Tropper was born in London in 1954, the daughter of mathematician A. Mary Tropper and electrical engineer Hans Tropper ; she spent her childhood in her father's high-voltage laboratory. She eventually studied physics at the Somerville College, Oxford, where she was taught by Nina Byers. She was encouraged by Byers to stay at Oxford for a doctoral degree, and joined the laboratory of Mike Leask. After earning her PhD Tropper was awarded a Lindemann Fellowship, and joined an engineering consultancy before moving to the Almaden Research Laboratory in San Jose, California.