Ashour started his career immediately after receiving his
B.Sc. degree in 1944 as a
graduate assistant at Fuad I University now Cairo University, Egypt. He worked for a year and two months before leaving for London for his PhD. He passed through the academic stages of
senior Lecturer and
assistant Professor till he became a
full Professor of
applied mathematics at the Faculty of Science, Cairo University in 1966 and he became
emeritus professor in 1984. He headed the Mathematics Department of Cairo University from 1959–1960, 1965–1969, 1971–1976 and 1980–1984. In 1954, he served as a visiting scientist at
Queen Mary College,
London University. He did the same at the Physics Institute,
Bonn University; the Institute de Radium,
University de Paris;
Exeter University, UK and Physics Department,
Ibadan University in 1954, 1955, 1955–1956, 1962–1963 and 1972 respectively. == Awards and memberships ==