Her doctoral thesis was on mathematical logic. The thesis, Languages with expressions of infinite length, was supervised by L Henkin and submitted to the University of Southern California in 1959. However Karp was teaching several years before the award of her Ph.D. having accepted a position as instructor at New Mexico College of Agriculture and Mechanic Arts in 1953. In 1960 the name of the New Mexico College of Agriculture and Mechanic Arts was changed to its present name of New Mexico State University. Karp spent a year at the College in Las Cruces, New Mexico.
Her thesis advisor had moved to Berkeley in 1953 and Karp was appointed as a teaching assistant here from 1954 to 1956 while she worked on her doctoral thesis. Karp had married Arthur L Karp in 1952 and, in 1957, she moved to Japan with her husband who was in the US Navy. On her return from Japan, Karp accepted a post as instructor at the University of Maryland.
Soon after the award of her doctorate Karp was promoted, in 1960, to assistant professor at the University of Maryland. She was to remain at the University of Maryland until her early death from cancer in 1972 but there she was promoted again, to associate professor in 1963 and then to full professor in 1966.
Karp was a mathematical logician but, as noted in , her work was closely related to algebra:-
Karp considered herself to be principally an 'algebraic logician'. Her inclination towards algebra was never completely forgotten and she always seemed to draw results concerning Boolean algebras from her results about infinitary languages.In 1964 she published a book on her research Languages with expressions of infinite length but she had hoped to write another work which would take her ideas considerably further. She lectured on this later work as described in :-
Karp did give lectures at Maryland in the Fall of 1970 on infinitary logic and recursion theory. Basically Karp wanted to return to Gödel's original proof-theoretic definitions of recursive sets but of course using more liberal notions of proof so as to obtain generalisations of recursion theory.It was both as a teacher and researcher that Karp made her reputation. She cared personally for her students and worried greatly for their futures during her illness. Again quoting from :-
To her, teaching had always been more than a duty, and even during her illness she taught all her classes in addition to carrying out all her administrative tasks. Her research, too, was pushed forward with her usual determination....Judy Green, who was one of Karp's doctoral students, wrote the article in . In it she writes:-
Karp's intellectual standards were extremely high, and she was unfailingly honest in applying them. Although she showed almost familial concern for her students and younger colleagues, she was consistently candid in appraising their mathematical contributions and promise. In particular, she advised working towards a doctorate only if one expected to make research the most important part of one's professional career, and she refused to allow her students to graduate until their results met her own high standard for publishability.
Article by: J J O'Connor and E F Robertson