John Hilton Grace
Encyclopedia
John Hilton Grace was a British
mathematician
.
, near Liverpool
, the eldest of the six children of a farmer. He was educated at the village school and the Liverpool Institute. From there in 1892 he went up to Peterhouse College, Cambridge to study mathematics.
on their book Algebra of Invariants.
He was elected a Fellow of the Royal Society in 1908.
He spent 1916-1917 as Visiting Professor in Lahore and deputised for Professor MacDonald at Aberdeen University during the latter part of the war.
In 1922 a breakdown in health forced his retirement from academic life and he spent the next part of his life in Norfolk.
He died in Huntingdon in 1958 and was buried in the family grave at St. Nicholas Church, Halewood.
,
are two polynomials that satisfy the apolarity condition, i.e.
, then every neighborhood that includes all zeros of one polynomial also includes at least one zero of the other.
and 
be defined as in the above theorem. If the zeros of both polynomials lie in the unit disk, then the zeros of the "composition" of the two, 
, also lie in the unit disk.
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
.
Early life
He was born in HalewoodHalewood
Halewood is in Merseyside, England and is located in the Metropolitan Borough of Knowsley. The district lies near Liverpool's southeastern boundary, bordered by the suburbs of Hunts Cross and Woolton....
, near Liverpool
Liverpool
Liverpool is a city and metropolitan borough of Merseyside, England, along the eastern side of the Mersey Estuary. It was founded as a borough in 1207 and was granted city status in 1880...
, the eldest of the six children of a farmer. He was educated at the village school and the Liverpool Institute. From there in 1892 he went up to Peterhouse College, Cambridge to study mathematics.
Career
He was made a Fellow of Peterhouse in 1897 and became a Lecturer of Mathematics at Peterhouse and Pembroke colleges. An example of his work was his 1902 paper on the The Zeros of a Polynomial. In 1903 he collaborated with Alfred YoungAlfred Young
Alfred Young, FRS was a British mathematician.He was born in Widnes, Lancashire, England and educated at Monkton Combe School in Somerset and Clare College, Cambridge, graduating BA as 10th Wrangler in 1895. He is known for his work in the area of group theory...
on their book Algebra of Invariants.
He was elected a Fellow of the Royal Society in 1908.
He spent 1916-1917 as Visiting Professor in Lahore and deputised for Professor MacDonald at Aberdeen University during the latter part of the war.
In 1922 a breakdown in health forced his retirement from academic life and he spent the next part of his life in Norfolk.
He died in Huntingdon in 1958 and was buried in the family grave at St. Nicholas Church, Halewood.
Theorem on zeros of a polynomial
If,are two polynomials that satisfy the apolarity condition, i.e.
, then every neighborhood that includes all zeros of one polynomial also includes at least one zero of the other.Corollary
Let and be defined as in the above theorem. If the zeros of both polynomials lie in the unit disk, then the zeros of the "composition" of the two, , also lie in the unit disk.