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Bernard Koopman

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Title: Bernard Koopman  
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Subject: Koopman–von Neumann classical mechanics, American operations researchers, William Fogg Osgood, Mathematical optimization, Dynamical system
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Bernard Koopman

Bernard Koopman
Born 1900
Died August 18, 1981
Randolph, New Hampshire
Nationality American
Fields Mathematics
Institutions Columbia University
Alma mater Harvard University
Doctoral advisor G. D. Birkhoff
Doctoral students Clifford Marshall
Francis J. Murray

Bernard Osgood Koopman (1900 – August 18, 1981) was a French-born American mathematician, known for his work in ergodic theory, the foundations of probability, statistical theory and operations research.

Education and work

After living in France and Italy, the Koopmans immigrated to the United States in 1915. Koopman was a student of dynamical systems and mathematical physics.

In 1931/1932, Koopman and John von Neumann proposed a Hilbert space formulation of classical mechanics, known as the Koopman–von Neumann classical mechanics.

During [1]

The Pitman–Koopman–Darmois theorem states that the only families of probability distributions that admit a sufficient statistic whose dimension remains bounded as the sample size increases are exponential families.


Koopman had two daughters from his first wife Mary Louise Harvey who died in 1946. In 1948 he married Jane Bridgman, daughter of his Harvard professor of thermodynamics, Percy Williams Bridgman, and they had three more daughters.[1]

Koopman's mother, née Louise Osgood, was a first cousin of William Fogg Osgood.[1]


Further reading


  1. ^ a b c d Philip M. Morse: In memoriam: Bernard Osgood Koopman, 1900–1981, Operations Research, Vol. 30, No. 3 (May - Jun., 1982), pp. viii+417-427. Published by: Institute for Operations Research and the Management Sciences (INFORMS), DOI: 10.2307/170181 (jstor 170181)
  2. ^ Gary Kinder: Ship of Gold in the Deep Blue Sea Grove/Atlantic Inc., 2009, ISBN 978-0802144256, p. 215
  3. ^ "Search theory [..] came to being during World War II with the work of B. O. Koopman and his colleagues in the Antisubmarine Warfare Operations Research Group (ASWORG)." Cited from: Henry R. Richardson, Search theory, Professional Paper 449, April 1986
  4. ^ Laura H. Nunn, An introduction to the literature on search theory, Professional Paper 305, June 1981, Center for Naval Analyses (CNA) Corporation (accessed 31.01.2012)

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