James William Cooley (1926 – June 29, 2016) was an
American
American(s) may refer to:
* American, something of, from, or related to the United States of America, commonly known as the "United States" or "America"
** Americans, citizens and nationals of the United States of America
** American ancestry, pe ...
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
. Cooley received a B.A. degree in 1949 from
Manhattan College, Bronx, NY, an M.A. degree in 1951 from
Columbia University
Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...
, New York, NY, and a Ph.D. degree in 1961 in
applied mathematics
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathemati ...
from
Columbia University
Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...
. He was a
programmer on
John von Neumann
John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...
's computer at the
Institute for Advanced Study
The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent schola ...
, Princeton, NJ, from 1953 to 1956, where he notably programmed the
Blackman–Tukey transformation.
He worked on
quantum mechanical computations at the
Courant Institute
The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU), and is among the most prestigious mathematics schools and mathematical sciences research cente ...
, New York University, from 1956 to 1962, when he joined the Research Staff at the
IBM Watson Research Center
The Thomas J. Watson Research Center is the headquarters for IBM Research. The center comprises three sites, with its main laboratory in Yorktown Heights, New York, Yorktown Heights, New York (state), New York, U.S., 38 miles (61 km) north ...
, Yorktown Heights, NY. Upon retirement from IBM in 1991, he joined the Department of
Electrical Engineering,
University of Rhode Island
The University of Rhode Island (URI) is a public land-grant research university with its main campus in Kingston, Rhode Island, United States. It is the flagship public research as well as the land-grant university of the state of Rhode Isla ...
, Kingston, where he served on the faculty of the
computer engineering program.
His most significant contribution to the world of
mathematics and
digital signal processing is re-discovering the
fast Fourier transform,
which he co-developed with
John Tukey (see
Cooley–Tukey FFT algorithm
The Cooley–Tukey algorithm, named after J. W. Cooley and John Tukey, is the most common fast Fourier transform (FFT) algorithm. It re-expresses the discrete Fourier transform (DFT) of an arbitrary composite size N = N_1N_2 in terms of ''N''1 s ...
) while working for the research division of
IBM in 1965.
The motivation for it was provided by Dr.
Richard L. Garwin at IBM Watson Research who was concerned about verifying a
nuclear arms
A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either nuclear fission, fission (fission bomb) or a combination of fission and nuclear fusion, fusion reactions (Thermonuclear weapon, thermonu ...
treaty with the
Soviet Union
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...
for the
SALT talks. Garwin thought that if he had a very much faster
Fourier Transform he could plant sensors in the ground in
countries surrounding the Soviet Union. He suggested to both Cooley and
Tukey
John Wilder Tukey (; June 16, 1915 – July 26, 2000) was an American mathematician and statistician, best known for the development of the Cooley–Tukey FFT algorithm, fast Fourier Transform (FFT) algorithm and box plot. The Tukey's range test ...
how Fourier transforms could be programmed to be much faster. They did the work, the sensors were planted, and he was able to locate
nuclear explosions
A nuclear explosion is an explosion that occurs as a result of the rapid release of energy from a high-speed nuclear reaction. The driving reaction may be nuclear fission or nuclear fusion or a multi-stage cascading combination of the two, tho ...
to within 15 kilometers of where they were occurring.
J. W. Cooley was a member of the ''Digital Signal Processing Committee'' of the
IEEE
The Institute of Electrical and Electronics Engineers (IEEE) is a 501(c)(3) professional association for electronic engineering and electrical engineering (and associated disciplines) with its corporate office in New York City and its operat ...
, was elected a Fellow of IEEE for his work on the FFT, and received the
IEEE Centennial Medal. In 2002 he received the
IEEE Jack S. Kilby Signal Processing Medal.
He considerably contributed to the establishing of terminology in
digital signal processing.
Publications
* James W. Cooley (1961): "An improved eigenvalue corrector formula for solving the Schrödinger equation for central fields", Math. Comput. 15, 363–374. DOI
10.1090/S0025-5718-1961-0129566-X This describes the so-called Numerov-Cooley method for numerically solving one-dimensional
Schrödinger equation
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of th ...
s.
* James W. Cooley & John W. Tukey (1965):
An algorithm for the machine calculation of complex Fourier series, Math. Comput. 19, 297–301.
*Cooley, James W., Timothy M. Toolan and Donald W. Tufts. "A Subspace Tracking Algorithm Using the Fast Fourier Transform." IEEE Signal Processing Letters. 11(1):30–32. January 2004.
*Real, Edward C., Donald W. Tufts and James W. Cooley. "Two Algorithms for Fast Approximate Subspace Tracking." IEEE Transactions on Signal Processing. 47(7):1936–1945. July 1999.
*Tufts, D. W., E. C. Real and J. W. Cooley. "Fast Approximate Subspace Tracking (FAST)." IN: Proceedings of the 1997 IEEE
. IEEE. 1997. I:547–550.
See also
*
List of pioneers in computer science
This is a list of people who made transformative breakthroughs in the creation, development and imagining of what computers could do.
Pioneers
: ''To arrange the list by date or person (ascending or descending), click that column's small "up-do ...
References
External links
*
{{DEFAULTSORT:Cooley, James
1926 births
2016 deaths
20th-century American mathematicians
21st-century American mathematicians
IBM employees
Manhattan College alumni
Columbia School of Engineering and Applied Science alumni
University of Rhode Island faculty
Members of the United States National Academy of Engineering
Courant Institute of Mathematical Sciences faculty
Fellow Members of the IEEE
IEEE Centennial Medal laureates