James William Cooley (September 18, 1926 – June 29, 2016) was an American

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, mathematical structure, structure, space, Mathematica ...

. Cooley received a B.A. degree in 1949 from

Manhattan College Manhattan University (previously Manhattan College) is a private, Catholic university in New York City. Originally established in 1853 by the De La Salle Christian Brothers (Institute of the Brothers of the Christian Schools) as an academy fo ...

, Bronx, NY, an M.A. degree in 1951 from

Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...

, New York, NY, and a Ph.D. degree in 1961 in

applied mathematics Applied mathematics is the application of mathematics, mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and Industrial sector, industry. Thus, applied mathematics is a ...

from

. He was a

programmer A programmer, computer programmer or coder is an author of computer source code someone with skill in computer programming. The professional titles Software development, ''software developer'' and Software engineering, ''software engineer' ...

John von Neumann John von Neumann ( ; ; December 28, 1903 – February 8, 1957) was a Hungarian and American mathematician, physicist, computer scientist and engineer. Von Neumann had perhaps the widest coverage of any mathematician of his time, in ...

's computer at the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

, Princeton, NJ, from 1953 to 1956, where he notably programmed the Blackman–Tukey transformation. He worked on quantum mechanical computations at the Courant Institute, 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. Its main laboratory is in Yorktown Heights, New York, 38 miles (61 km) north of New York City. It also operates facilities in Cambridge, Massachusetts and Albany, N ...

, Yorktown Heights, NY. Upon retirement from IBM in 1991, he joined the Department of

Electrical Engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems that use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...

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 Rhode Island. The univer ...

, Kingston, where he served on the faculty of the

computer engineering Computer engineering (CE, CoE, or CpE) is a branch of engineering specialized in developing computer hardware and software. It integrates several fields of electrical engineering, electronics engineering and computer science. Computer engi ...

program. His most significant contribution to the world of

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

and

digital signal processing Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are a ...

is re-discovering the

fast Fourier transform A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). A Fourier transform converts a signal from its original domain (often time or space) to a representation in ...

, which he co-developed with

John Tukey John Wilder Tukey (; June 16, 1915 – July 26, 2000) was an American mathematician and statistician, best known for the development of the fast Fourier Transform (FFT) algorithm and box plot. The Tukey range test, the Tukey lambda distributi ...

(see

Cooley–Tukey FFT algorithm The Cooley–Tukey algorithm, named after James Cooley, 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 number, composite size ...

) while working for the research division of

IBM International Business Machines Corporation (using the trademark IBM), nicknamed Big Blue, is an American Multinational corporation, multinational technology company headquartered in Armonk, New York, and present in over 175 countries. It is ...

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 fission (fission or atomic bomb) or a combination of fission and fusion reactions (thermonuclear weapon), producing a nuclear expl ...

treaty with the

Soviet Union The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

for the SALT talks. Garwin thought that if he had a very much faster

Fourier Transform In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the tr ...

he could plant sensors in the ground in countries surrounding the Soviet Union. He suggested to both Cooley and Tukey 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 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 an American 501(c)(3) organization, 501(c)(3) public charity professional organization for electrical engineering, electronics engineering, and other related disciplines. The IEEE ...

, 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

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 partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after E ...

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

International Conference on Acoustics, Speech, and Signal Processing ICASSP, the International Conference on Acoustics, Speech, and Signal Processing, is an annual flagship conference organized by IEEE Signal Processing Society. Ei Compendex has indexed all papers included in its proceedings. The first ICASSP w ...

. IEEE. 1997. I:547–550.

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 Fellows of the IEEE IEEE Centennial Medal laureates

Publications

See also

References

External links