J. W. S. Cassels

John William Scott Cassels, Ian Cassels, ( born June 11, 1922 in Durham ) is a British mathematician who deals with number theory and arithmetic algebraic geometry.

Cassels, whose father oversaw agriculture in County Durham, went to Durham and Edinburgh to school and studied at Edinburgh University ( master's degree, 1943 ) and at the University of Cambridge ( Trinity College), where he received his doctorate in 1949 at Louis Mordell. In between, he worked during the Second World War, like many other mathematicians in Enigma decryption project at Bletchley Park. In the same year he was appointed a Fellow of Trinity College. Cassels was then Lecturer in Manchester and from 1950 in Cambridge, where he became in 1963 reader in arithmetic. In 1967 he was Sadleirian Professor of Pure Mathematics at Cambridge. From 1969 he was also chairman of the Department of Pure Mathematics and Mathematical Statistics at Cambridge, a position he held until his retirement in 1984.

Cassels worked among other things on the geometry of numbers, rational quadratic forms, the arithmetic of elliptic curves ( a series of works Arithmetic of Curves of genus 1 in the Journal of the London Mathematical Society and the Journal of Pure and Applied Mathematics 1959-1965 ) Diophantine approximation and local bodies. He showed, for example, that the order of the Tate - Shafarevich group is a square number, if it is finite.

Cassels is a member since 1963 ( "Fellow" ) of the Royal Society, the Sylvester Medal he received in 1973. 1976 to 1978 he was President of the London Mathematical Society, the De Morgan Medal he received in 1986. He is since 1981 a Fellow of the Royal Society of Edinburgh. 1978 to 1982 he was in the Council of the International Mathematical Union. 1974 to 1978 he was Vice President of the Royal Society in London. In 1970 he was invited speaker at the International Congress of Mathematicians in Nice (On cubic trigonometric sums ).

Writings

  • Introduction to Diophantine approximation, Cambridge Tracts 1957, 1972
  • An introduction to the geometry of numbers, 1959, Springer, 1971 ( basic teachings of the mathematical sciences ), 1997 by Springer in the series " Classics in Mathematics"
  • Rational quadratic forms, Academic Press, London Mathematical Society Monographs, 1978
  • Economics for mathematicians, Cambridge 1981
  • Local Fields, Cambridge, LMS Student Texts 1986
  • Lectures on Elliptic Curves, Cambridge, LMS Student Texts, 1991
  • With E.Flynn: Prolegomena to a middlebrow arithmetic of Curves of Genus 2, Cambridge, LMS Lecture Note Series, 1996
  • Publisher Albrecht Fröhlich: Algebraic Number Theory, Academic Press 1967
  • Rational Quadratic Forms, DMV Annual Report 1980, p.81
  • Diophantine equations with special reference to elliptic curves, Journal London Math.Soc. Vol 41, 1966, p.193 -291
  • Arithmetic on elliptic curve at, International Congress of Mathematicians 1962
  • Interview, Mathematical Intelligencer, Bd.23, 2001, No.2
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