Sheila Oates Williams (born 1939, also published as Sheila Oates and Sheila Oates Macdonald) is a British and Australian mathematician specializing in
abstract algebra. She is the namesake of the Oates–Powell theorem in
group theory, and a winner of the B. H. Neumann Award.
Education and career
Sheila Oates was originally from
Cornwall, where her father was a primary school headmaster in
Tintagel. She was educated at
Sir James Smith's Grammar School, and inspired to become a mathematician by a teacher there, Alfred Hooper. She read mathematics in
St Hugh's College, Oxford
St Hugh's College is one of the constituent colleges of the University of Oxford. It is located on a site on St Margaret's Road, to the north of the city centre. It was founded in 1886 by Elizabeth Wordsworth as a women's college, and accepte ...
, with
Ida Busbridge as her tutor, and continued at Oxford as a doctoral student of
Graham Higman. She completed her doctorate (D.Phil.) in 1963.
She became a lecturer and fellow at
St Hilda's College, Oxford
St Hilda's College is one of the Colleges of the University of Oxford, constituent colleges of the University of Oxford in England. The college is named after the Anglo-Saxon Saint, Hilda of Whitby and was founded in 1893 as a hall for women; it ...
, before moving to Australia in 1965. In 1966, she took a position as senior lecturer at the
University of Newcastle and later moved again to the
University of Queensland, as reader. She retired in 1997.
Contributions
As a student at Oxford, with Martin B. Powell, another student of Higman, she proved the Oates–Powell theorem. This is an analogue for
group theory of
Hilbert's basis theorem, and states that all
finite group
Finite is the opposite of infinite. It may refer to:
* Finite number (disambiguation)
* Finite set, a set whose cardinality (number of elements) is some natural number
* Finite verb, a verb form that has a subject, usually being inflected or marked ...
s have a finite system of axioms from which can be derived all equations that are true of the group. That is, every finite group is finitely based.
As well as for her research, Williams is known for her work setting Australian mathematics competitions, including the
International Mathematical Olympiad
The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except i ...
in 1988 and the
Australian Mathematics Competition The Australian Mathematics Competition is a mathematics competition run by the Australian Maths Trust for students from year 3 up to year 12 in Australia, and their equivalent grades in other countries. Since its inception in 1976 in the Australian ...
. She also participated several times in the Australian edition of the ''
Mastermind'' television quiz show.
Recognition
Williams was a 2002 recipient of the B. H. Neumann Award for Excellence in Mathematics Enrichment of the Australian Maths Trust.
References
{{DEFAULTSORT:Williams, Sheila Oates
1939 births
Living people
Australian mathematicians
Australian women mathematicians
British mathematicians
British women mathematicians
Alumni of St Hugh's College, Oxford
Fellows of St Hilda's College, Oxford
Academic staff of the University of Newcastle (Australia)
Academic staff of the University of Queensland
People from Tintagel