undergraduates at UWA, and when that faded away, organised the Blakers Mathematics Competition for Year 1 to 3 Undergraduates in all Western Australian Universities. This started in 1997 and continues to attract entries from talented students throughout WA.

Let me deal now with Research. I managed to extract two publications [1] and [2] from my PhD thesis. (The numbers refer to the List of Publications). Then followed a lean three years during which I seemed to be getting nowhere. During these years, I suggested to Larry Blakers the idea which eventually led to the Research Report series. Then two events occurred which gave my research a new lease of life. Firstly, the arrival of the very active Cheryl Praeger sparked my interest in group actions on graphs and their connection with abelian group presentations. This led to my paper [14] and , in collaboration with her and others, [17] and [22].

Secondly, we acquired a talented post-doctoral fellow named Rod Bowshell who found some wonderful new ideas in my earlier papers that I had not noticed myself! We wrote a joint paper for Math. Annalen [6] which inaugurated the concept of E-ring, an idea whose time had come. Over twenty papers in the area appeared over the next few years, and fortunately for my ego, they all cited Bowshell-Schultz. After this, the notion became too well-known, and is now used without any citation, a sign I suppose of real success.

Incidentally, a similar thing happened in the 1990s. In 1988, I wrote a Research Report on self-splitting abelian groups, that is, groups G for which every extension of G by G splits. (The definition makes sense in the non-abelian group context--but is it interesting?). Because the Report contained no definitive theorems, I did not submit it for publication. It did however contain four unsolved problems in the borderline area among abelian groups, category theory and logic. Somehow, these problems captured the imagination of some first-rate mathematicians, including Shelah, and at least ten papers were published solving and extending my problems. This led to a steady demand for the Research Report which was typed in a nasty format in the days before TeX or even word-processors in the Department. In self-defence, I submitted the original 1988 paper in 2000 to the Bulletin of the Aust. Math. Soc. and it appeared in 2001, [44].

Returning now to the annus mirabilis 1977, the Bowshell-Schultz paper lead to a number of invitations to meetings and visits, and I have probably averaged one international conference each 18 months since then. Such Conferences, usually held in a salubrious part of the world, have enabled Beth and me to visit some amazing places, including Oberwolfach, Dublin, Wuerzburg, Honolulu, Padova, Venice, Crete, Mexico, Las Cruces, New York, Houston, Seattle and the major cities of Australia. Unfortunately, Rod Bowshell, to whom I owe so much, retired from professional mathematics after his post-doc and opened a bookshop in Sydney. He has continued his mathematical studies on an amateur basis, but as far as I know, has not published his work.

Since 1977, I have averaged one major paper per year. My areas of research have mainly been abelian p-groups and their endomorphism rings and automorphism groups, torsion-free abelian groups in general and almost completely decomposable groups in particular, and general module theory which most occupies my mind at the moment. I have also published minor papers in the areas of history of mathematics, graph theory, elementary geometry and calculus for mathematics teachers, book reviews and (believe it or not) Library Science, [11]. Apart from editing three Conference Proceedings, I have up to now 30 sole author papers and 25 joint publications, with collaborators from Australia, USA, Germany, Mexico, Russia, Romania and Bulgaria. Thanks to Nick Wormald, I have Erdos Number two.

I have organised three International Conferences here in Perth, one on Algebraic Structures and Applications in 1980, which was organised around an extended visit of Laszlo Fuchs, one on Abelian Group Theory in 1987, and one on Abelian Groups, Rings and Modules in 2000. In each case, we managed to attract over 40 overseas visitors, and the Proceedings were published by Marcel Dekker [12], or the American Mathematical Society, [24] and [42].

In 2000, I retired from paid employment but have continued to teach and do research. My main interests continue to be in Algebra, particularly modules and their endomorphism rings.

Author: Phill Schultz,

Last update: 24 January, 2005