Koopman was a student of George David Birkhoff and his initial work concentrated on dynamical systems and mathematical physics.
During World War II, he joined the Anti-Submarine Warfare Operations Research Group (ASWORG, later ORG) in Washington, D.C., directed by Philip M. Morse, to work for the U.S.
[1] The work of Koopman and his colleagues at ASWORG concerned the development of techniques for the US Navy to hunt U-boats.
[2] The theoretical work laid the foundations for search theory which subsequently became a field of its own within operations research.
[3] Their results remained classified Confidential for many years after the war; after 1955 Koopman set out to publish three articles on easily declassifiable portions of the work in the Journal of the Operations Research Society of America.