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• 43/1C)81

THE AUSTRALIAN NATIONAL UNIVERSITY

FACULTY OF SCIENCE

DEPARTMENT OF PURE MATHEMATICS

ANNUAL REPORT 1980

GENERAL COMMENTS

This year saw a substantial increase in First Year numbers, reversing

the trend of recent years. A number of new post-graduate students joined

the Department this year; however a smaller than usual flow-on from First

to Second Year courses combined with the change to the staffing formula

kept staffing as a major concern for the Department, particularly with the

resignation in mid-year of our full-time tutor Dr J. Cresp.

New developments for mathematics generally in the University and for

the two departments in the Faculty of Science appear imminent with the

formation of the Mathematical Sciences Research Centre, two major new

appointments in the Mathematics Department, R.S.Phys.S. with which we work

closely, and of course the convening late this year of the Review Committee

for Pure and Applied Mathematics.

A particularly pleasing feature of this year was the One Day Seminar

on Mathematics in Industry, organised by Dr R. Anderssen and Dr F. de Hoag

of the Division of Mathematics and Statistics, C.S.I.R.O., co-sponsored by

D.M.S., this Department and the Applied Mathematics Department.

STUDENT MATTERS

Enrolment figures and examination results are appended. Apart from

the smaller than usual Second Year numbers no comment seems called for.

The Departmental Committee met as usual throughout the year.

Discussions largely centered on the staffing situation and the review of

departments. Fourth Year student, Mr Ian Mason was Deputy Chairman of the

Committee.

GRADUATE STUDENTS

Three students were awarded the Ph.D. degree. Dr Jonathan Hillman

whose degree was granted in 1979, was awarded the Crawford Prize. Mr Mark Lukas won the Cherry Prize awarded by the Applied Mathematics

Division of the Australian Mathematical Society.

Two students enrolled in the Masters Qualifying course; one has satisfactorily completed this year, the other is expected to complete next

year.

Ph.D. Scholars

S.S. Chow C. Kanes M.A. Lukas D. Sachse-Akerlind H. Soliman M. Yamin.

M.A. Qualifying

G. Lewis A. Gray

43/1981 • STAFF

FULL TIME

Head of Department & Senior Lecturer

Professor

Senior Lecturers

Lecturers

Lecturing/Research Fellow

Temporary Lecturer, 1980

Senior Tutors

Research Assistant

PART TIME

Lecturers

Tutors

N. Smythe, B.Sc. (NSW), Ph.D. (Princeton)

N.S. Trudinger, B.Sc. (NE), M.S., Ph.D. (Stan), F.A.A. (on leave February-·september 1980)

R.A. Bryce, M.Sc. (Q'ld), Ph.D. (ANU) P.J. Cossey, B.Sc. (Q'ld), Ph.D. (ANU) T.K. Donaldson, B.S. (Kentucky),

M.S., Ph.D. (Chic) A. Howe, B.Sc. (NE), Ph.D. (i\NU) R.J. Loy, A.R.M.I.T., B.Sc. (Melb),

M.Sc., Ph.D. (Monash) M.A. Ward, B.Sc. (Melb), B.;L, Ph.D. (ANU)

J.E. Hutchinson, B.Sc. (NSW) M.S., Ph.D. (Stan)

J.G. Oxley, B.Sc. (Tas), D.Phil. (Oxf), M.Sc. (on leave 1980)

G.W. Riley, B.Sc. (WA), M.Sc., Ph.D. (War.UK)

J.D. Cresp, B.Sc. (WA), Ph.D. (Ncle,UK) (resigned June 1980)

R.H. Levingston, B.Sc. (Q'ld), M.Sc., Ph.D. (Syd) (from June-December 1980)

P.F. Price, B.Sc., Ph.D. (WA)

J. Dawson F. de Hoog F. Gross

G. Bode S.S. Chow D. Cullen D. Easdown W. Gross D. Heath

J. c. P. I. D. D. D.

Howard Kanes Kenne Mason Sachse-A1rnrlind Thorpe Walker.

VISITORS

Dr R. Lapwood (Cambridge) to May 1980. Dr L. Jennings (W.A.) May-November 1980. Professor F. Gross (Utah) July 1980 - June 1981. Professor Leon Simon and Dr Graharne Williams (Melbourne) August 1980. Professor F.J. Almgren Jr., (Princeton) and Professor J. Taylor

(Rutgers) August 1980. Professor Bazlcy (Cologne) November 1980. Dr G. Tee (Auckland) November 1980. Professor R. Schoen (Berkeley) and Professor Doris Fischer-Colbrie

(Columbia) November 1980.

• 43/1981

STAFF NOTES

Dr R.J. Loy continued his appointment as Sub-Dean, Faculty of Science.

Dr John Cresp, Senior Tutor, resigned in June to take up a position

with Westrail. Dr Richard Levingston was appointed Temporary Tutor from July to

December 1980. Dr G. Riley was appointed Temporary Lecturer in February until

December 1980. Dr P. Price was appointed Research Assistant in March.

Professor Trudinger was on leave February to September and November

1980 at Stanford University, and as an invited lecturer in the

Scuola Matematica Interuniversitaria, Cortona, Italy and at the

University of Pennsylvania.

Dr John Cossey was an invited speaker at the Group Theory Meeting

Mathematisches Forschungsinstitut, Oberwohlfach in May.

Dr James Oxley was on leave at the University of North Carolina.

Members of the Department attended conferences and gave talks at

the University of California at Berkeley, the American Mathematical

Society April meeting in Illinois, the University of Wisconsin, the

University of Minnesota, Stanford University, the University of

Florence, the Courant Institute, M.I.T., Princeton University, Cortona,

the University of Freiburg, the University of Kiel, the University of

Mainz, the Surmner Research Institute of the Australian Mathematical

Society in Canberra, the University of Adelaide, Flinders University,

the University of New South Wales, the ANZAAS-Australian Mathematical

Society Annual General Meeting in Adelaide, the History of Mathematics

Conference at Monash University, the University of Tasmania, the

University of Melbourne, the Applied Mathematics Conference at Cowes,

and an International conference on Matroid Theory and its

Applications, Varenna Italy, as well as the local seminar series.

The One Day Seminar on Mathematics in Industry held on December

3rd, has been noted above.

PUBLICATIONS

* (1) ANDERSSEN, R.S. , On the use of linear functionals for Abel type

integral equations. Applications and Numerical Solution of

Integral Equations. (Eds. R.S. Anderssen, F.R. de Hoog and

M.A. Lukas) Sijthoff and Noordhoff, The Netherlands, 1980.

* (2) ANDERSSEN, R.S. , de HOOG, F.R. & LUKAS, M.A., Editors, Applications

and Numerical Solution of Integral Equations. Sijthoff and

Noordhoff, The Netherlands, 1980.

(3) BRYCE, R.A. & SMYTHE, N., A note on ranking tournaments.

Australian Math. Soc. Gazette. Vol.7, (1980) pp.5-10.

(4) t ** 1 "d "t" f h BRYLAWSKI, Tom & OXLEY, James , Severa i enti ies or t e

(5)

characteristic polynomial of a combinatorial geometry.

Discrete Mathematics, 31, pp.161-170 (1980).

* CHANDLER, G.A. , Superconvergence.

*

Solution of Integral Equations.

F.R. de Hoog and M.A. Lukas)

Netherlands, 1980. pp.103-117.

former member of the Department.

t not a member of this University.

Applications and Numerical

(Eds. R.S. Anderssen,

Sijthoff and Noordhoff, The

** based on work done prior to joining this University

43/1981

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(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

COSSEY, P.J., Injectors for subgroup closed classes of finite

soluble groups. Archiv der Math. Vol.35, (1980) pp.49-55.

COSSEY, P.J., KEGEL, O.H.t & KOVACS, L.G. §'Maximal Frattini

extensions. Archiv der Math. Vol.35, (1980) pp.210-217.

* HILLMAN, J.A. , Orientability, asphericity and two-knots.

Houston J. Math. Vol.6, (1980) pp67-76.

* HILLMAN, J.A. , Spanning links by non-orientable surface s.

•

guart. J. of Math. Oxford Ser(2). Vol.31, (1980) pp.169-179.

** LEVINGSTON, R.H. , Primitive permutation groups containing a cycle

of prime-power length. (Abstract) Bull. Aust. Math. Soc.,

Vol.22, (1980) pp.315-317.

LUKAS, M.A., Regularisation. Applications and Numerical Solution

of Integral Equations. (Eds. R.S. Anderssen, F.R. de Hoog

and M.A. Lukas) Sijthoff and Noordhoff, The Netherlands, 1980.

pp.151-182.

MASON, J.H.t & OXLEY J.G., A circuit covering result for matroids,

Mathematical Proceedings of the Cambridge Philosophical Society,

Vol.87, (1980) pp.25-27.

* * PAINE, J.W. , & ANDERSSEN, R.S. , Uniformly valid approximation of

eigenvalues of Sturm-Liouville problems in geophysics.

Geophys. J.R. Astro Soc., 1980.

OXLEY, James G., A generalization of a covering problem of Mullin

and Stanton for matroids, Combinatorial Mathematics VI,

(Eds. A.F. Horadam & W.D. Wallis) Lecture Notes in Mathematics,

Vol.748, pp.92-97. Springer-Verlag, Berlin, Heidelberg,

New York, 1979.

OXLEY, James G., On Hartfiel and Maxson's definition of connected

sets of a matroid. Journal of Combinatorial Theory Series B,

Vol.28, (1980) pp.249-250.

** OXLEY, James G. , On a covering problem of Mullin and Stanton for

binary matroids, Aequationes Mathematicae, 19, (1979) p.118, and

20, (1980) pp.104-112.

** t OXLEY J.G. WELSH, D.J.A. , On some percolation results of

J.M. Hamme rsley, Journal of Applied Probability, 16, (1979)

pp.526-540.

TRUDINGER, N.S., Local e stimates for subsolutions of general second

order elliptic quasilinear equations. Inventiones Math.

Vol.61, (1980) pp.67-80.

TRUDINGER, N.S., On the first eige nvalue of non-uniformly e lliptic

boundary value problems. Math. Zeit. 1980.

* WATSON, K.S. , Sylvester's problem on spreads of curves. Canad. J.

Math., Vol. 32, (1980) pp. 219-239.

t not a membe r of t h is Unive r sity . * forme r membe r o f t he Departme nt.

** base d on work § member of the Mathematics Department, R.S.Phys.S. done prior to joining this University.

43/1981

• Mathematics Research Report Series

1980

1. SMYTHE, N.: An Analogue of Grushko's Theorem for Mapping Cyliner Groups.

2. SMYTHE, N.: A Presentation for a Group of Integer Matrices.

3. TRUDINGER, Neil S.: Local Estimates for Subsolutions and Supersolutions of General Second Order Elliptic Quasilinear Equations.

5. COSSEY, John: On Fitting Classes that are Schunck Classes.

6. LEVINGSTON, Richard: The Laws of Some Metabelian Varieties.

10. LOY, Richard J.: The Uniqueness of Norm Problem in Banach Algebras with Finite Dimensional Radical.

11. GROSS, Fletcher: Existence and Conjugacy of Complements of Direct Products.

THE AUSTRALIAN NATIONAL UN IVERS ITV 43/1981

DEPARTMENT OF PURE MATHEMATICS AN ANALYSIS OF STUDENT PERFORMANCE

Number Enrolled Number Sitting

Enrolled Failure as at WastaJe inc High

Unit 19.5.80 Sitting (2-3 ABS/N,W/N Sitting Dist Dist Credit Pass Failure % % % % % % % % % %

AOl 75 (100) 58 (77) 1 7 (23) 25 (33) 58 (100) 1 ( 2) 2 ( 3) 9 (16) 38 (66) 8 (14)

A02 109 (100) 102 (94) 7 ( 6) 25 (27) 102 (100) 8 ( 8) 16 (16) 25 (25) 3 5 ( 34) 18 (18)

A03 156 (100) 143 (92) 13 ( 8) 24 (15) 143 (100) 8 ( 6) 24 (17) 66 (46) 34 (24) 11 ( 8)

A04 136 (100) 126 (93) 10 ( 7) 21 (15) 126 (100) 5 ( 4) 35 (28) 30 (24) 4 5 (36) 11 ( 9)

A05H 49 (100) 39 (80) 10 (20) 11 (22) 39 (100) 6 (15) 1 0 (26) 1 0 (26) 12 (31) 1 ( 3)

A06H 30 (100) 28 (93) 2 ( 7) 4 (13) 28 (100) 3 (11) 4 (14) 8 (29) 11 ( 40) 2 ( 7)

802 1 1 1 1 803 49 (100) 40 (82) 9 (18) 11 (22) 40 (100) 6 (15) 4 (10) 12 (30) 1 6 ( 40) 2 ( 5)

804 51 (100) 45 (88) 6 (12) 7 (14) 45 (100) 7 (16) 10 (22) 1 5 ( 33) 12 (27) 1 ( 2)

805H 11 1 0 1 10 3 3 4

806H 5 5 1 5 3 1 1

807H 10 9 1 1 9 2 5 2

808H 7 6 4 2 6 2 2 1 1

812 1 2 9 3 4 9 1 1 2 4 1

COl 20 1 7 3 6 1 7 3 6 5 3

C02 24 21 3 9 21 2 3 2 8 6

C03 33 28 5 8 28 2 3 7 1 3 3

C04 22 21 1 2 21 3 6 3 8 1

C05H 13 1 3 13 6 1 3 3

C06H 1 2 1 0 2 3 10 6 1 2 1

C07H 9 7 2 2 7 2 4 1

C08H 7 6 1 2 6 2 2 1 1

C09 1 0 9 1 2 9 1 7 1

Cl OH 5 4 1 3 4 1 2

IVH MY p/t 2 2 2

IVH 2 2 2

IVH results: ( 2 part-time continuing from 1979; 3 First Class Honours • 1 Second Division A combined Honours with Applied Mathematics.)

Pos tgraduate enrolment. 2 M.A. (Qualifying)