After a year at Swarthmore College, she worked at Mount Holyoke College as an assistant professor from 1952 until 1956, when she moved to Barnard College.[6] In 1958, she was the supervisor of Doris Stockton's doctorate at Brown University.[7] In 1961, as an associate professor at Barnard, she was funded by the National Science Foundation to visit the Institute for Advanced Study in Princeton, New Jersey for postdoctoral research.[8] She also worked at the Institute for Defense Analyses in Princeton in the early 1960s.[2]
She came to Rutgers University in 1964, at a time when Rutgers had a much higher number of female faculty than many mathematics departments then or later.[9] Among her graduate students at Rutgers was Edward R. Dougherty, later a distinguished professor of electrical engineering at Texas A&M University.[5] She chaired the Rutgers mathematics department from 1974 to 1977.[9] Elliott retired from Rutgers in 1991, in a year in which the university was cutting costs by offering early retirement to its employees.[9]
Elliott died in Titusville, New Jersey on March 5, 2023, at the age of 97.[10]
