Dr John C Turner

12.12.2007

John Christopher TURNER

Department of Mathematics,
University of Waikato,
Private Bag,
Hamilton 3200,
New Zealand.

(private: 6 Hardley Street, Hamilton
email: [email protected])

Date of Birth:   1st October, 1928.

Marital Status:  Married 37 years (wife Barbara Rosemary, nee Payne,
born 18 April 1927, died 27 April 1997);
five children: Neil and Jeremy Orton (step-sons),
Roseanna Jane, Louise Margaret, Harry John Turner;
ten grandchildren.

Hobbies:              Music (plays piano, ‘cello, guitar, treble recorder and mandolin)
‘Cello in Waikato Symphony Orchestra (six years),�
jazz piano in Reeds Keys Duo; treble recorder
in Lyric Players Orchestra (over 500 concerts)
Solo entertainer with voice and piano.
Snooker/Pool; Bridge; Chess.

Higher Education:

(i) H.N.D. at Doncaster College of Technology, England.
Gained the Higher National Diploma in Mechanical Engineering (1951).
Qualified for G.M.I.M.E. Awarded a Technical State Scholarship.

(ii) B.Sc. and M.Sc. at University of Leeds, England.
Gained the B.Sc.(Special Honours in Mathematics) in 1954; and
M.Sc., by research thesis on `Reliability of Networks of Components':
awarded  with distinction , in 1966.

(iii) D.Phil. at University of Waikato, Hamilton, New Zealand.
Gained the D.Phil. degree in 1984. Thesis on `Studies of Knot Graphs.’

Mathematics Career:

1954-56 Scientific Officer, Armaments Research Development
Establishment, Mathematics Division, Kent, England.

1956-60 Tutor in Mathematics Physics, Mombasa Institute of
Muslim Education, Mombasa, Kenya.

1960-62 Lecturer in Mathematics, Nottingham College of
Technology, England

1962-65 Lecturer in Applied Mathematics, University of Sierra
Leone, West Africa

1965-67 Senior Lecturer in Statistics, Huddersfield Polytechnic,
England.

1967-70 Principal Lecturer in Statistics Operations Research,
Leeds Polytechnic, England.

1970-86 Reader in Mathematics, University of Waikato, New
Zealand.

1986-90 Foundation Dean, School of Computing and
Mathematical Sciences.

1986-94 Associate Professor in Mathematics, retired in
February 1994.

Elected Honorary Life Member of NZ Mathematical
Society, 1993.

Elected Honorary Fellow, University of Waikato, 1994.

Positions of Responsibility:

(i) Deputy Head of the Department of Mathematics & Computer
Science, Leeds Polytechnic, 1967-70: responsible for organising
degree and diploma courses at all levels, with a staff of thirty.

(ii) Responsible for direction of teaching and research in Statistics
and Operations Research in the Department of Mathematics,
University of Waikato, 1970-1986; the Department has 19 staff
members, offering pure mathematics, mathematical physics, and
statistics and O.R., from under-graduate to Ph.D. levels.

(iii) Acting Director of Computing Services, University of
Waikato, 1971-73.

(iv) Chief Examiner for the Bursary and Scholarship Examinations in
Applied Mathematics (final High School examinations, set by the
N.Z. Department of Education for the University Grants Committee)
1981 and 1982. This involved the setting of papers and
organisation of marking teams, to deal with over 5000 scripts per
year from schools throughout the country.

(v) Acting Head of Mathematics Department, University of Waikato,
seven months within 1983/84.

(vi) Dean, School of Computing & Mathematical Sciences,
June 1986 – January 1990. Foundation Dean, establishing
the School’s organisation, and the BCMS and other degrees
which it offers.

(vii) Reviewer (ten years) for American Mathematics Reviews.

Membership of Professional Societies:

Fellow of the Royal Statistical Society, London, 1956 to 1992.

Member of the N.Z. Mathematical Society, since 1971.

Member of the N.Z. Statistical Society, 1971 to 1985.

Member of the N.Z. Operations Research Society, 1971 to 1978

Member of the N.Z. Computer Society, 1971 to 1977.

Member of the N.Z. Association for Research in Education,
1984 to 1990.

Member of the Waikato Mathematical Association, 1971 to 1993.

Sustaining Member of The Fibonacci Association, 1986 to present.
N.Z. member of Overseas Committee, The Fibonacci Association.

Society Officerships:

(i) New Zealand Mathematical Society:
National Committee Member, 1979.
President, 1980.
Vice-President, 1981.

(ii) New Zealand Computer Society:
National Council Member, 1972/73.

(iii) Waikato and Bay of Plenty Computer Society:
Founding member, 1971.
Chairman, 1971/2/3.

(iv) New Zealand Statistical Society:
Area Convenor, Waikato and Bay of Plenty, 1973-79.

(v) Waikato Mathematical Association:
Committee Member, 1980-1985.

(vi) New Zealand Federation of Classical Guitar Societies:
Founding Member (Proposer), 1977.
President, 1977/8/9.
Treasurer, 1983/4/5.

(vii) Hamilton Classical Guitar Society:
Committee Member, 1971-present.
President, 1973-75; 1985-1987.

(viii) University of Waikato Bridge Club:
President, 1976-1980.

(ix) Hamilton Hang-Gliding Society:
Founder, President, 1976/77.

(x) Founder member, Waikato Branch of the
University of the Third Age, Committee
Member, since 1995.
President 1999/2000.

PUBLICATIONS

Books:

1. J.C. Turner, `Modern Applied Mathematics – Probability, Statistics, Operational
Research.'(1970), 502 pp., E.U.P. (later Hodder Stoughton).
Reprinted many times and still in print. Published in Spanish
as Matematica Moderna Aplicada by Alianza Universidad, Madrid
(1974), and still in print with them. Chosen by the English
Language Book Society in 1978 for distributing in a low-priced
edition to third-world countries.

2. J.C. Turner, `Probability and Operational Research.’ (1971), 350 pp.; under
contract with E.U.P., 250 pp. written, but finally unpublished.

3. J.C. Turner, `Forty Steps to Fortran.’ (1972), 155 pp.; issued in typed form by the
Department of Mathematics, for teaching Fortran to large
Mathematical Techniques classes. Successfully used for four
years.

4. `First Steps in Numerical Analysis.’ (1978), 202 pp. (with Hosking and
Joyce), Hodder Stoughton. Reprinted many times, and in
print until 2000.
Revised Second Edition (with Stephen Joe) published in 1996.

5. `STATUS – a Statistical Computing Language.’ (1980), 173 pp., New
Zealand Mathematical Society. Published annually until 1986.

6. `Probability and Statistics.’ (1980), 135 pp., (with Cornwell), in the
Mathematics Syllabus Series, for Bursary Applied Mathematics;
New Zealand Mathematical Society. Reprinted each year, 1500-
2000 copies, until 1985.

7. J.C. Turner, `Mathematics for Statistics and Operations Research.’ (1984), 150 pp., printed by offset, as a Notebook for course 23.207,
University of Waikato, N.Z.

8. A.G. Schaake, J.C. Turner and D.A. Sedgwick, `Braiding – Regular Knots.’
Book, pub. by Department of Mathematics Statistics, University of Waikato, N.Z. August 1988, pp. 1-117.

9. A.G. Schaake and J.C. Turner, `A New Chapter for Pythagorean
Triples.’ Book, pub. Department of Mathematics Statistics,
University of Waikato, Hamilton, N.Z., Oct. 1989: 155 pp.

10. A.G. Schaake, J.C. Turner and D.A. Sedgwick,
`Braiding – Regular Fiador Knots.’
Book, pub. Department of Mathematics, U. Waikato, Sep 1990: 159pp.

11. A.G. Schaake and J.C. Turner,
`Braiding – Standard Herringbone Pineapple Knots.’
Book, pub. Department of Mathematics Statistics,
University of Waikato, Hamilton, N.Z., May 1991: 202 pp.

12. A.G. Schaake, T. Hall and J.C. Turner,
`Braiding – Standard Herringbone Knots.’
Book, pub. Department of Mathematics Statistics,
University of Waikato, Hamilton, N.Z., May 1992: 208 pp.

13. J.C. Turner and P. van de Griend (authors and eds.),
`History and Science of Knots.’
Book, pub. World Scientific Pub. Inc., N.Y., Singapore,
Jun. 1996: 480 pp.
[Part written, edited, and completely computer type-set by J. C. Turner.]

14. K. Atanassov, V. Atanassova, A.G. Shannon, and J.C. Turner,
`New Visual Perspectives on Fibonacci Numbers.’
World Scientific Pub. Co., Singapore, 2002: 313 pp.
[Three-quarters written, edited and fully computer type-set by J. C. Turner.]

In preparation:

A Mathematics Anthology – a collection of quotations and other
short items relating to mathematics. Over 1400 items have been
collected so far, and all are stored in computer form, ready
for sorting, merging and cross-referencing. Eventually some
2500 items will be included. A publisher’s contract is being
sought. [Project resurrected, Apl. 2003]

Pamphlets: (by A.G. Schaake (main), J.C. Turner et al.)

1. A.G. Schaake and J.C. Turner, `Introducing Grid-diagrams in Braiding.’
Pamphlet, pub. Department of Mathematics Statistics,
University of Waikato, Hamilton, N.Z., 1991: 32 pp.

2. A.G. Schaake and J.C. Turner, `Edge Lacing-the Double Cordovan Stitch.’
Pamphlet, pub. Department of Mathematics Statistics,
University of Waikato, Hamilton, N.Z., 1991: 23 pp.

3. A.G. Schaake and J.C. Turner, `Braiding Application-Horse Halter.’
Pamphlet, pub. Department of Mathematics Statistics,
University of Waikato, Hamilton, N.Z., 1991: 24 pp.

4. A.G. Schaake and J.C. Turner, `The Regular Knot Tree and Enlargement Processes.’
Pamphlet, pub. Department of Mathematics Statistics,
University of Waikato, Hamilton, N.Z., 1991: 38 pp.
4+ Supplement to No. 4, {\it Casa-Coded Regular Knots.}, 1995: 31 pp.

5. A.G. Schaake and J.C. Turner, `An Introduction to Flat Braids.’
Pamphlet, pub. Department of Mathematics Statistics,
University of Waikato, Hamilton, N.Z., 1991: 36 pp.

6. A.G. Schaake and J.C. Turner,
`An Introduction to Evolution Processes (Part I).’
Pamphlet, pub. Department of Mathematics Statistics,
University of Waikato, Hamilton, N.Z., 1992: 82 pp.
6+ Supplement to No. 6, {\it Headhunter-Fan Knots.}, 1994: 18 pp.

7. A.G. Schaake and J.C. Turner,
`The Braiding of Column-Coded Regular Knots.’
Pamphlet, pub. Department of Mathematics Statistics,
University of Waikato, Hamilton, N.Z., 1992: 37 pp.

9. A.G. Schaake and J.C. Turner,
`The Braiding of Row-Coded Regular Knots.’
Pamphlet, pub. Department of Mathematics Statistics,
University of Waikato, Hamilton, N.Z., 1993: 43 pp.

12. A.G. Schaake and J.C. Turner, `The Braiding of Wheelknots.’
Pamphlet, pub. Department of Mathematics Statistics,
University of Waikato, Hamilton, N.Z., 1994: 110 pp.
12+ Supplement to No. 12, {\it Wheelknots.}, 1995: 49 pp.

Research Theses:

1. `Reliability of Networks of Components.’ (1966), 130 pp., awarded
M.Sc. with distinction.

2. `Study of Knot-Graphs,'(1984), 200 pp., awarded D.Phil.
Journal Papers, Articles, etc.:

1. `Reliability and Operability of Systems of Components in Series and
in Parallel’ first published as a research report for the War
Office, by the Armanents Research Development Establishment,
Kent. Later selected for inclusion in the first volume of the
Journal `Electronics Reliability and Microminiaturization,’
Pergamon Press, (1962), pp. 21-26.

2. `A Statistical Study of the Fish Population of Sierra Leone, 1960- 1965.’
(1966), J. West African Science Association, Vol. 11, pp.150-166.

3. `On a Network Inequality.’ (1968), (with Conway), SIAM Review, 10,
107-8. This paper treated an attractive inequality arising out
of studies of reliability networks; it gave a proof using
network properties, but invited a direct analytic proof.
Submitted proofs and further discussion were published in Siam
Review, Vol. 11, pp. 402-406, (1969). In 1970, the inequality
was listed in two places (pp. 280 and 385) in the book:
`Analytic Inequalities.’ by D.S. Mitrinovic (Springer-Verlag).
In 1980, the inequality and the relationships between
probability and analytic methods which it had revealed, were
selected for inclusion in a paper on educating graduate level
Statistics students, by I.R. Savage: `International Statistical
Review.’ (1980), pp. 103-116.

4. `Variation in Hibolithes Arkelli Arkelli-2.’ (1975), (with
Challinor), New Zealand Journal of Geology and Geophysics, Vol.
18, No. 6, pp. 837-848.

5. `A Classification of Statistics Courses (a framework for studying
statistical education).’ (1976), Int. J. Math. Ed. Sci.
Technol., Vol. 7, No. 4, pp. 409-440.

6. `A Special Purpose Language (STATUS) for Teaching Statistics: some of
its design principles, and values as an education tool.’ (1979),
pp. 915-920, DEC Users Society, Vol. 5, No. 2.

7. `A Study of Knot-Graphs.’ (D.Phil. abstract), Bulletin of the
Australian Mathematical Society, Vol. 31, No. 2, pp. 317-318.

8. J.C. Turner, `On Caterpillars, Trees, and Stochastic Processes.’
The American Mathematical Monthly, Vol.93, No.3, 1986, pp. 205-213.

9. J.C. Turner, `On a Sequence of Trees with Fibonacci Weights.’
Mathematical Spectrum, Vol.18, No.1, Mar. 1986.

10. J.C. Turner, `On a Class of Knots with Fibonacci Invariant Numbers.’
The Fibonacci Quarterly, Vol.24, No.1, 1986, pp. 61-66.

11. J.C. Turner, `On Doodles and 4-Regular Graphs.’ Mathematical
Spectrum, Vol.19, No.1, 1986, pp. 14-18.

12. J.C. Turner, `Fibonacci-T Arithmetic Triangles.’ Fibonacci
Quarterly, Vol. 25, No. 2, 1987 (problem pages, 190/191).

13. J.C. Turner (with A. Zulauf), `Fibonacci Sequences of Sets and Their
Duals.’ Fibonacci Quarterly, Vol. 26, No. 2, 1988; pp. 152-156.

14. J.C. Turner, `On Folyominoes and Feudominoes.’ Fibonacci Quarterly,
Vol. 26, No. 3, 1988; pp. 205-218.

15. J.C. Turner, `Fibonacci Word Patterns and Binary Sequences.’
Fibonacci Quarterly, Vol. 26, No. 3, 1988; pp. 233-246.

16. J.C. Turner, `Convolution Trees and Pascal-T Triangles.’ Fibonacci
Quarterly, Vol. 26, No. 4, 1988; pp. 354-365.

17. Problem: `On a missing set.’ J.C. Turner, E.3266: Amer. Math. Monthly
95, No. 3, May 1988: p.456.

18. J.C. Turner,`The Alpha and the Omega of the Wythoff Pairs.’ The
Fibonacci Quarterly, Vol. 27, No. 1, Feb. 1989: pp.76-86.

19. J.C. Turner,`Problem on multisets and Euler’s phi-function.’
(Advanced Problems Section) H-429. The Fibonacci Quarterly,
Vol. 27, No. 1, Feb. 1989: p.92.

20. `On kth Order Colored Convolution Trees and a Generalized
Zeckendorf Integer Representation Theorem.’ J.C. Turner, and
A.G. Shannon, The Fibonacci Quarterly, Vol. 27, Nov. 1989:
pp.439-447.

21. `Hausdorff Dimension and Perron-Fr\”{o}benius Theory.’ V. Drobot and
J.C. Turner, Illinois Journal of Mathematics, Vol.33, No.1,
Spring 1989: pp.1-9.

22. `Problem on an infinite sum of reciprocals of Fibonacci
expressions.’ J.C. Turner, B-637. The Fibonacci Quarterly, Vol.

27, No. 1, Feb. 1989: p.87.

23. `Note on a Family of Fibonacci-like Sequences.’ J.C. Turner, The
Fibonacci Quarterly, Vol. 27, No. 2, Feb. 1989: pp. 76-86.

24. Turner, J. C. `Three number trees – their growth rules and related number properties.
International Conference on Fibonacci Numbers and Their Applications,
Jul. 1988 (Proceedings, Vol. 3, Kluwer A.P. 1990, 335-350.)

25. `Generating the Pythagorean Triples via simple continued fractions.’
Schaake, A. G. and Turner, J. C.,{International Conference on
Fibonacci Numbers and Their Applications, Jul. 1990
(Proceedings, Vol. 4, Kluwer A.P. 1991, 247-256.)

26. `On the Moebius Knot Tree and Euclid’s Algorithm.’
Schaake, A. G. and Turner, J. C., International Conference on
Fibonacci Numbers and Their Applications, Jul. 1990
(Proceedings, Vol. 4, Kluwer A.P. 1991, 257-270.)

27. `A generalised tableau associated with colored convolution trees.’
Shannon A. G., Turner J. C. and Atanassov K. T.
Discrete Maths., 92}, (1991): 329-340.

28. `Colored Convolution Trees.’
A.G. Shannon, J.C. Turner, K.T. Atanassov; in B.D.McKay, J.R. Seberry
and S.A. Vanstone (eds.), Selected Papers in Combinatorics,
in honour of R.G. Stanton; North Holland, Amsterdam, 1992, 329-340.

29. `On an inhomogeneous, non-linear, second-order recurrence relation.’
Turner J. C. and Shannon A. G., International Journal of Mathematical
Education in Science and Technology, 24, 2, 1993, 324-327.

30. `The Elements of Enteger Geometry.’
Turner, J. C. and Schaake, A. G., {\it International Conference on}
Fibonacci Numbers and Their Applications,
July, 1992 (Proceedings, Vol. 5, Kluwer A.P. 1993, 569-583.)

31. `Totient Functions on the Euler Number Tree.’
Turner, J. C., Garcia, H. and Schaake, A. G., {\it International Conference}
{\it on Fibonacci Numbers and Their Applications,}
July, 1992 (Proceedings, Vol. 5, Kluwer A.P. 1993, 585-600.)

32. `The generation of trees from coupled third-order recurrence relations.’
Atanassov K. T., Shannon A. G. and Turner J. C.
In S. Shtrakov Iv Mirchov (eds), {\it Discrete Mathematics and Applications.}
Blagoevgrad: Neofit Rilski University, 1995, pp. 46-56.

33. `On a Model of the Modular Group.’
Turner, J. C. and Schaake, A. G., {\it International Conference}
{\it on Fibonacci Numbers and Their Applications and Their Applications,}
July, 1994 (Proceedings, Vol. 6, Kluwer A.P. 1996, 487-504.)

34. ‘Remark on Fibonacci Sequences and Fuzzy Sets.’
Atanassov, K.T., Shannon A.G., and Turner J.C.
Comptes rendus de l’Acad\'{e}mie bulgare des Sciences, Tome 50, No. 2, 1997.

35. `Introduction to a Fibonacci Vector Geometry.’
Turner J.C. and Shannon A.G.,
International Conference on Fibonacci Numbers and Their Applications,
15-19 July, 1996 (Proceedings, Vol. 7, published by Kluwer AP, Spring 1998).

36. `On Vector Sequence Recurrence Equations in Fibonacci Vector Geometry.’
Turner J.C.,
International Conference on Fibonacci Numbers and Their Applications,
June/July, 1998 (Proceedings, Vol. 8, pub.by Kluwer AP, 1999: 353-368.)

37. `On Triangles and Squares Marked with Goldpoints – Studies of Golden Tiles.’
Atassanova, V. and Turner J.C.,
International Conference on Fibonacci Numbers and Their Applications,
June/July, 1998 (Proceedings, Vol. 8, pub.by Kluwer AP, 1999: 11-26.)
(A diagram from this – the Fibonacci Star – appears
on the front cover of the Proceedings.)

38. `The Fibonacci Track Form, with Applications in Fibonacci Vector Geometry.’
Turner, J.C., in dedicatory volume (70th birthday) to J.C. Turner,
Notes on Number Theory and Discrete Mathematics, Bulgarian
Academy of Sciences. Vol. 4, No. 4 1998: 136-147

39. `On Fibonacci Sequences, Geometry, and the m-Squares Equation.’
Turner J.C. and Shannon A.G.,
The Fibonacci Quarterly, Vol. 38, No. 2, May 2000: 98-103

40. `Some Fractals in Goldpoint Geometry.’
Turner, J.C., (Dedicated to the memory of Herta Freitag.)
The Fibonacci Quarterly, Feb. 2003.

41. `On Fibonacci Tracks, Groups and Plus-Minus Sequences.’
Turner, J. C., presented at the International Conference
on Fibonacci Numbers and their Applications, Luxembourg, July, 2000.
[No Proceedings; published later in the book `New Visual …’, 2002]

42. `Some Constructions and Theorems in Goldpoint Geometry.’
Turner, J.C., presented at the International Conference on Fibonacci
Numbers and their Applications, Flagstaff 2002. Accepted for
publication in the Proceedings. 19 pp.

43.`Some Applications of Triangle Transformations in Fibonacci Geometry.’
Turner, J.C., presented at the International Conference on Fibonacci
Numbers and their Applications, Flagstaff 2002. Accepted for
publication in the Proceedings. 25 pp.

Research Reports:

1. Turner, J.C. and Beder, B. `Stochastic Processes on Fibonacci Trees.’
(Research Report No 142, Nov. 1985).

2. Turner, J.C. `Fibonacci Word Patterns and Binary Sequences.’ Research
Report No. 138, Department of Mathematics, University of
Waikato, July 1985.

3. J.C. Turner, `Tree Sequences with Shade Z+ and Parity-driven
Growth.’ Research Report No. 151, University of Waikato,
Hamilton.

4. J.C. Turner, A.G. Shannon T.D. Robb; `On Generalizations of
Fibonacci Trees and Zeckendorf Integer Representation
Theorems.’ Department of Mathematics Statistics, RR. No. 164
(July, 1988); pp. 1-24.

5. A.G. Schaake, J.C. Turner, `A New Theory of Braiding.’ Department of
Mathematics Statistics, RR 1/1, No. 165 (July, 1988); pp. 1-42.

6. `A New Theory of Braiding (RR1/2) – Algorithms for Regular Knots.’
J.C. Turner (with A.G. Schaake; Research Report No. 168, Dept.
of Mathematics Statistics , University of Waikato, 1988; pp.41.

7. A.G. Schaake and J.C. Turner, `New Methods for Solving Quadratic
Diophantine Equations : Part I – Investigations of Rational
Numbers using Rooted Trees and other Directed Graphs; Part II –

The Pythagorean Triples.’ Research Report No. 192 (1989),
Department of Mathematics Statistics, University of Waikato,
Hamilton, N.Z., Dec. 1989: 75 pp.

Magazine or Newsletter Articles:

1. `New Jobs for Old.’ J.C. Turner, (on the new types of professions open to those
educated in computing, electronics, and O.R.). Published in the Huddersfield
Examiner, 1966.

2. `Cuckoos in the Mathematics Nest.’ paper presented to the Member
Bodies’ Meeting of the Royal N.Z. Scientific Society, 30th
April 1980; published in the R.N.Z.S.S. magazine, and also in
the N.Z. Math. Soc. Newsletter. (Presented in my capacity as President of
the N.Z. Mathematical Society, that year.)

3. `On Mathematics and Poetry.’ (1983), N.Z.Mathematics Magazine, Vol.
20, No. 3, 10 pp.

4. `Fibonacci Convolution Trees and Integer Representations.’ (April,
1985), feature article in the N.Z. Math. Soc. Newsletter, pp.16-21.

5. Turner, J.C. `Fibonacci Convolution Trees and Integer
Representations.’ published as an invited feature article in
N.Z.M.S. Newsletter, May 1985.

6. J.C. Turner, `Problem 18: Counting Folyominoes on an nvn F-lattice.’
NZ Mathematical Society Newsletter Dec. 1985. (Also appeared in
N.Z. Mathematics Magazine, Vol.23, No.2, Aug. 1986).

7. J.C. Turner, `Words can be Fibonacci too.’ N.Z. Mathematics
Magazine, Vol.23, No.1, May 1986.

8. J.C. Turner, `On Fibonacci Trees and Arithmetic Progressions.’ N.Z.
Mathematics Magazine, Vol.24, No.1, Apl. 1987, pp. 34-37.

9. A.G. Schaake and J.C. Turner, `Pythagorean Triples – a New Solution
after 2500 Years.’ Article, The New Zealand Mathematical
Society Newsletter, No. 47, Dec. 1989: 6 pp.
Other Writings, Publications, Editorships:

Mathematics Syllabus Series: I initiated this series in 1980;
published by the N.Z. Mathematical Society to provide texts for
Bursary and Undergraduate students; Editor (with Vere-Jones and
Wake) of the first three. The Series has provided a considerable
source of funds for furthering the aims of the Society.

English Universities Press: contracted (in 1969) to be Editor/author
of a series on Mathematics for Operational Research: arranged
for two books to be written, one on matrices and the other on
probability for O.R.: although partial drafts were produced, the
series fell through when I moved from England to New Zealand.

`Albert in the Land of The Dees.’ (1972, 190 pp), children’s fantasy,
based on mathematical ideas; unpublished (re-edited, 1998; Europa Chang
is now illustrating it, view to publication in 2003).
Editor and Publisher of Music for the N.Z. Federation of Classical
Guitar Societies:
(i) Music from the Hamilton Society Competitions, (1979).
(ii) Two New Zealand Composers – Solos and Duets for Classical
Guitar, (1981); Matthew Marshall and Pieter v.d. Werden.
(iii) FOLIO ONE – New Music for Classical Guitar, various composers (1983).
Seminars and Conference Papers Presented:

The following are only half a dozen of talks whose titles I remember. An
estimate of the total of all seminars etc. which I have presented is given
at the end of this section.

May 1984, NZ Mathematics Colloquium, Victoria University, Wellington.
(i) On Knot Invariants and Number Theory.
(ii) Large Class Management of Computer Aided Teaching.

August 1984, International Conference on Mathematics Education (ICME IV),

Adelaide University, poster paper on Computer Aided Teaching.

November 1984, Joint Mathematics/Computer Departments Seminar.
Two talks on Stochastic Processes on Trees.

March 1985, Department of Mathematics seminar.
Talk: In the shade of the old AP tree, and other flights of forest fancy.

May 1985, Third Australasian Mathematics Convention, UNSW, Sydney.
Paper: Integral Multinumbers and their Shades.

I have presented many papers that are not recorded here. Seminars in the
Department in my University and others; talks in San Jos\'{e}, Santa Clara and
San Francisco; talks at Fourah Bay University, Leeds University, St. Andrews University;
and many at the annual (about 40) NZ Mathematics Colloquia in the period 1971 to 1994.

Estimates of numbers of seminar or conference talks are: New Zealand (40), U.S.A. (15),
Britain (6), Australia (3), Italy (2), Austria (2), Tasmania (1): TOTAL 69. I
have not kept records of titles, etc. of these talks, except those which
appeared in Conference Proceedings.
A Retirement Symposium:

My Department kindly organized one for me, on 9 December 1993.
I presented the last of seven papers. Mine was entitled `On Models of the Modular Group and some of its Geometric and
Number Sequence Properties’. (The other papers were: `How to Draw a Nice Seifert
Surface.’ D. Gauld, U. Auckland; `Nonlinear Fourier Analysis.’ E. Kalnins, U.
Waikato; `Pen-based User Interfaces in Symbolic Computation.’ W. Rogers, U.
Waikato; `History in Mathematics, or the History of Mathematics.’ M. Schroder,
U. Waikato; `The Saga of the Meccano Computer.’ G. Tee, U. Auckland;
`Pentagonal Cells.’ G. Wake, Massey U.)
Innovations in Statistical and Mathematical Education:

1. Leeds Polytechnic (1967-70):

(i) Developed laboratory equipment and documented practical methods for
statistics teaching; also equipment for operations research
demonstrations. These included a student kit for a set of
statistics experiments, and machines for demonstrating
formation and dispersion of customers in queues as modelled by
queue theory. Several devices for generating random customers
and passing them through queue systems were built and used at
the Polytechnic. Negotiations with manufacturers to produce
the equipment for wide distribution were in progress when I
moved to New Zealand.

(ii) Introduced a 4-year sandwich-degree course, viz. B.Sc.(Hons) in
Operational Research with Computing. This required over two
years’ planning, negotiations with other polytechnics, steering
through many committees, and gaining acceptance from the
central committee for polytechnic degrees in London. I was
responsible for the detailed documentation of every aspect of
the degree course, from its philosophy through week-to-week
details of all its syllabuses, to estimates of student numbers,
job prospects, and so on. To my knowledge this degree course
still proceeds today, in much the same form as its original

design.

2. University of Waikato (1970 – 1994):

(i) Introduced various methods for providing statistical computing
projects to our students, keeping pace with developments of
computer use in statisticl work.
In particular I invented, and with the aid of a young computer
scientist brought to full fruition, a high-level computing
language called STATUS (STATistical computing Ultra-Simple).
This language was designed to enable students to carry out
sampling exercises and do statistical analyses, learning the
theory and practice of all the statistical methods taught (up
to M.Sc. level) in our courses. Facilities for studying some
O.R. models were also included. It is very much more than a
mere package of sub-routines; up to the mid-70’s it was the
only language of its kind to be really useful for educational
purposes. It may be compared with MINITAB, which is now the
leading world language of that type: but in 1977 or thereabouts
STATUS was much in advance of MINITAB. It still has the edge
in some respects, but MINITAB is supported by a technical and
sales support team, whereas no such support was available for
STATUS. My language was used extensively at U. Waikato for
over 10 years, and for a time was used widely elsewhere in New
Zealand. It was also introduced to two Polytechnics and a
University in England; in Singapore; and one copy was sent to
an American University

(ii) In the years 1982/3/4 I designed and implemented (with the aid of
Statistics staff at U. Waikato) a large system of Computer-aided
Learning, mainly with a view to giving help to the weaker first
year students. The emphasis of the material put into the
system is on remedial mathematics; but there are also units for
revision of self-teaching of a variety of basic statistical
topics. The system is continually being appraised and
developed, and as better graphics facilities become available I
intend to improve the kinds of instructions given [N.B. This didn’t
happen; its use at U. Waikato was discontinued about 1990].
As well as containing much teaching material, mainly of the
programmed-text variety, there are several other facilities
in the system, for teacher-student communication.

(iii) In the years 1982-1986 I took part in the planning for a new
School of Computing and Mathematical Sciences. From 1986 to 1990 I
was foundation Dean of the School, and was responsible for
establishing the School’s administrative structures and for
designing and introducing four-year, professions-oriented study
programmes leading to a Bachelor of Computing and Mathematical
Sciences degree, to be awarded with or without Honours. Programmes
were also established for Diplomas, Masters and Ph.D. awards.
In 1989 the School moved into a new building, designed for it.
I oversaw this move, and helped establish many new laboratories
and teaching facilities for computing and mathematical sciences.

`Cultural’ Innnovation:

In 1976 I pursuaded a small group of University personnel to form
the Waikato Art Group, with the objective of supporting New
Zealand artists and building up an art collection which the
campus could enjoy. Each member has paid \$20.00 a month since,
into a purchasing fund; and from time to time the group has
visited exhibitions and bought works for the collection. The
works are exhibited in various locations on campus; and several
full exhibitions have been presented. The collection now has
considerable value; no doubt most of it will eventually be
gifted to the University.
Although there are several groups now operating in New Zealand, ours
has the honour of being the first to be formed.
[Addendum: this Group was wound up in 1988, and the bulk of the
collection was donated to the University.]
Directory Entries:

An entry of my achievements has appeared in the following directories,
for several years in each.

Directory of British Scientists.
Directory of British Authors.
The International Authors and Writers Who’s Who.
The New Zealand Who’s Who.
Marquis Who’s Who in the World.